Nonlinearity and Strain-Rate Dependence in the Deformation Response of Polymer Matrix Composites Modeled

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

2000-01-01

There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.

Influence of mechanically-induced dilatation on the shape memory behavior of amorphous polymers at large deformation

NASA Astrophysics Data System (ADS)

Hanzon, Drew W.; Lu, Haibao; Yakacki, Christopher M.; Yu, Kai

2018-01-01

In this study, we explore the influence of mechanically-induced dilatation on the thermomechanical and shape memory behavior of amorphous shape memory polymers (SMPs) at large deformation. The uniaxial tension, glass transition, stress relaxation and free recovery behaviors are examined with different strain levels (up to 340% engineering strain). A multi-branched constitutive model that incorporates dilatational effects on the polymer relaxation time is established and applied to assist in discussions and understand the nonlinear viscoelastic behaviors of SMPs. It is shown that the volumetric dilatation results in an SMP network with lower viscosity, faster relaxation, and lower Tg. The influence of the dilatational effect on the thermomechanical behaviors is significant when the polymers are subject to large deformation or in a high viscosity state. The dilation also increases the free recovery rate of SMP at a given recovery temperature. Even though the tested SMPs are far beyond their linear viscoelastic region when a large programming strain is applied, the free recovery behavior still follows the time-temperature superposition (TTSP) if the dilatational effect is considered during the transformation of time scales; however, if the programming strain is different, TTSP fails in predicting the recovery behavior of SMPs because the network has different entropy state and driving force during shape recovery. Since most soft active polymers are subject to large deformation in practice, this study provides a theoretical basis to better understand their nonlinear viscoelastic behaviors, and optimize their performance in engineering applications.

Design of materials with prescribed nonlinear properties

NASA Astrophysics Data System (ADS)

Wang, F.; Sigmund, O.; Jensen, J. S.

2014-09-01

We systematically design materials using topology optimization to achieve prescribed nonlinear properties under finite deformation. Instead of a formal homogenization procedure, a numerical experiment is proposed to evaluate the material performance in longitudinal and transverse tensile tests under finite deformation, i.e. stress-strain relations and Poissons ratio. By minimizing errors between actual and prescribed properties, materials are tailored to achieve the target. Both two dimensional (2D) truss-based and continuum materials are designed with various prescribed nonlinear properties. The numerical examples illustrate optimized materials with rubber-like behavior and also optimized materials with extreme strain-independent Poissons ratio for axial strain intervals of εi∈[0.00, 0.30].

Large strain deformation behavior of polymeric gels in shear- and cavitation rheology

NASA Astrophysics Data System (ADS)

Hashemnejad, Seyed Meysam; Kundu, Santanu

Polymeric gels are used in many applications including in biomedical and in food industries. Investigation of mechanical responses of swollen polymer gels and linking that to the polymer chain dynamics are of significant interest. Here, large strain deformation behavior of two different gel systems and with different network architecture will be presented. We consider biologically relevant polysaccharide hydrogels, formed through ionic and covalent crosslinking, and physically associating triblock copolymer gels in a midblock selective solvent. Gels with similar low-strain shear modulus display distinctly different non-linear rheological behavior in large strain shear deformation. Both these gels display strain-stiffening behavior in shear-deformation prior to macroscopic fracture of the network, however, only the alginate gels display negative normal stress. The cavitation rheology data show that the critical pressure for cavitation is higher for alginate gels than that observed for triblock gels. These distinctly different large-strain deformation behavior has been related to the gel network structure, as alginate chains are much stiffer than the triblock polymer chains.

Exact solutions for postbuckling of a graded porous beam

NASA Astrophysics Data System (ADS)

Ma, L. S.; Ou, Z. Y.

2018-06-01

An exact, closed-form solution for the postbuckling responses of graded porous beams subjected to axially loading is obtained. It was assumed that the properties of the graded porous materials vary continuously through thickness of the beams, the equations governing the axial and transverse deformations are derived based on the classical beam theory and the physical neutral surface concept. The two equations are reduced to a single nonlinear fourth-order integral-differential equation governing the transverse deformations. The nonlinear equation is directly solved without any use of approximation and a closed-form solution for postbuckled deformation is obtained as a function of the applied load. The exact solutions explicitly describe the nonlinear equilibrium paths of the buckled beam and thus are able to provide insight into deformation problems. Based on the exact solutions obtained herein, the effects of various factors such as porosity distribution pattern, porosity coefficient and boundary conditions on postbuckling behavior of graded porous beams have been investigated.

Nonlinear finite element modeling of corrugated board

Treesearch

A. C. Gilchrist; J. C. Suhling; T. J. Urbanik

1999-01-01

In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...

Nonlinear Constitutive Relations for High Temperature Applications

NASA Technical Reports Server (NTRS)

1983-01-01

The topics of discussion addressed were material behavior, design analysis, deformation kinetics, metallurgical characterization, mechanical subelement models, stress analysis, fracture mechanics, viscoplasticity, and thermal loading.

Large deformation of uniaxially loaded slender microbeams on the basis of modified couple stress theory: Analytical solution and Galerkin-based method

NASA Astrophysics Data System (ADS)

Kiani, Keivan

2017-09-01

Large deformation regime of micro-scale slender beam-like structures subjected to axially pointed loads is of high interest to nanotechnologists and applied mechanics community. Herein, size-dependent nonlinear governing equations are derived by employing modified couple stress theory. Under various boundary conditions, analytical relations between axially applied loads and deformations are presented. Additionally, a novel Galerkin-based assumed mode method (AMM) is established to solve the highly nonlinear equations. In some particular cases, the predicted results by the analytical approach are also checked with those of AMM and a reasonably good agreement is reported. Subsequently, the key role of the material length scale on the load-deformation of microbeams is discussed and the deficiencies of the classical elasticity theory in predicting such a crucial mechanical behavior are explained in some detail. The influences of slenderness ratio and thickness of the microbeam on the obtained results are also examined. The present work could be considered as a pivotal step in better realizing the postbuckling behavior of nano-/micro- electro-mechanical systems consist of microbeams.

Time-dependent behavior of passive skeletal muscle

NASA Astrophysics Data System (ADS)

Ahamed, T.; Rubin, M. B.; Trimmer, B. A.; Dorfmann, L.

2016-03-01

An isotropic three-dimensional nonlinear viscoelastic model is developed to simulate the time-dependent behavior of passive skeletal muscle. The development of the model is stimulated by experimental data that characterize the response during simple uniaxial stress cyclic loading and unloading. Of particular interest is the rate-dependent response, the recovery of muscle properties from the preconditioned to the unconditioned state and stress relaxation at constant stretch during loading and unloading. The model considers the material to be a composite of a nonlinear hyperelastic component in parallel with a nonlinear dissipative component. The strain energy and the corresponding stress measures are separated additively into hyperelastic and dissipative parts. In contrast to standard nonlinear inelastic models, here the dissipative component is modeled using an evolution equation that combines rate-independent and rate-dependent responses smoothly with no finite elastic range. Large deformation evolution equations for the distortional deformations in the elastic and in the dissipative component are presented. A robust, strongly objective numerical integration algorithm is used to model rate-dependent and rate-independent inelastic responses. The constitutive formulation is specialized to simulate the experimental data. The nonlinear viscoelastic model accurately represents the time-dependent passive response of skeletal muscle.

Thermo-elastoviscoplastic snapthrough behavior of cylindrical panels

NASA Technical Reports Server (NTRS)

Song, Y.; Simitses, G. J.

1992-01-01

The thermo-elastoviscoplastic snapthrough behavior of simply supported cylindrical panels is investigated. The analysis is based on nonlinear kinematic relations and nonlinear rate-dependent unified constitutive equations which include both Bodner-Partom's and Walker's material models. A finite element approach is employed to predict the inelastic buckling behavior. Numerical examples are given to demonstrate the effects of several parameters which include the temperature, thickness and flatness of the panel. Comparisons of buckling responses between Bodner-Partom's model and Walker's model are given. The creep buckling behavior, as an example of time-dependent inelastic deformation, is also presented.

Plastic Deformation of Magnesium Alloy Subjected to Compression-First Cyclic Loading

NASA Astrophysics Data System (ADS)

Lee, Soo Yeol; Gharghouri, Michael A.; Root, John H.

In-situ neutron diffraction has been employed to study the deformation mechanisms in a precipitation-hardened and extruded Mg-8.5wt.% Al alloy subjected to compression followed by reverse tension. The starting texture is such that the basal poles of most grains are oriented normal to the extrusion axis and a small portion of grains are oriented with the basal pole parallel to the extrusion axis. Diffraction peak intensities for several grain orientations monitored in-situ during deformation show that deformation twinning plays an important role in the elastic-plastic transition and subsequent plastic deformation behavior. Significant non-linear behavior is observed during unloading after compression and appears to be due to detwinning. This effect is much stronger after compressive loading than after tensile loading.

Predicting the flexure response of wood-plastic composites from uni-axial and shear data using a finite-element model

Treesearch

Scott E. Hamel; John C. Hermanson; Steven M. Cramer

2014-01-01

Wood-plastic composites (WPCs), commonly used in residential decks and railings, exhibit mechanical behavior that is bimodal, anisotropic, and nonlinear viscoelastic. They exhibit different stress-strain responses to tension and compression, both of which are nonlinear. Their mechanical properties vary with respect to extrusion direction, their deformation under...

A study of hyperelastic models for predicting the mechanical behavior of extensor apparatus.

PubMed

Elyasi, Nahid; Taheri, Kimia Karimi; Narooei, Keivan; Taheri, Ali Karimi

2017-06-01

In this research, the nonlinear elastic behavior of human extensor apparatus was investigated. To this goal, firstly the best material parameters of hyperelastic strain energy density functions consisting of the Mooney-Rivlin, Ogden, invariants, and general exponential models were derived for the simple tension experimental data. Due to the significance of stress response in other deformation modes of nonlinear models, the calculated parameters were used to study the pure shear and balance biaxial tension behavior of the extensor apparatus. The results indicated that the Mooney-Rivlin model predicts an unstable behavior in the balance biaxial deformation of the extensor apparatus, while the Ogden order 1 represents a stable behavior, although the fitting of experimental data and theoretical model was not satisfactory. However, the Ogden order 6 model was unstable in the simple tension mode and the Ogden order 5 and general exponential models presented accurate and stable results. In order to reduce the material parameters, the invariants model with four material parameters was investigated and this model presented the minimum error and stable behavior in all deformation modes. The ABAQUS Explicit solver was coupled with the VUMAT subroutine code of the invariants model to simulate the mechanical behavior of the central and terminal slips of the extensor apparatus during the passive finger flexion, which is important in the prediction of boutonniere deformity and chronic mallet finger injuries, respectively. Also, to evaluate the adequacy of constitutive models in simulations, the results of the Ogden order 5 were presented. The difference between the predictions was attributed to the better fittings of the invariants model compared with the Ogden model.

Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

PubMed Central

Kononova, Olga; Snijder, Joost; Kholodov, Yaroslav; Marx, Kenneth A.; Wuite, Gijs J. L.; Roos, Wouter H.; Barsegov, Valeri

2016-01-01

The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams’ deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young’s moduli for Hertzian and bending deformations, and the structural damage dependent beams’ survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications. PMID:26821264

Deformed photon-added entangled squeezed vacuum and one-photon states: Entanglement, polarization, and nonclassical properties

NASA Astrophysics Data System (ADS)

A, Karimi; M, K. Tavassoly

2016-04-01

In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variable-type entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f-deformed creation operator A = f (n)a † on the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the two-mode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f-deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes-Cummings model.

A nonlinear theory for elastic plates with application to characterizing paper properties

Treesearch

M. W. Johnson; Thomas J. Urbanik

1984-03-01

A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...

Real-time simulation of the nonlinear visco-elastic deformations of soft tissues.

PubMed

Basafa, Ehsan; Farahmand, Farzam

2011-05-01

Mass-spring-damper (MSD) models are often used for real-time surgery simulation due to their fast response and fairly realistic deformation replication. An improved real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was developed and tested. The mechanical realization of conventional MSD models was improved using nonlinear springs and nodal dampers, while their high computational efficiency was maintained using an adapted implicit integration algorithm. New practical algorithms for model parameter tuning, collision detection, and simulation were incorporated. The model was able to replicate complex biological soft tissue mechanical properties under large deformations, i.e., the nonlinear and viscoelastic behaviors. The simulated response of the model after tuning of its parameters to the experimental data of a deer liver sample, closely tracked the reference data with high correlation and maximum relative differences of less than 5 and 10%, for the tuning and testing data sets respectively. Finally, implementation of the proposed model and algorithms in a graphical environment resulted in a real-time simulation with update rates of 150 Hz for interactive deformation and haptic manipulation, and 30 Hz for visual rendering. The proposed real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was efficient, realistic, and accurate in ex vivo testing. This model is a suitable candidate for testing in vivo during laparoscopic surgery.

The role of nonlinear viscoelasticity on the functionality of laminating shortenings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Macias-Rodriguez, Braulio A.; Peyronel, Fernanda; Marangoni, Alejandro G.

The rheology of fats is essential for the development of homogeneous and continuous layered structures of doughs. Here, we define laminating shortenings in terms of rheological behavior displayed during linear-to-nonlinear shear deformations, investigated by large amplitude oscillatory shear rheology. Likewise, we associate the rheological behavior of the shortenings with structural length scales elucidated by ultra-small angle x-ray scattering and cryo-electron microscopy. Shortenings exhibited solid-like viscoelastic and viscoelastoplastic behaviors in the linear and nonlinear regimes respectively. In the nonlinear region, laminating shortenings dissipated more viscous energy (larger normalized dynamic viscosities) than a cake bakery shortening. The fat solid-like network of laminatingmore » shortening displayed a three-hierarchy structure and layered crystal aggregates, in comparison to two-hierarchy structure and spherical-like crystal aggregates of a cake shortening. We argue that the observed rheology, correlated to the structural network, is crucial for optimal laminating performance of shortenings.« less

Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector

NASA Technical Reports Server (NTRS)

Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)

2001-01-01

Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.

Nonlinear deformation of composites with consideration of the effect of couple-stresses

NASA Astrophysics Data System (ADS)

Lagzdiņš, A.; Teters, G.; Zilaucs, A.

1998-09-01

Nonlinear deformation of spatially reinforced composites under active loading (without unloading) is considered. All the theoretical constructions are based on the experimental data on unidirectional and ±π/4 cross-ply epoxy plastics reinforced with glass fibers. Based on the elastic properties of the fibers and EDT-10 epoxy binder, the linear elastic characteristics of a transversely isotropic unidirectionally reinforced fiberglass plastic are found, whereas the nonlinear characteristics are obtained from experiments. For calculating the deformation properties of the ±π/4 cross-ply plastic, a refined version of the Voigt method is applied taking into account also the couple-stresses arising in the composite due to relative rotation of the reinforcement fibers. In addition, a fourth-rank damage tensor is introduced in order to account for the impact of fracture caused by the couple-stresses. The unknown constants are found from the experimental uniaxial tension curve for the cross-ply composite. The comparison between the computed curves and experimental data for other loading paths shows that the description of the nonlinear behavior of composites can be improved by considering the effect of couple-stresses generated by rotations of the reinforcing fibers.

A Shear Deformable Shell Element for Laminated Composites

NASA Technical Reports Server (NTRS)

Chao, W. C.; Reddy, J. N.

1984-01-01

A three-dimensional element based on the total Lagrangian description of the motion of a layered anisotropic composite medium is developed, validated, and used to analyze layered composite shells. The element contains the following features: geometric nonlinearity, dynamic (transient) behavior, and arbitrary lamination scheme and lamina properties. Numerical results of nonlinear bending, natural vibration, and transient response are presented to illustrate the capabilities of the element.

Constrained hierarchical least square nonlinear equation solvers. [for indefinite stiffness and large structural deformations

NASA Technical Reports Server (NTRS)

Padovan, J.; Lackney, J.

1986-01-01

The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

A mechano-acoustic indentor system for in vivo measurement of nonlinear elastic properties of soft tissue.

PubMed

Koo, Terry K; Cohen, Jeffrey H; Zheng, Yongping

2011-11-01

Soft tissue exhibits nonlinear stress-strain behavior under compression. Characterizing its nonlinear elasticity may aid detection, diagnosis, and treatment of soft tissue abnormality. The purposes of this study were to develop a rate-controlled Mechano-Acoustic Indentor System and a corresponding finite element optimization method to extract nonlinear elastic parameters of soft tissue and evaluate its test-retest reliability. An indentor system using a linear actuator to drive a force-sensitive probe with a tip-mounted ultrasound transducer was developed. Twenty independent sites at the upper lateral quadrant of the buttock from 11 asymptomatic subjects (7 men and 4 women from a chiropractic college) were indented at 6% per second for 3 sessions, each consisting of 5 trials. Tissue thickness, force at 25% deformation, and area under the load-deformation curve from 0% to 25% deformation were calculated. Optimized hyperelastic parameters of the soft tissue were calculated with a finite element model using a first-order Ogden material model. Load-deformation response on a standardized block was then simulated, and the corresponding area and force parameters were calculated. Between-trials repeatability and test-retest reliability of each parameter were evaluated using coefficients of variation and intraclass correlation coefficients, respectively. Load-deformation responses were highly reproducible under repeated measurements. Coefficients of variation of tissue thickness, area under the load-deformation curve from 0% to 25% deformation, and force at 25% deformation averaged 0.51%, 2.31%, and 2.23%, respectively. Intraclass correlation coefficients ranged between 0.959 and 0.999, indicating excellent test-retest reliability. The automated Mechano-Acoustic Indentor System and its corresponding optimization technique offers a viable technology to make in vivo measurement of the nonlinear elastic properties of soft tissue. This technology showed excellent between-trials repeatability and test-retest reliability with potential to quantify the effects of a wide variety of manual therapy techniques on the soft tissue elastic properties. Copyright © 2011 National University of Health Sciences. Published by Mosby, Inc. All rights reserved.

The viscoelastic behavior of notched glassy polymers

NASA Technical Reports Server (NTRS)

Crook, R. A.; Letton, Alan

1993-01-01

In the bulk, glassy polymers exhibit a nonlinear viscoelastic response during deformation. Stress or strain induced damage (i.e. crazing, microshear banding) results in the production of nonrecoverable work and observed nonlinearity. Stress or strain dependent shift factors have been used to mathematically model the mechanical behavior of these polymers. Glassy polymers that have been notched, may exhibit very different load displacement response compared to the same material under bulk deformation. If a sharp notch is introduced into the body then loaded, the load displacement trace may appear to be single-valued in the absence of viscoelasticity and crack growth. This suggests the volume of damaged material is small compared to the overall dimensions of the specimen. The ability to produce a single-valued load-load-line displacement trace through the use of the Correspondence Principle may prove to be useful for fracture of viscoelastic materials.

In-process, non-destructive multimodal dynamic testing of high-speed composite rotors

NASA Astrophysics Data System (ADS)

Kuschmierz, Robert; Filippatos, Angelos; Langkamp, Albert; Hufenbach, Werner; Czarske, Jürgern W.; Fischer, Andreas

2014-03-01

Fibre reinforced plastic (FRP) rotors are lightweight and offer great perspectives in high-speed applications such as turbo machinery. Currently, novel rotor structures and materials are investigated for the purpose of increasing machine efficiency, lifetime and loading limits. Due to complex rotor structures, high anisotropy and non-linear behavior of FRP under dynamic loads, an in-process measurement system is necessary to monitor and to investigate the evolution of damages under real operation conditions. A non-invasive, optical laser Doppler distance sensor measurement system is applied to determine the biaxial deformation of a bladed FRP rotor with micron uncertainty as well as the tangential blade vibrations at surface speeds above 300 m/s. The laser Doppler distance sensor is applicable under vacuum conditions. Measurements at varying loading conditions are used to determine elastic and plastic deformations. Furthermore they allow to determine hysteresis, fatigue, Eigenfrequency shifts and loading limits. The deformation measurements show a highly anisotropic and nonlinear behavior and offer a deeper understanding of the damage evolution in FRP rotors. The experimental results are used to validate and to calibrate a simulation model of the deformation. The simulation combines finite element analysis and a damage mechanics model. The combination of simulation and measurement system enables the monitoring and prediction of damage evolutions of FRP rotors in process.

Modeling the Nonlinear, Strain Rate Dependent Deformation of Shuttle Leading Edge Materials with Hydrostatic Stress Effects Included

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Carney, Kelly S.

2004-01-01

An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites, such as the Reinforced Carbon Carbon (RCC) material used on the leading edges of the Space Shuttle. In the developed model, the differences in the tension and compression deformation behaviors have also been accounted for. State variable viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear response is independent of the stiffness in the normal directions. The developed equations have been implemented into LS-DYNA through the use of user defined subroutines (UMATs). Several sample qualitative calculations have been conducted, which demonstrate the ability of the model to qualitatively capture the features of the deformation response present in woven ceramic matrix composites.

Macroscopic models for shape memory alloy characterization and design

NASA Astrophysics Data System (ADS)

Massad, Jordan Elias

Shape memory alloys (SMAs) are being considered for a number of high performance applications, such as deformable aircraft wings, earthquake-resistant structures, and microdevices, due to their capability to achieve very high work densities, produce large deformations, and generate high stresses. In general, the material behavior of SMAs is nonlinear and hysteresic. To achieve the full potential of SMA actuators, it is necessary to develop models that characterize the nonlinearities and hysteresis inherent in the constituent materials. Additionally, the design of SMA actuators necessitates the development of control algorithms based on those models. We develop two models that quantify the nonlinearities and hysteresis inherent to SMAs, each in formulations suitable for subsequent control design. In the first model, we employ domain theory to quantify SMA behavior under isothermal conditions. The model involves a single first-order, nonlinear ordinary differential equation and requires as few as seven parameters that are identifiable from measurements. We develop the second model using the Muller-Achenbach-Seelecke framework where a transition state theory of nonequilibrium processes is used to derive rate laws for the evolution of material phase fractions. The fully thermomechanical model predicts rate-dependent, polycrystalline SMA behavior, and it accommodates heat transfer issues pertinent to thin-film SMAs. Furthermore, the model admits a low-order formulation and has a small number of parameters which can be readily identified using attributes of measured data. We illustrate aspects of both models through comparison with experimental bulk and thin-film SMA data.

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

NASA Technical Reports Server (NTRS)

Stein, M.; Stein, P. A.

1978-01-01

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

NASA Astrophysics Data System (ADS)

Gholami, Raheb; Ansari, Reza

2018-02-01

This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.; Hodges, Dewey H.

1987-01-01

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.

Creep model of unsaturated sliding zone soils and long-term deformation analysis of landslides

NASA Astrophysics Data System (ADS)

Zou, Liangchao; Wang, Shimei; Zhang, Yeming

2015-04-01

Sliding zone soil is a special soil layer formed in the development of a landslide. Its creep behavior plays a significant role in long-term deformation of landslides. Due to rainfall infiltration and reservoir water level fluctuation, the soils in the slide zone are often in unsaturated state. Therefore, the investigation of creep behaviors of the unsaturated sliding zone soils is of great importance for understanding the mechanism of the long-term deformation of a landslide in reservoir areas. In this study, the full-process creep curves of the unsaturated soils in the sliding zone in different net confining pressure, matric suctions and stress levels were obtained from a large number of laboratory triaxial creep tests. A nonlinear creep model for unsaturated soils and its three-dimensional form was then deduced based on the component model theory and unsaturated soil mechanics. This creep model was validated with laboratory creep data. The results show that this creep model can effectively and accurately describe the nonlinear creep behaviors of the unsaturated sliding zone soils. In order to apply this creep model to predict the long-term deformation process of landslides, a numerical model for simulating the coupled seepage and creep deformation of unsaturated sliding zone soils was developed based on this creep model through the finite element method (FEM). By using this numerical model, we simulated the deformation process of the Shuping landslide located in the Three Gorges reservoir area, under the cycling reservoir water level fluctuation during one year. The simulation results of creep displacement were then compared with the field deformation monitoring data, showing a good agreement in trend. The results show that the creeping deformations of landslides have strong connections with the changes of reservoir water level. The creep model of unsaturated sliding zone soils and the findings obtained by numerical simulations in this study are conducive to reveal the mechanisms of the dynamic process of landslide deformation, and serve as an important basis for the prediction and evaluation of landslides.

Nonlinear flow response of soft hair beds

NASA Astrophysics Data System (ADS)

Alvarado, José

2017-11-01

We are hairy inside: beds of passive fibers anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. Such hairs are soft enough to deform in response to stresses from fluid flows. Fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem which is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear- driven Stokes flows. We characterize this system with a theoretical model which accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers toward the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter which controls nonlinear behavior. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps. J.A. acknowledges support the U. S. Army Research Office under Grant Number W911NF-14-1-0396.

Nonlocal postbuckling analysis of graphene sheets with initial imperfection based on first order shear deformation theory

NASA Astrophysics Data System (ADS)

Soleimani, Ahmad; Naei, Mohammad Hasan; Mashhadi, Mahmoud Mosavi

In this paper, the first order shear deformation theory (FSDT) is used to investigate the postbuckling behavior of orthotropic single-layered graphene sheet (SLGS) under in-plane loadings. Nonlocal elasticity theory and von-Karman nonlinear model in combination with the isogeometric analysis (IGA) have been applied to study the postbuckling characteristics of SLGSs. In contrast to the classical model, the nonlocal continuum model developed in this work considers the size-effects on the postbuckling characteristics of SLGSs. FSDT takes into account effects of shear deformations through-the-thickness of plate. Geometric imperfection which is defined as a very small transverse displacement of the mid-plane is applied on undeformed nanoplate to create initial deviation in graphene sheet from being perfectly flat. Nonlinear governing equations of motion for SLGS are derived from the principle of virtual work and a variational formulation. At the end, the results are presented as the postbuckling equilibrium paths of SLGS. The influence of various parameters such as edge length, nonlocal parameter, compression ratio, boundary conditions and aspect ratio on the postbuckling path is investigated. The results of this work show the high accuracy of nonlocal FSDT-based analysis for postbuckling behavior of graphene sheets.

Nonlinear viscoelastic response of highly filled elastomers under multiaxial finite deformation

NASA Technical Reports Server (NTRS)

Peng, Steven T. J.; Landel, Robert F.

1990-01-01

A biaxial tester was used to obtain precise biaxial stress responses of highly filled, high strain capability elastomers. Stress-relaxation experiments show that the time-dependent part of the relaxation response can be reasonably approximated by a function which is strain and biaxiality independent. Thus, isochronal data from the stress-relaxation curves can be used to determine the stored energy density function. The complex behavior of the elastomers under biaxial deformation may be caused by dewetting.

Non-linear flow law of rockglacier creep determined from geomorphological observations: A case study from the Murtèl rockglacier (Engadin, SE Switzerland)

NASA Astrophysics Data System (ADS)

Frehner, Marcel; Amschwand, Dominik; Gärtner-Roer, Isabelle

2016-04-01

Rockglaciers consist of unconsolidated rock fragments (silt/sand-rock boulders) with interstitial ice; hence their creep behavior (i.e., rheology) may deviate from the simple and well-known flow-laws for pure ice. Here we constrain the non-linear viscous flow law that governs rockglacier creep based on geomorphological observations. We use the Murtèl rockglacier (upper Engadin valley, SE Switzerland) as a case study, for which high-resolution digital elevation models (DEM), time-lapse borehole deformation data, and geophysical soundings exist that reveal the exterior and interior architecture and dynamics of the landform. Rockglaciers often feature a prominent furrow-and-ridge topography. For the Murtèl rockglacier, Frehner et al. (2015) reproduced the wavelength, amplitude, and distribution of the furrow-and-ridge morphology using a linear viscous (Newtonian) flow model. Arenson et al. (2002) presented borehole deformation data, which highlight the basal shear zone at about 30 m depth and a curved deformation profile above the shear zone. Similarly, the furrow-and-ridge morphology also exhibits a curved geometry in map view. Hence, the surface morphology and the borehole deformation data together describe a curved 3D geometry, which is close to, but not quite parabolic. We use a high-resolution DEM to quantify the curved geometry of the Murtèl furrow-and-ridge morphology. We then calculate theoretical 3D flow geometries using different non-linear viscous flow laws. By comparing them to the measured curved 3D geometry (i.e., both surface morphology and borehole deformation data), we can determine the most adequate flow-law that fits the natural data best. Linear viscous models result in perfectly parabolic flow geometries; non-linear creep leads to localized deformation at the sides and bottom of the rockglacier while the deformation in the interior and top are less intense. In other words, non-linear creep results in non-parabolic flow geometries. Both the linear (power-law exponent, n=1) and strongly non-linear models (n=10) do not match the measured data well. However, the moderately non-linear models (n=2-3) match the data quite well indicating that the creep of the Murtèl rockglacier is governed by a moderately non-linear viscous flow law with a power-law exponent close to the one of pure ice. Our results are crucial for improving existing numerical models of rockglacier flow that currently use simplified (i.e., linear viscous) flow-laws. References: Arenson L., Hoelzle M., and Springman S., 2002: Borehole deformation measurements and internal structure of some rock glaciers in Switzerland, Permafrost and Periglacial Processes 13, 117-135. Frehner M., Ling A.H.M., and Gärtner-Roer I., 2015: Furrow-and-ridge morphology on rockglaciers explained by gravity-driven buckle folding: A case study from the Murtèl rockglacier (Switzerland), Permafrost and Periglacial Processes 26, 57-66.

Anisotropic constitutive model incorporating multiple damage mechanisms for multiscale simulation of dental enamel.

PubMed

Ma, Songyun; Scheider, Ingo; Bargmann, Swantje

2016-09-01

An anisotropic constitutive model is proposed in the framework of finite deformation to capture several damage mechanisms occurring in the microstructure of dental enamel, a hierarchical bio-composite. It provides the basis for a homogenization approach for an efficient multiscale (in this case: multiple hierarchy levels) investigation of the deformation and damage behavior. The influence of tension-compression asymmetry and fiber-matrix interaction on the nonlinear deformation behavior of dental enamel is studied by 3D micromechanical simulations under different loading conditions and fiber lengths. The complex deformation behavior and the characteristics and interaction of three damage mechanisms in the damage process of enamel are well captured. The proposed constitutive model incorporating anisotropic damage is applied to the first hierarchical level of dental enamel and validated by experimental results. The effect of the fiber orientation on the damage behavior and compressive strength is studied by comparing micro-pillar experiments of dental enamel at the first hierarchical level in multiple directions of fiber orientation. A very good agreement between computational and experimental results is found for the damage evolution process of dental enamel. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Sparse 4D TomoSAR imaging in the presence of non-linear deformation

NASA Astrophysics Data System (ADS)

Khwaja, Ahmed Shaharyar; ćetin, Müjdat

2018-04-01

In this paper, we present a sparse four-dimensional tomographic synthetic aperture radar (4D TomoSAR) imaging scheme that can estimate elevation and linear as well as non-linear seasonal deformation rates of scatterers using the interferometric phase. Unlike existing sparse processing techniques that use fixed dictionaries based on a linear deformation model, we use a variable dictionary for the non-linear deformation in the form of seasonal sinusoidal deformation, in addition to the fixed dictionary for the linear deformation. We estimate the amplitude of the sinusoidal deformation using an optimization method and create the variable dictionary using the estimated amplitude. We show preliminary results using simulated data that demonstrate the soundness of our proposed technique for sparse 4D TomoSAR imaging in the presence of non-linear deformation.

Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics

NASA Astrophysics Data System (ADS)

Bun Tse, Bosco Chun

This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.

Deformation Response of Unsymmetrically Laminated Plates Subjected to Inplane Loading

NASA Technical Reports Server (NTRS)

Ochinero, Tomoya T.; Hyer, Michael W.

2002-01-01

This paper discusses the out-of-plane deformation behavior of unsymmetric cross-ply composite plates compressed inplane by displacing one edge of the plate a known amount. The plates are assumed to be initially flat and several boundary conditions are considered. Geometrically nonlinear behavior is assumed. The primary objectives are to study the out-of-plane behavior as a function of increasing inplane compression and to determine if bifurcation behavior and secondary buckling can occur. It is shown that, depending on the boundary conditions, both can occur, though the characteristics are different than the pre and post-buckling behavior of a companion symmetric cross-ply plate. Furthermore, while a symmetric cross-ply plate can postbuckle with either a positive or negative out-of-plane displacement, the unsymmetric cross-ply plates studied deflect out-of-plane only in one direction throughout the range of inplane compression, the direction again depending on the boundary conditions

Constitutive Modeling, Nonlinear Behavior, and the Stress-Optic Law

DTIC Science & Technology

2011-01-01

estimates of D̂ from dynamic mechanical measurements. Some results are shown in Figure 58 for a filled EPDM rubber [116]. There is rough agreement with...elastomers and filler-reinforced rubber . 5.1 Linearity and the superposition principle The problem of analyzing viscoelastic mechanical behavior is greatly...deformation such as shear. For crosslinked rubber the strain can be defined in terms of the strain function suggested by the statistical theories of

Efficient excitation of nonlinear phonons via chirped pulses: Induced structural phase transitions

NASA Astrophysics Data System (ADS)

Itin, A. P.; Katsnelson, M. I.

2018-05-01

Nonlinear phononics play important role in strong laser-solid interactions. We discuss a dynamical protocol for efficient phonon excitation, considering recent inspiring proposals: inducing ferroelectricity in paraelectric perovskites, and inducing structural deformations in cuprates [Subedi et al., Phys. Rev. B 89, 220301(R) (2014), 10.1103/PhysRevB.89.220301; Phys. Rev. B 95, 134113 (2017), 10.1103/PhysRevB.95.134113]. High-frequency phonon modes are driven by midinfrared pulses, and coupled to lower-frequency modes those indirect excitations cause structural deformations. We study in more detail the case of KTaO3 without strain, where it was not possible to excite the needed low-frequency phonon mode by resonant driving of the higher frequency one. Behavior of the system is explained using a reduced model of coupled driven nonlinear oscillators. We find a dynamical mechanism which prevents effective excitation at resonance driving. To induce ferroelectricity, we employ driving with sweeping frequency, realizing so-called capture into resonance. The method can be applied to many other related systems.

Comparative Analysis of Volcanic Inflation—Deflation Cycles

NASA Astrophysics Data System (ADS)

Walwer, D.; Ghil, M.; Calais, E.

2016-12-01

GPS geodetic data together with INSAR images are often used to formulate kinematic models of the sources of volcanic deformations. The increasing amount of data now available allows one to produce time series that are several years long and thus capture continuously the history of volcanic deformations, in particular their nonlinear behavior. This information is highly valuable in helping understand the dynamics of volcanic systems.Nonlinear deformation signals are, however, difficult to extract from the background noise inherent in the GPS time series. It is also arduous to unravel the signal of interest from other nonlinear signals, such as the seasonal oscillations associated with mass variations in the atmosphere, the ocean, and the hydrological reservoirs. Here we use Multichannel Singular Spectrum Analysis (M-SSA) — an advanced, data-adaptive method for time series analysis that exploits simultaneously the temporal and spatial correlations of geophysical fields — to extract such deformation signals.We apply M-SSA to GPS data sets from four volcanoes: Akutan, Alaska; Okmok, Alaska; Westdahl, Alaska; and Piton de la Fournaise, La Reunion. Our analyses show that all four volcanoes share similar features in their deformation history, suggesting similarities in the dynamics that generate the inflation-deflation cycles. In particular, all four volcanic systems exhibit sawtooth-shaped oscillations with slow inflations followed by slower deflations, with time scales that vary from 6 months to 4 years. This relation of dynamical similarity is further highlighted by the phase portrait reconstruction of the four systems in the plane of deformation vs. rate-of-deformation, as obtained from the deformation signals extracted from the GPS time series using M-SSA.The inflating phase of these oscillations is followed by eruptions at Okmok volcano and at Piton de la Fournaise. These analysis results suggest that these volcanic inflation—deflation cycles are associated with the destabilization of a volcanic system and may lead to the identification of premonitory signals for an eruptive regime.

A constitutive model for developing blood clots with various compositions and their nonlinear viscoelastic behavior.

PubMed

van Kempen, Thomas H S; Donders, Wouter P; van de Vosse, Frans N; Peters, Gerrit W M

2016-04-01

The mechanical properties determine to a large extent the functioning of a blood clot. These properties depend on the composition of the clot and have been related to many diseases. However, the various involved components and their complex interactions make it difficult at this stage to fully understand and predict properties as a function of the components. Therefore, in this study, a constitutive model is developed that describes the viscoelastic behavior of blood clots with various compositions. Hereto, clots are formed from whole blood, platelet-rich plasma and platelet-poor plasma to study the influence of red blood cells, platelets and fibrin, respectively. Rheological experiments are performed to probe the mechanical behavior of the clots during their formation. The nonlinear viscoelastic behavior of the mature clots is characterized using a large amplitude oscillatory shear deformation. The model is based on a generalized Maxwell model that accurately describes the results for the different rheological experiments by making the moduli and viscosities a function of time and the past and current deformation. Using the same model with different parameter values enables a description of clots with different compositions. A sensitivity analysis is applied to study the influence of parameter variations on the model output. The relative simplicity and flexibility make the model suitable for numerical simulations of blood clots and other materials showing similar behavior.

Mechanical biocompatibility of highly deformable biomedical materials.

PubMed

Mazza, Edoardo; Ehret, Alexander E

2015-08-01

Mismatch of mechanical properties between highly deformable biomedical materials and adjacent native tissue might lead to short and long term health impairment. The capability of implants to deform at the right level, i.e. similar to the macroscopic mechanical response of the surrounding biological materials, is often associated with dissimilar microstructural deformation mechanisms. This mismatch on smaller length scales might lead to micro-injuries, cell damage, inflammation, fibrosis or necrosis. Hence, the mechanical biocompatibility of soft implants depends not only on the properties and composition of the implant material, but also on its organization, distribution and motion at one or several length scales. The challenges related to the analysis and attainment of mechanical biocompatibility are illustrated with two examples: prosthetic meshes for hernia and pelvic repair and electrospun scaffolds for tissue engineering. For these material systems we describe existing methods for characterization and analysis of the non-linear response to uniaxial and multiaxial stress states, its time and history dependence, and the changes in deformation behavior associated with tissue in-growth and material resorption. We discuss the multi-scale deformation behavior of biomaterials and adjacent tissue, and indicate major interdisciplinary questions to be addressed in future research. Copyright © 2015 Elsevier Ltd. All rights reserved.

Soft tissue modelling through autowaves for surgery simulation.

PubMed

Zhong, Yongmin; Shirinzadeh, Bijan; Alici, Gursel; Smith, Julian

2006-09-01

Modelling of soft tissue deformation is of great importance to virtual reality based surgery simulation. This paper presents a new methodology for simulation of soft tissue deformation by drawing an analogy between autowaves and soft tissue deformation. The potential energy stored in a soft tissue as a result of a deformation caused by an external force is propagated among mass points of the soft tissue by non-linear autowaves. The novelty of the methodology is that (i) autowave techniques are established to describe the potential energy distribution of a deformation for extrapolating internal forces, and (ii) non-linear materials are modelled with non-linear autowaves other than geometric non-linearity. Integration with a haptic device has been achieved to simulate soft tissue deformation with force feedback. The proposed methodology not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply changing diffusion coefficients.

Analytical and Experimental Characterization of Gravity Induced Deformations In Subscale Gossamer Structures

NASA Technical Reports Server (NTRS)

Johnston, John D.; Blandino, Joseph R.; McEvoy, Kiley C.

2004-01-01

The development of gossamer space structures such as solar sails and sunshields presents many challenges due to their large size and extreme flexibility. The post-deployment structural geometry exhibited during ground testing may significantly depart from the in-space configuration due to the presence of gravity-induced deformations (gravity sag) of lightly preloaded membranes. This paper describes a study carried out to characterize gravity sag in two subscale gossamer structures: a single quadrant from a 2 m, 4 quadrant square solar sail and a 1.7 m membrane layer from a multi-layer sunshield The behavior of the test articles was studied over a range of preloads and in several orientations with respect to gravity. An experimental study was carried out to measure the global surface profiles using photogrammetry, and nonlinear finite element analysis was used to predict the behavior of the test articles. Comparison of measured and predicted surface profiles shows that the finite dement analysis qualitatively predicts deformed shapes comparable to those observed in the laboratory. Quantitatively, finite element analysis predictions for peak gravity-induced deformations in both test articles were within 10% of measured values. Results from this study provide increased insight into gravity sag behavior in gossamer structures, and demonstrates the potential to analytically predict gravity-induced deformations to within reasonable accuracy.

Nonlinear mechanics of a ring structure subjected to multi-pairs of evenly distributed equal radial forces

NASA Astrophysics Data System (ADS)

Chen, Q.; Sun, F.; Li, Z. Y.; Taxis, L.; Pugno, N.

2017-10-01

Combining the elastica theory, finite element (FE) analysis, and a geometrical topological experiment, we studied the mechanical behavior of a ring subjected to multi-pairs of evenly distributed equal radial forces by looking at its seven distinct states. The results showed that the theoretical predictions of the ring deformation and strain energy matched the FE results very well, and that the ring deformations were comparable to the topological experiment. Moreover, no matter whether the ring was compressed or tensioned by N-pairs of forces, the ring always tended to be regular polygons with 2 N sides as the force increased, and a proper compressive force deformed the ring into exquisite flower-like patterns. The present study solves a basic mechanical problem of a ring subjected to lateral forces, which can be useful for studying the relevant mechanical behavior of ring structures from the nano- to the macro-scale.

Nanoindentation of the surface layer of Hadfield's steel after sliding friction

NASA Astrophysics Data System (ADS)

Kolubaev, A. V.; Kolubaev, E. A.; Sizova, O. V.

2007-12-01

We have measured the nanohardness of a deformed near-surface layer of Hadfield’s steel upon friction testing. The phenomenon of shape recovery upon indentation has been observed, which is retained for several days after tribological tests. It s suggested that the strained material exhibits behavior analogous to nonlinear elasticity.

Finite element methods in a simulation code for offshore wind turbines

NASA Astrophysics Data System (ADS)

Kurz, Wolfgang

1994-06-01

Offshore installation of wind turbines will become important for electricity supply in future. Wind conditions above sea are more favorable than on land and appropriate locations on land are limited and restricted. The dynamic behavior of advanced wind turbines is investigated with digital simulations to reduce time and cost in development and design phase. A wind turbine can be described and simulated as a multi-body system containing rigid and flexible bodies. Simulation of the non-linear motion of such a mechanical system using a multi-body system code is much faster than using a finite element code. However, a modal representation of the deformation field has to be incorporated in the multi-body system approach. The equations of motion of flexible bodies due to deformation are generated by finite element calculations. At Delft University of Technology the simulation code DUWECS has been developed which simulates the non-linear behavior of wind turbines in time domain. The wind turbine is divided in subcomponents which are represented by modules (e.g. rotor, tower etc.).

Nonlinear Deformation Behavior of New Braided Composites with Six-axis Yarn Orientations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahn, H.-C.; Yu, W.-R.; Guo, Z.

The braiding technology is one of fabrication methods that can produce three-dimensional fiber preforms. Braided composites have many advantages over other two-dimensional composites such as no delamination, high impact and fatigue properties, near-net shape preform, etc. Due to the undulated yarns in the braided preforms, however, their axial stiffness is lower than that of uni-directional or woven composites. To improve the axial stiffness, the longitudinal axial yarns were already introduced along with the braiding axis (five-axis braiding technology). In this study, we developed a new braided structure using six-axis braiding technology. In addition to braiding and longitudinal axial yarns, transversemore » axial yarn was introduced. New braided composites, so called six-axis braiding composites, were manufactured using ultra high molecular weight polyethylene and epoxy resin and their mechanical properties were characterized. To investigate the mechanical performance of these braided composites according to their manufacturing conditions, a numerical analysis was performed using their unit-cell modeling and finite element analysis. In the analysis the nonlinear deformation behavior will be included.« less

Linear and Nonlinear Elasticity of Networks Made of Comb-like Polymers and Bottle-Brushes

NASA Astrophysics Data System (ADS)

Liang, H.; Dobrynin, A.; Everhart, M.; Daniel, W.; Vatankhah-Varnoosfaderani, M.; Sheiko, S.

We study mechanical properties of networks made of combs and bottle-brushes by computer simulations, theoretical calculations and experimental techniques. The networks are prepared by cross-linking backbones of combs or bottle-brushes with linear chains. This results in ``hybrid'' networks consisting of linear chains and strands of combs or bottle-brushes. In the framework of the phantom network model, the network modulus at small deformations G0 can be represented as a sum of contributions from linear chains, G0 , l, and strands of comb or bottle-brush, G0 , bb. If the length of extended backbone between crosslinks, Rmax, is much longer than the Kuhn length, bk, the modulus scales with the degree of polymerization of the side chains, nsc, and number of monomers between side chains, ng, as G0 , bb (nsc/ng + 1)-1. In the limit when bk becomes of the order of Rmax, the combs and bottle-brushes can be considered as semiflexible chains, resulting in a network modulus to be G0 , bb (nsc/ng + 1)-1(nsc2/2/ng) . In the nonlinear deformation regime, the strain-hardening behavior is described by the nonlinear network deformation model, which predicts that the true stress is a universal function of the structural modulus, G, first strain invariant, I1, and deformation ratio, β. The results of the computer simulations and predictions of the theoretical model are in a good agreement with experimental results. NSF DMR-1409710, DMR-1407645, DMR-1624569, DMR-1436201.

Buckling Behavior of Compression-Loaded Composite Cylindrical Shells With Reinforced Cutouts

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Sarnes, James H., Jr.

2004-01-01

Results from a numerical study of the response of thin-walled compression-loaded quasi-isotropic laminated composite cylindrical shells with unreinforced and reinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The results indicate that a local buckling response occurs in the shell near the cutout when subjected to load and is caused by a nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, reinforcement around a cutout in a compression-loaded shell is shown to retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell. However, some results show that certain reinforcement configurations can cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved buckling response characteristics.

Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

NASA Astrophysics Data System (ADS)

Lefèvre, Victor; Lopez-Pamies, Oscar

2017-02-01

This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi-)conducting/high-permittivity particles to dielectric elastomers does not lead to the extreme electrostriction enhancements observed in experiments. It is posited that such extreme enhancements are the manifestation of interphasial phenomena.

Nonlinear softening of unconsolidated granular earth materials

NASA Astrophysics Data System (ADS)

Lieou, Charles K. C.; Daub, Eric G.; Guyer, Robert A.; Johnson, Paul A.

2017-09-01

Unconsolidated granular earth materials exhibit softening behavior due to external perturbations such as seismic waves, namely, the wave speed and elastic modulus decrease upon increasing the strain amplitude above dynamics strains of about 10-6 under near-surface conditions. In this letter, we describe a theoretical model for such behavior. The model is based on the idea that shear transformation zones—clusters of grains that are loose and susceptible to contact changes, particle displacement, and rearrangement—are responsible for plastic deformation and softening of the material. We apply the theory to experiments on simulated fault gouge composed of glass beads and demonstrate that the theory predicts nonlinear resonance shifts, reduction of the P wave modulus, and attenuation, in agreement with experiments. The theory thus offers insights on the nature of nonlinear elastic properties of a granular medium and potentially into phenomena such as triggering on earthquake faults.

Out-of-plane buckling of pantographic fabrics in displacement-controlled shear tests: experimental results and model validation

NASA Astrophysics Data System (ADS)

Barchiesi, Emilio; Ganzosch, Gregor; Liebold, Christian; Placidi, Luca; Grygoruk, Roman; Müller, Wolfgang H.

2018-01-01

Due to the latest advancements in 3D printing technology and rapid prototyping techniques, the production of materials with complex geometries has become more affordable than ever. Pantographic structures, because of their attractive features, both in dynamics and statics and both in elastic and inelastic deformation regimes, deserve to be thoroughly investigated with experimental and theoretical tools. Herein, experimental results relative to displacement-controlled large deformation shear loading tests of pantographic structures are reported. In particular, five differently sized samples are analyzed up to first rupture. Results show that the deformation behavior is strongly nonlinear, and the structures are capable of undergoing large elastic deformations without reaching complete failure. Finally, a cutting edge model is validated by means of these experimental results.

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

NASA Technical Reports Server (NTRS)

Wang, P. K. C.; Hadaegh, F. Y.

1996-01-01

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

Buckling Behavior of Compression-Loaded Composite Cylindrical Shells with Reinforced Cutouts

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Starnes, James H., Jr.

2002-01-01

Results from a numerical study of the response of thin-wall compression-loaded quasi-isotropic laminated composite cylindrical shells with reinforced and unreinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A high-fidelity nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate how a compression-loaded shell with an unreinforced cutout can exhibit a complex nonlinear response. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, the addition of reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell, as expected. However, results are presented that show how certain reinforcement configurations can actually cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved response characteristics.

Wide-range simulation of elastoplastic wave fronts and failure of solids under high-speed loading

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saveleva, Natalia, E-mail: saveleva@icmm.ru; Bayandin, Yuriy, E-mail: buv@icmm.ru; Naimark, Oleg, E-mail: naimark@icmm.ru

2015-10-27

The aim of this paper is numerical study of deformation processes and failure of vanadium under shock-wave loading. According developed statistical theory of solid with mesoscopic defects the constitutive equations were proposed in terms of two structural variables characterizing behavior of defects ensembles: defect density tensor and structural scaling parameter. On the basis of wide-range constitutive equations the mathematical model of deformation behavior and failure of vanadium was developed taking into account the bond relaxation mechanisms, multistage of fracture and nonlinearity kinetic of defects. Results of numerical simulation allow the description of the major effects of shock wave propagation (elasticmore » precursor decay, grow of spall strength under grow strain rate)« less

GPU-based acceleration of computations in nonlinear finite element deformation analysis.

PubMed

Mafi, Ramin; Sirouspour, Shahin

2014-03-01

The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation. Copyright © 2013 John Wiley & Sons, Ltd.

A Nonlinear Viscoelastic Model for Ceramics at High Temperatures

NASA Technical Reports Server (NTRS)

Powers, Lynn M.; Panoskaltsis, Vassilis P.; Gasparini, Dario A.; Choi, Sung R.

2002-01-01

High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the nonlinear, asymmetric time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Element deletion has been implemented within ABAQUS. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. The analytical model is intended to be used to predict the creep rupture lives of ceramic parts in arbitrary stress conditions.

Nonlinear electrohydrodynamics of a viscous droplet

NASA Astrophysics Data System (ADS)

Salipante, Paul; Vlahovska, Petia

2012-02-01

A classic result due to G.I.Taylor is that a drop placed in a uniform electric field adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. We report an instability and transition to a nonaxisymmetric rotational flow in strong fields, similar to the rotation of solid dielectric spheres observed by Quincke in the 19th century. Our experiments reveal novel droplet behaviors such as tumbling, oscillations and chaotic dynamics even under creeping flow conditions. A phase diagram demonstrates the dependence of these behaviors on drop size, viscosity ratio and electric field strength. The theoretical model, which includes anisotropy in the polarization relaxation, elucidates the interplay of interface deformation and charging as the source of the rich nonlinear dynamics.

Analysis of metal-matrix composite structures. I - Micromechanics constitutive theory. II - Laminate analyses

NASA Technical Reports Server (NTRS)

Arenburg, R. T.; Reddy, J. N.

1991-01-01

The micromechanical constitutive theory is used to examine the nonlinear behavior of continuous-fiber-reinforced metal-matrix composite structures. Effective lamina constitutive relations based on the Abouli micromechanics theory are presented. The inelastic matrix behavior is modeled by the unified viscoplasticity theory of Bodner and Partom. The laminate constitutive relations are incorporated into a first-order deformation plate theory. The resulting boundary value problem is solved by utilizing the finite element method. Attention is also given to computational aspects of the numerical solution, including the temporal integration of the inelastic strains and the spatial integration of bending moments. Numerical results the nonlinear response of metal matrix composites subjected to extensional and bending loads are presented.

Characterization of Nonlinear Rate Dependent Response of Shape Memory Polymers

NASA Technical Reports Server (NTRS)

Volk, Brent; Lagoudas, Dimitris C.; Chen, Yi-Chao; Whitley, Karen S.

2007-01-01

Shape Memory Polymers (SMPs) are a class of polymers, which can undergo deformation in a flexible state at elevated temperatures, and when cooled below the glass transition temperature, while retaining their deformed shape, will enter and remain in a rigid state. Upon heating above the glass transition temperature, the shape memory polymer will return to its original, unaltered shape. SMPs have been reported to recover strains of over 400%. It is important to understand the stress and strain recovery behavior of SMPs to better develop constitutive models which predict material behavior. Initial modeling efforts did not account for large deformations beyond 25% strain. However, a model under current development is capable of describing large deformations of the material. This model considers the coexisting active (rubber) and frozen (glass) phases of the polymer, as well as the transitions between the material phases. The constitutive equations at the continuum level are established with internal state variables to describe the microstructural changes associated with the phase transitions. For small deformations, the model reduces to a linear model that agrees with those reported in the literature. Thermomechanical characterization is necessary for the development, calibration, and validation of a constitutive model. The experimental data reported in this paper will assist in model development by providing a better understanding of the stress and strain recovery behavior of the material. This paper presents the testing techniques used to characterize the thermomechanical material properties of a shape memory polymer (SMP) and also presents the resulting data. An innovative visual-photographic apparatus, known as a Vision Image Correlation (VIC) system was used to measure the strain. The details of this technique will also be presented in this paper. A series of tensile tests were performed on specimens such that strain levels of 10, 25, 50, and 100% were applied to the material while it was above its glass transition temperature. After deforming the material to a specified applied strain, the material was then cooled to below the glass transition temperature (Tg) while retaining the deformed shape. Finally, the specimen was heated again to above the transition temperature, and the resulting shape recovery profile was measured. Results show that strain recovery occurs at a nonlinear rate with respect to time. Results also indicate that the ratio of recoverable strain/applied strain increases as the applied strain increases.

Analysis of Composite Panels Subjected to Thermo-Mechanical Loads

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Peters, Jeanne M.

1999-01-01

The results of a detailed study of the effect of cutout on the nonlinear response of curved unstiffened panels are presented. The panels are subjected to combined temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order, shear deformation, Sanders-Budiansky-type shell theory with the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, as well as in the material properties of the individual layers. Numerical results are presented for cylindrical panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities as well as their sensitivity to changes in the various panel, layer, and micromechanical parameters.

Flexible Foam Model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Neilsen, Michael K.; Lu, Wei-Yang; Werner, Brian T.

Experiments were performed to characterize the mechanical response of a 15 pcf flexible polyurethane foam to large deformation at different strain rates and temperatures. Results from these experiments indicated that at room temperature, flexible polyurethane foams exhibit significant nonlinear elastic deformation and nearly return to their original undeformed shape when unloaded. However, when these foams are cooled to temperatures below their glass transition temperature of approximately -35 o C, they behave like rigid polyurethane foams and exhibit significant permanent deformation when compressed. Thus, a new model which captures this dramatic change in behavior with temperature was developed and implemented intomore » SIERRA with the name Flex_Foam to describe the mechanical response of both flexible and rigid foams to large deformation at a variety of temperatures and strain rates. This report includes a description of recent experiments. Next, development of the Flex Foam model for flexible polyurethane and other flexible foams is described. Selection of material parameters are discussed and finite element simulations with the new Flex Foam model are compared with experimental results to show behavior that can be captured with this new model.« less

Experimental Nonlinear Dynamics and Snap-Through of Post-Buckled Thin Laminated Composite Plates

NASA Astrophysics Data System (ADS)

Kim, Han-Gyu

Modern aerospace systems are increasingly being designed with composite panels and plates to achieve light weight and high specific strength and stiffness. For constrained panels, thermally-induced axial loading may cause buckling of the structure, which can lead to nonlinear and potentially chaotic behavior. When post-buckled composite plates experience snap-through, they are subjected to large-amplitude deformations and in-plane compressive loading. These phenomena pose a potential threat to the structural integrity of composite structures. In this work, the nonlinear dynamic behavior of post-buckled composite plates was investigated experimentally and computationally. For the experimental work, an electrodynamic shaker was used to apply harmonic loads and the dynamic response of plate specimens was measured using a single-point displacement-sensing laser, a double-point laser vibrometer (velocity-sensing), and a set of digital image correlation cameras. Both chaotic and periodic steady-state snap-through behaviors were investigated. The experimental data were used to characterize snap-through behaviors of the post-buckled specimens and their boundaries in the harmonic forcing parameter space. The nonlinear behavior of post-buckled plates was modeled using the classical laminated plate theory (CLPT) and the von Karman strain-displacement relations. The static equilibrium paths of the post-buckled plates were analyzed using an arc-length method with a branch-switching technique. For the dynamic analysis, the nonlinear equations of motion were derived based on CLPT and the nonlinear finite element model of the equations was constructed using the Hermite cubic interpolation functions for both conforming and nonconforming elements. The numerical analyses were conducted using the model and were compared with the experimental data.

Computer Simulations of Bottlebrush Melts and Soft Networks

NASA Astrophysics Data System (ADS)

Cao, Zhen; Carrillo, Jan-Michael; Sheiko, Sergei; Dobrynin, Andrey

We have studied dense bottlebrush systems in a melt and network state using a combination of the molecular dynamics simulations and analytical calculations. Our simulations show that the bottlebrush macromolecules in a melt behave as ideal chains with the effective Kuhn length bK. The bottlebrush induced bending rigidity is due to redistribution of the side chains upon backbone bending. Kuhn length of the bottlebrushes increases with increasing the side-chain degree of polymerization nsc as bK ~nsc0 . 46 . This model of bottlebrush macromolecules is extended to describe mechanical properties of bottlebrush networks in linear and nonlinear deformation regimes. In the linear deformation regime, the network shear modulus scales with the degree of polymerization of the side chains as G0 ~nsc + 1 - 1 as long as the ratio of the Kuhn length to the size of the fully extended bottlebrush backbone between crosslinks, Rmax, is smaller than unity, bK /Rmax < < 1 . Bottlebrush networks with bK /Rmax ~ 1 demonstrate behavior similar to that of networks of semiflexible chains with G0 ~nsc- 0 . 5 . In the nonlinear deformation regime, the deformation dependent shear modulus is a universal function of the first strain invariant I1 and bottlebrush backbone deformation ratio β describing stretching ability of the bottlebrush backbone between crosslinks. Nsf DMR-1409710 DMR-1436201.

High Strain Rate Deformation Modeling of a Polymer Matrix Composite. Part 2; Composite Micromechanical Model

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Stouffer, Donald C.

1998-01-01

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this second paper of a two part report, a three-dimensional composite micromechanical model is described which allows for the analysis of the rate dependent, nonlinear deformation response of a polymer matrix composite. Strain rate dependent inelastic constitutive equations utilized to model the deformation response of a polymer are implemented within the micromechanics method. The deformation response of two representative laminated carbon fiber reinforced composite materials with varying fiber orientation has been predicted using the described technique. The predicted results compare favorably to both experimental values and the response predicted by the Generalized Method of Cells, a well-established micromechanics analysis method.

Strain Rate Dependent Deformation and Strength Modeling of a Polymer Matrix Composite Utilizing a Micromechanics Approach. Degree awarded by Cincinnati Univ.

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

1999-01-01

Potential gas turbine applications will expose polymer matrix composites to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under extreme conditions. Specifically, analytical methods designed for these applications must have the capability of properly capturing the strain rate sensitivities and nonlinearities that are present in the material response. The Ramaswamy-Stouffer constitutive equations, originally developed to analyze the viscoplastic deformation of metals, have been modified to simulate the nonlinear deformation response of ductile, crystalline polymers. The constitutive model is characterized and correlated for two representative ductile polymers. Fiberite 977-2 and PEEK, and the computed results correlate well with experimental values. The polymer constitutive equations are implemented in a mechanics of materials based composite micromechanics model to predict the nonlinear, rate dependent deformation response of a composite ply. Uniform stress and uniform strain assumptions are applied to compute the effective stresses of a composite unit cell from the applied strains. The micromechanics equations are successfully verified for two polymer matrix composites. IM7/977-2 and AS4/PEEK. The ultimate strength of a composite ply is predicted with the Hashin failure criteria that were implemented in the composite micromechanics model. The failure stresses of the two composite material systems are accurately predicted for a variety of fiber orientations and strain rates. The composite deformation model is implemented in LS-DYNA, a commercially available transient dynamic explicit finite element code. The matrix constitutive equations are converted into an incremental form, and the model is implemented into LS-DYNA through the use of a user defined material subroutine. The deformation response of a bulk polymer and a polymer matrix composite are predicted by finite element analyses. The results compare reasonably well to experimental values, with some discrepancies. The discrepancies are at least partially caused by the method used to integrate the rate equations in the polymer constitutive model.

Analysis for Material Behavior of Sabot/Rods During Launch by Finite Element Method

NASA Astrophysics Data System (ADS)

Kim, Jin Bong; Kim, Man Geun

This study has been investigated to predict the deformation and states of stress and strain by axial and lateral acceleration during launch. Because a gun tube is not perfectly straight at its initial state while under gravity loading, the projectile deforms due to the change of contacts points with the flexible gun tube. Numerical simulations were used for gravity loading and the other type is initial shape and gravity loading. The ANSYS engineering analysis code was used to generate a parametric model of the projectile and conduct finite element analyses. Four types of nonlinear material and contact elements were incorporated into the model to account for the plastic deformation and contact between the penetrator, sabot, and tube.

Brain shift computation using a fully nonlinear biomechanical model.

PubMed

Wittek, Adam; Kikinis, Ron; Warfield, Simon K; Miller, Karol

2005-01-01

In the present study, fully nonlinear (i.e. accounting for both geometric and material nonlinearities) patient specific finite element brain model was applied to predict deformation field within the brain during the craniotomy-induced brain shift. Deformation of brain surface was used as displacement boundary conditions. Application of the computed deformation field to align (i.e. register) the preoperative images with the intraoperative ones indicated that the model very accurately predicts the displacements of gravity centers of the lateral ventricles and tumor even for very limited information about the brain surface deformation. These results are sufficient to suggest that nonlinear biomechanical models can be regarded as one possible way of complementing medical image processing techniques when conducting nonrigid registration. Important advantage of such models over the linear ones is that they do not require unrealistic assumptions that brain deformations are infinitesimally small and brain tissue stress-strain relationship is linear.

Toward high-speed 3D nonlinear soft tissue deformation simulations using Abaqus software.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2015-12-01

We aim to achieve a fast and accurate three-dimensional (3D) simulation of a porcine liver deformation under a surgical tool pressure using the commercial finite element software Abaqus. The liver geometry is obtained using magnetic resonance imaging, and a nonlinear constitutive law is employed to capture large deformations of the tissue. Effects of implicit versus explicit analysis schemes, element type, and mesh density on computation time are studied. We find that Abaqus explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. This study provides new insights and guidance on accurate and relatively fast nonlinear soft tissue simulations. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents.

An inverse finite-element model of heel-pad indentation.

PubMed

Erdemir, Ahmet; Viveiros, Meredith L; Ulbrecht, Jan S; Cavanagh, Peter R

2006-01-01

A numerical-experimental approach has been developed to characterize heel-pad deformation at the material level. Left and right heels of 20 diabetic subjects and 20 nondiabetic subjects matched for age, gender and body mass index were indented using force-controlled ultrasound. Initial tissue thickness and deformation were measured using M-mode ultrasound; indentation forces were recorded simultaneously. An inverse finite-element analysis of the indentation protocol using axisymmetric models adjusted to reflect individual heel thickness was used to extract nonlinear material properties describing the hyperelastic behavior of each heel. Student's t-tests revealed that heel pads of diabetic subjects were not significantly different in initial thickness nor were they stiffer than those from nondiabetic subjects. Another heel-pad model with anatomically realistic surface representations of the calcaneus and soft tissue was developed to estimate peak pressure prediction errors when average rather than individualized material properties were used. Root-mean-square errors of up to 7% were calculated, indicating the importance of subject-specific modeling of the nonlinear elastic behavior of the heel pad. Indentation systems combined with the presented numerical approach can provide this information for further analysis of patient-specific foot pathologies and therapeutic footwear designs.

Computational aeroelastic analysis of aircraft wings including geometry nonlinearity

NASA Astrophysics Data System (ADS)

Tian, Binyu

The objective of the present study is to show the ability of solving fluid structural interaction problems more realistically by including the geometric nonlinearity of the structure so that the aeroelastic analysis can be extended into the onset of flutter, or in the post flutter regime. A nonlinear Finite Element Analysis software is developed based on second Piola-Kirchhoff stress and Green-Lagrange strain. The second Piola-Kirchhoff stress and Green-Lagrange strain is a pair of energetically conjugated tensors that can accommodate arbitrary large structural deformations and deflection, to study the flutter phenomenon. Since both of these tensors are objective tensors, i.e., the rigid-body motion has no contribution to their components, the movement of the body, including maneuvers and deformation, can be included. The nonlinear Finite Element Analysis software developed in this study is verified with ANSYS, NASTRAN, ABAQUS, and IDEAS for the linear static, nonlinear static, linear dynamic and nonlinear dynamic structural solutions. To solve the flow problems by Euler/Navier equations, the current nonlinear structural software is then embedded into ENSAERO, which is an aeroelastic analysis software package developed at NASA Ames Research Center. The coupling of the two software, both nonlinear in their own field, is achieved by domain decomposition method first proposed by Guruswamy. A procedure has been set for the aeroelastic analysis process. The aeroelastic analysis results have been obtained for fight wing in the transonic regime for various cases. The influence dynamic pressure on flutter has been checked for a range of Mach number. Even though the current analysis matches the general aeroelastic characteristic, the numerical value not match very well with previous studies and needs farther investigations. The flutter aeroelastic analysis results have also been plotted at several time points. The influences of the deforming wing geometry can be well seen in those plots. The movement of shock changes the aerodynamic load distribution on the wing. The effect of viscous on aeroelastic analysis is also discussed. Also compared are the flutter solutions with, or without the structural nonlinearity. As can be seen, linear structural solution goes to infinite, which can not be true in reality. The nonlinear solution is more realistic and can be used to understand the fluid and structure interaction behavior, to control, or prevent disastrous events. (Abstract shortened by UMI.)

Characterization of the anisotropic mechanical behavior of human abdominal wall connective tissues.

PubMed

Astruc, Laure; De Meulaere, Maurice; Witz, Jean-François; Nováček, Vit; Turquier, Frédéric; Hoc, Thierry; Brieu, Mathias

2018-06-01

Abdominal wall sheathing tissues are commonly involved in hernia formation. However, there is very limited work studying mechanics of all tissues from the same donor which prevents a complete understanding of the abdominal wall behavior and the differences in these tissues. The aim of this study was to investigate the differences between the mechanical properties of the linea alba and the anterior and posterior rectus sheaths from a macroscopic point of view. Eight full-thickness human anterior abdominal walls of both genders were collected and longitudinal and transverse samples were harvested from the three sheathing connective tissues. The total of 398 uniaxial tensile tests was conducted and the mechanical characteristics of the behavior (tangent rigidities for small and large deformations) were determined. Statistical comparisons highlighted heterogeneity and non-linearity in behavior of the three tissues under both small and large deformations. High anisotropy was observed under small and large deformations with higher stress in the transverse direction. Variabilities in the mechanical properties of the linea alba according to the gender and location were also identified. Finally, data dispersion correlated with microstructure revealed that macroscopic characterization is not sufficient to fully describe behavior. Microstructure consideration is needed. These results provide a better understanding of the mechanical behavior of the abdominal wall sheathing tissues as well as the directions for microstructure-based constitutive model. Copyright © 2018 Elsevier Ltd. All rights reserved.

Bifurcation and response analysis of a nonlinear flexible rotating disc immersed in bounded compressible fluid

NASA Astrophysics Data System (ADS)

Remigius, W. Dheelibun; Sarkar, Sunetra; Gupta, Sayan

2017-03-01

Use of heavy gases in centrifugal compressors for enhanced oil extraction have made the impellers susceptible to failures through acousto-elastic instabilities. This study focusses on understanding the dynamical behavior of such systems by considering the effects of the bounded fluid housed in a casing on a rotating disc. First, a mathematical model is developed that incorporates the interaction between the rotating impeller - modelled as a flexible disc - and the bounded compressible fluid medium in which it is immersed. The nonlinear effects arising due to large deformations of the disc have been included in the formulation so as to capture the post flutter behavior. A bifurcation analysis is carried out with the disc rotational speed as the bifurcation parameter to investigate the dynamical behavior of the coupled system and estimate the stability boundaries. Parametric studies reveal that the relative strengths of the various dissipation mechanisms in the coupled system play a significant role that affect the bifurcation route and the post flutter behavior in the acousto-elastic system.

Revisit to three-dimensional percolation theory: Accurate analysis for highly stretchable conductive composite materials

PubMed Central

Kim, Sangwoo; Choi, Seongdae; Oh, Eunho; Byun, Junghwan; Kim, Hyunjong; Lee, Byeongmoon; Lee, Seunghwan; Hong, Yongtaek

2016-01-01

A percolation theory based on variation of conductive filler fraction has been widely used to explain the behavior of conductive composite materials under both small and large deformation conditions. However, it typically fails in properly analyzing the materials under the large deformation since the assumption may not be valid in such a case. Therefore, we proposed a new three-dimensional percolation theory by considering three key factors: nonlinear elasticity, precisely measured strain-dependent Poisson’s ratio, and strain-dependent percolation threshold. Digital image correlation (DIC) method was used to determine actual Poisson’s ratios at various strain levels, which were used to accurately estimate variation of conductive filler volume fraction under deformation. We also adopted strain-dependent percolation threshold caused by the filler re-location with deformation. When three key factors were considered, electrical performance change was accurately analyzed for composite materials with both isotropic and anisotropic mechanical properties. PMID:27694856

Quantitative research on microscopic deformation behavior of Ti-6Al-4V two-phase titanium alloy based on finite element method

NASA Astrophysics Data System (ADS)

Peng, Yan; Chen, Guoxing; Sun, Jianliang; Shi, Baodong

2018-04-01

The microscopic deformation of Ti-6Al-4V titanium alloy shows great inhomogeneity due to its duplex-microstructure that consists of two phases. In order to study the deformation behaviors of the constituent phases, the 2D FE model based on the realistic microstructure is established by MSC.Marc nonlinear FE software, and the tensile simulation is carried out. The simulated global stress-strain response is confirmed by the tensile testing result. Then the strain and stress distribution in the constituent phases and their evolution with the increase of the global strain are analyzed. The results show that the strain and stress partitioning between the two phases are considerable, most of the strain is concentrated in soft primary α phase, while hard transformed β matrix undertakes most of the stress. Under the global strain of 0.05, the deformation bands in the direction of 45° to the stretch direction and the local stress in primary α phase near to the interface between the two phases are observed, and they become more significant when the global strain increases to 0.1. The strain and stress concentration factors of the two phases are obviously different at different macroscopic deformation stages, but they almost tend to be stable finally.

Bridge Structure Deformation Prediction Based on GNSS Data Using Kalman-ARIMA-GARCH Model

PubMed Central

Li, Xiaoqing; Wang, Yu

2018-01-01

Bridges are an essential part of the ground transportation system. Health monitoring is fundamentally important for the safety and service life of bridges. A large amount of structural information is obtained from various sensors using sensing technology, and the data processing has become a challenging issue. To improve the prediction accuracy of bridge structure deformation based on data mining and to accurately evaluate the time-varying characteristics of bridge structure performance evolution, this paper proposes a new method for bridge structure deformation prediction, which integrates the Kalman filter, autoregressive integrated moving average model (ARIMA), and generalized autoregressive conditional heteroskedasticity (GARCH). Firstly, the raw deformation data is directly pre-processed using the Kalman filter to reduce the noise. After that, the linear recursive ARIMA model is established to analyze and predict the structure deformation. Finally, the nonlinear recursive GARCH model is introduced to further improve the accuracy of the prediction. Simulation results based on measured sensor data from the Global Navigation Satellite System (GNSS) deformation monitoring system demonstrated that: (1) the Kalman filter is capable of denoising the bridge deformation monitoring data; (2) the prediction accuracy of the proposed Kalman-ARIMA-GARCH model is satisfactory, where the mean absolute error increases only from 3.402 mm to 5.847 mm with the increment of the prediction step; and (3) in comparision to the Kalman-ARIMA model, the Kalman-ARIMA-GARCH model results in superior prediction accuracy as it includes partial nonlinear characteristics (heteroscedasticity); the mean absolute error of five-step prediction using the proposed model is improved by 10.12%. This paper provides a new way for structural behavior prediction based on data processing, which can lay a foundation for the early warning of bridge health monitoring system based on sensor data using sensing technology. PMID:29351254

Bridge Structure Deformation Prediction Based on GNSS Data Using Kalman-ARIMA-GARCH Model.

PubMed

Xin, Jingzhou; Zhou, Jianting; Yang, Simon X; Li, Xiaoqing; Wang, Yu

2018-01-19

Bridges are an essential part of the ground transportation system. Health monitoring is fundamentally important for the safety and service life of bridges. A large amount of structural information is obtained from various sensors using sensing technology, and the data processing has become a challenging issue. To improve the prediction accuracy of bridge structure deformation based on data mining and to accurately evaluate the time-varying characteristics of bridge structure performance evolution, this paper proposes a new method for bridge structure deformation prediction, which integrates the Kalman filter, autoregressive integrated moving average model (ARIMA), and generalized autoregressive conditional heteroskedasticity (GARCH). Firstly, the raw deformation data is directly pre-processed using the Kalman filter to reduce the noise. After that, the linear recursive ARIMA model is established to analyze and predict the structure deformation. Finally, the nonlinear recursive GARCH model is introduced to further improve the accuracy of the prediction. Simulation results based on measured sensor data from the Global Navigation Satellite System (GNSS) deformation monitoring system demonstrated that: (1) the Kalman filter is capable of denoising the bridge deformation monitoring data; (2) the prediction accuracy of the proposed Kalman-ARIMA-GARCH model is satisfactory, where the mean absolute error increases only from 3.402 mm to 5.847 mm with the increment of the prediction step; and (3) in comparision to the Kalman-ARIMA model, the Kalman-ARIMA-GARCH model results in superior prediction accuracy as it includes partial nonlinear characteristics (heteroscedasticity); the mean absolute error of five-step prediction using the proposed model is improved by 10.12%. This paper provides a new way for structural behavior prediction based on data processing, which can lay a foundation for the early warning of bridge health monitoring system based on sensor data using sensing technology.

Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat

2017-01-01

For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

Anatomically accurate individual face modeling.

PubMed

Zhang, Yu; Prakash, Edmond C; Sung, Eric

2003-01-01

This paper presents a new 3D face model of a specific person constructed from the anatomical perspective. By exploiting the laser range data, a 3D facial mesh precisely representing the skin geometry is reconstructed. Based on the geometric facial mesh, we develop a deformable multi-layer skin model. It takes into account the nonlinear stress-strain relationship and dynamically simulates the non-homogenous behavior of the real skin. The face model also incorporates a set of anatomically-motivated facial muscle actuators and underlying skull structure. Lagrangian mechanics governs the facial motion dynamics, dictating the dynamic deformation of facial skin in response to the muscle contraction.

Nonlinear Dynamical Model of a Soft Viscoelastic Dielectric Elastomer

NASA Astrophysics Data System (ADS)

Zhang, Junshi; Chen, Hualing; Li, Dichen

2017-12-01

Actuated by alternating stimulation, dielectric elastomers (DEs) show a behavior of complicated nonlinear vibration, implying a potential application as dynamic electromechanical actuators. As is well known, for a vibrational system, including the DE system, the dynamic properties are significantly affected by the geometrical sizes. In this article, a nonlinear dynamical model is deduced to investigate the geometrical effects on dynamic properties of viscoelastic DEs. The DEs with square and arbitrary rectangular geometries are considered, respectively. Besides, the effects of tensile forces on dynamic performances of rectangular DEs with comparably small and large geometrical sizes are explored. Phase paths and Poincaré maps are utilized to detect the periodicity of the nonlinear vibrations of DEs. The resonance characteristics of DEs incorporating geometrical effects are also investigated. The results indicate that the dynamic properties of DEs, including deformation response, vibrational periodicity, and resonance, are tuned when the geometrical sizes vary.

Mixed formulation for seismic analysis of composite steel-concrete frame structures

NASA Astrophysics Data System (ADS)

Ayoub, Ashraf Salah Eldin

This study presents a new finite element model for the nonlinear analysis of structures made up of steel and concrete under monotonic and cyclic loads. The new formulation is based on a two-field mixed formulation. In the formulation, both forces and deformations are simultaneously approximated within the element through independent interpolation functions. The main advantages of the model is the accuracy in global and local response with very few elements while maintaining rapid numerical convergence and robustness even under severe cyclic loading. Overall four elements were developed based on the new formulation: an element that describes the behavior of anchored reinforcing bars, an element that describes the behavior of composite steel-concrete beams with deformable shear connectors, an element that describes the behavior of reinforced concrete beam-columns with bond-slip, and an element that describes the behavior of pretensioned or posttensioned, bonded or unbonded prestressed concrete structures. The models use fiber discretization of beam sections to describe nonlinear material response. The transfer of forces between steel and concrete is described with bond elements. Bond elements are modeled with distributed spring elements. The non-linear behavior of the composite element derives entirely from the constitutive laws of the steel, concrete and bond elements. Two additional elements are used for the prestressed concrete models, a friction element that models the effect of friction between the tendon and the duct during the posttensioning operation, and an anchorage element that describes the behavior of the prestressing tendon anchorage in posttensioned structures. Two algorithms for the numerical implementation of the new proposed model are presented; an algorithm that enforces stress continuity at element boundaries, and an algorithm in which stress continuity is relaxed locally inside the element. Stability of both algorithms is discussed. Comparison with standard displacement based models and earlier flexibility based models is presented through numerical studies. The studies prove the superiority of the mixed model over both displacement and flexibility models. Correlation studies of the proposed model with experimental results of structural specimens are conducted. The studies show the accuracy of the model and its numerical robustness even under severe cyclic loading conditions.

The elastic and inelastic behavior of woven graphite fabric reinforced polyimide composites

NASA Astrophysics Data System (ADS)

Searles, Kevin H.

In many aerospace and conventional engineering applications, load-bearing composite structures are designed with the intent of being subjected to uniaxial stresses that are predominantly tensile or compressive. However, it is likely that biaxial and possibly triaxial states of stress will exist throughout the in-service life of the structure or component. The existing paradigm suggests that unidirectional tape materials are superior under uniaxial conditions since the vast majority of fibers lie in-plane and can be aligned to the loading axis. This may be true, but not without detriment to impact performance, interlaminar strength, strain to failure and complexity of part geometry. In circumstances where a sufficient balance of these properties is required, composites based on woven fabric reinforcements become attractive choices. In this thesis, the micro- and mesoscale elastic behavior of composites based on 8HS woven graphite fabric architectures and polyimide matrices is studied analytically and numerically. An analytical model is proposed to predict the composite elastic constants and is verified using numerical strain energy methods of equivalence. The model shows good agreement with the experiments and numerical strain energy equivalence. Lamina stresses generated numerically from in-plane shear loading show substantial shear and transverse normal stress concentrations in the transverse undulated tow which potentially leads to intralaminar damage. The macroscale inelastic behavior of the same composites is also studied experimentally and numerically. On an experimental basis, the biaxial and modified biaxial Iosipescu test methods are employed to study the weaker-mode shear and biaxial failure properties at room and elevated temperatures. On a numerical basis, the macroscale inelastic shear behavior of the composites is studied. Structural nonlinearities and material nonlinearities are identified and resolved. In terms of specimen-to-fixture interactions, load eccentricities, geometric (large strains and rotations) nonlinearities and boundary contact (friction) nonlinearities are explored. In terms of material nonlinearities, anisotropic plasticity and progressive damage are explored. A progressive damage criterion is proposed which accounts for the elastic strain energy densities in three directions. Of the types of nonlinearities studied, the nonlinear shear stress-strain behavior of the composites is principally from progressive intralaminar damage. Structural nonlinearities and elastoplastic deformation appear to be inconsequential.

Non-linear regime of the Generalized Minimal Massive Gravity in critical points

NASA Astrophysics Data System (ADS)

Setare, M. R.; Adami, H.

2016-03-01

The Generalized Minimal Massive Gravity (GMMG) theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. In the present paper we obtain exact solutions to the GMMG field equations in the non-linear regime of the model. GMMG model about AdS_3 space is conjectured to be dual to a 2-dimensional CFT. We study the theory in critical points corresponding to the central charges c_-=0 or c_+=0, in the non-linear regime. We show that AdS_3 wave solutions are present, and have logarithmic form in critical points. Then we study the AdS_3 non-linear deformation solution. Furthermore we obtain logarithmic deformation of extremal BTZ black hole. After that using Abbott-Deser-Tekin method we calculate the energy and angular momentum of these types of black hole solutions.

Toward Effective Shell Modeling of Wrinkled Thin-Film Membranes Exhibiting Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2004-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns. An element-level, strain-energy density criterion is suggested for facilitating automated, adaptive mesh refinements specifically aimed at the modeling of thin-film membranes undergoing wrinkling deformations.

Accidental degeneracies in nonlinear quantum deformed systems

NASA Astrophysics Data System (ADS)

Aleixo, A. N. F.; Balantekin, A. B.

2011-09-01

We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.

Deformed Palmprint Matching Based on Stable Regions.

PubMed

Wu, Xiangqian; Zhao, Qiushi

2015-12-01

Palmprint recognition (PR) is an effective technology for personal recognition. A main problem, which deteriorates the performance of PR, is the deformations of palmprint images. This problem becomes more severe on contactless occasions, in which images are acquired without any guiding mechanisms, and hence critically limits the applications of PR. To solve the deformation problems, in this paper, a model for non-linearly deformed palmprint matching is derived by approximating non-linear deformed palmprint images with piecewise-linear deformed stable regions. Based on this model, a novel approach for deformed palmprint matching, named key point-based block growing (KPBG), is proposed. In KPBG, an iterative M-estimator sample consensus algorithm based on scale invariant feature transform features is devised to compute piecewise-linear transformations to approximate the non-linear deformations of palmprints, and then, the stable regions complying with the linear transformations are decided using a block growing algorithm. Palmprint feature extraction and matching are performed over these stable regions to compute matching scores for decision. Experiments on several public palmprint databases show that the proposed models and the KPBG approach can effectively solve the deformation problem in palmprint verification and outperform the state-of-the-art methods.

Analysis of Shock Compression of Strong Single Crystals With Logarithmic Thermoelastic-Plastic Theory

DTIC Science & Technology

2014-05-01

Royal Society of London Series A, 465, 307–334. Clayton, J. (2010a). Modeling nonlinear electromechanical behavior of shocked silicon carbide . Journal...and fourth-order longitudinal elastic constants by shock compression techniques–application to sapphire and fused quartz. Journal of the Acoustical...Vogler, T., & Clayton, J. (2008). Heterogeneous deformation and spall of an extruded tungsten alloy: Plate impact experiments and crystal plasticity

Hurst exponent: A Brownian approach to characterize the nonlinear behavior of red blood cells deformability

NASA Astrophysics Data System (ADS)

Mancilla Canales, M. A.; Leguto, A. J.; Riquelme, B. D.; León, P. Ponce de; Bortolato, S. A.; Korol, A. M.

2017-12-01

Ektacytometry techniques quantifies red blood cells (RBCs) deformability by measuring the elongation of suspended RBCs subjected to shear stress. Raw shear stress elongation plots are difficult to understand, thus most research papers apply data reduction methods characterizing the relationship between curve fitting. Our approach works with the naturally generated photometrically recorded time series of the diffraction pattern of several million of RBCs subjected to shear stress, and applies nonlinear quantifiers to study the fluctuations of these elongations. The development of new quantitative methods is crucial for restricting the subjectivity in the study of the cells behavior, mainly if they are capable of analyze at the same time biological and mechanical aspects of the cells in flowing conditions and compare their dynamics. A patented optical system called Erythrocyte Rheometer was used to evaluate viscoelastic properties of erythrocytes by Ektacytometry. To analyze cell dynamics we used the technique of Time Delay Coordinates, False Nearest Neighbors, the forecasting procedure proposed by Sugihara and May, and Hurst exponent. The results have expressive meaning on comparing healthy samples with parasite treated samples, suggesting that apparent noise associated with deterministic chaos can be used not only to distinguish but also to characterize biological and mechanical aspects of cells at the same time in flowing conditions.

Towards improved NDE and SHM methodologies incorporating nonlinear structural features

NASA Astrophysics Data System (ADS)

Chillara, Vamshi Krishna

Ultrasound is widely employed in Nondestructive Evaluation (NDE) and Structural Health Monitoring (SHM) applications to detect and characterize damage/defects in materials. In particular, ultrasonic guided waves are considered a foremost candidate for in-situ monitoring applications. Conventional ultrasonic techniques rely on changes/discontinuities in linear elastic material properties, namely the Young's modulus and shear modulus to detect damage. On the other hand, nonlinear ultrasonic techniques that rely on micro-scale nonlinear material/structural behavior are proven to be sensitive to damage induced microstructural changes that precede macro-scale damage and are hence capable of early damage detection. The goal of this thesis is to investigate the capabilities of nonlinear guided waves --- a fusion of nonlinear ultrasonic techniques with the guided wave methodologies for early damage detection. To that end, the thesis focuses on two important aspects of the problem: 1. Wavemechanics - deals with ultrasonic guided wave propagation in nonlinear waveguides; 2. Micromechanics - deals with correlating ultrasonic response with micro-scale nonlinear material behavior. For the development of efficient NDE and SHM methodologies that incorporate nonlinear structural features, a detailed understanding of the above aspects is indispensable. In this thesis, the wavemechanics aspect of the problem is dealt with from both theoretical and numerical standpoints. A generalized theoretical framework is developed to study higher harmonic guided waves in plates. This was employed to study second harmonic guided waves in pipes using a large-radius asymptotic approximation. Second harmonic guided waves in plates are studied from a numerical standpoint. Theoretical predictions are validated and some key aspects of higher harmonic generation in waveguides are outlined. Finally, second harmonic guided waves in plates with inhomogeneous and localized nonlinearities are studied and some important aspects of guided wave mode selection are addressed. The other part of the work focused on developing a micromechanics based understanding of ultrasonic higher harmonic generation. Three important aspects of micro-scale material behavior, namely tension-compression asymmetry, shearnormal coupling and deformation induced asymmetry are identified and their role in ultrasonic higher harmonic generation is discussed. Tension-compression asymmetry is identified to cause second (even) harmonic generation in materials. Then, shearnormal coupling is identified to cause generation of secondary waves of different polarity than the primary waves. In addition, deformation induced anisotropy due to the presence of residual stress/strain and its contribution to ultrasonic higher harmonic generation is qualitatively discussed. Also, the tension-compression asymmetry in the material is quantified using an energy based measure. The above measure is employed to develop a homogenization based approach amenable to multi-scale analysis to correlate microstructure with ultrasonic higher harmonic generation. Finally, experimental investigations concerning third harmonic SH wave generation in plates are carried out and the effect of load and temperature changes on nonlinear ultrasonic measurements are discussed in the context of SHM. It was found that while nonlinear ultrasound is sensitive to micro-scale damage, the relative nonlinearity parameter may not always be the best measure to quantify the nonlinearity as it is subject to spurious effects from changes in environmental factors such as loads and temperature.

Large Deformation Behavior of Long Shallow Cylindrical Composite Panels

NASA Technical Reports Server (NTRS)

Carper, Douglas M.; Hyer, Michael W.; Johnson, Eric R.

1991-01-01

An exact solution is presented for the large deformation response of a simply supported orthotropic cylindrical panel subjected to a uniform line load along a cylinder generator. The cross section of the cylinder is circular and deformations up to the fully snapped through position are investigated. The orthotropic axes are parallel to the generator and circumferential directions. The governing equations are derived using laminated plate theory, nonlinear strain-displacement relations, and applying variational principles. The response is investigated for the case of a panel loaded exactly at midspan and for a panel with the load offset from midspan. The mathematical formulation is one dimensional in the circumferential coordinate. Solutions are obtained in closed-form. An experimental apparatus was designed to load the panels. Experimental results of displacement controlled tests performed on graphite-epoxy curved panels are compared with analytical predictions.

Implementation of Free-Formulation-Based Flat Shell Elements into NASA Comet Code and Development of Nonlinear Shallow Shell Element

NASA Technical Reports Server (NTRS)

Barut, A.; Madenci, Erdogan; Tessler, A.

1997-01-01

This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.

Analysis of intelligent hinged shell structures: deployable deformation and shape memory effect

NASA Astrophysics Data System (ADS)

Shi, Guang-Hui; Yang, Qing-Sheng; He, X. Q.

2013-12-01

Shape memory polymers (SMPs) are a class of intelligent materials with the ability to recover their initial shape from a temporarily fixable state when subjected to external stimuli. In this work, the thermo-mechanical behavior of a deployable SMP-based hinged structure is modeled by the finite element method using a 3D constitutive model with shape memory effect. The influences of hinge structure parameters on the nonlinear loading process are investigated. The total shape memory of the processes the hinged structure goes through, including loading at high temperature, decreasing temperature with load carrying, unloading at low temperature and recovering the initial shape with increasing temperature, are illustrated. Numerical results show that the present constitutive theory and the finite element method can effectively predict the complicated thermo-mechanical deformation behavior and shape memory effect of SMP-based hinged shell structures.

A Finite Element Study of Micropipette Aspiration of Single Cells: Effect of Compressibility

PubMed Central

Jafari Bidhendi, Amirhossein; Korhonen, Rami K.

2012-01-01

Micropipette aspiration (MA) technique has been widely used to measure the viscoelastic properties of different cell types. Cells experience nonlinear large deformations during the aspiration procedure. Neo-Hookean viscohyperelastic (NHVH) incompressible and compressible models were used to simulate the creep behavior of cells in MA, particularly accounting for the effect of compressibility, bulk relaxation, and hardening phenomena under large strain. In order to find optimal material parameters, the models were fitted to the experimental data available for mesenchymal stem cells. Finally, through Neo-Hookean porohyperelastic (NHPH) material model for the cell, the influence of fluid flow on the aspiration length of the cell was studied. Based on the results, we suggest that the compressibility and bulk relaxation/fluid flow play a significant role in the deformation behavior of single cells and should be taken into account in the analysis of the mechanics of cells. PMID:22400045

Measuring the nonlinear elastic properties of tissue-like phantoms.

PubMed

Erkamp, Ramon Q; Skovoroda, Andrei R; Emelianov, Stanislav Y; O'Donnell, Matthew

2004-04-01

A direct mechanical system simultaneously measuring external force and deformation of samples over a wide dynamic range is used to obtain force-displacement curves of tissue-like phantoms under plain strain deformation. These measurements, covering a wide deformation range, then are used to characterize the nonlinear elastic properties of the phantom materials. The model assumes incompressible media, in which several strain energy potentials are considered. Finite-element analysis is used to evaluate the performance of this material characterization procedure. The procedures developed allow calibration of nonlinear elastic phantoms for elasticity imaging experiments and finite-element simulations.

Soft tissue modelling with conical springs.

PubMed

Omar, Nadzeri; Zhong, Yongmin; Jazar, Reza N; Subic, Aleksandar; Smith, Julian; Shirinzadeh, Bijan

2015-01-01

This paper presents a new method for real-time modelling soft tissue deformation. It improves the traditional mass-spring model with conical springs to deal with nonlinear mechanical behaviours of soft tissues. A conical spring model is developed to predict soft tissue deformation with reference to deformation patterns. The model parameters are formulated according to tissue deformation patterns and the nonlinear behaviours of soft tissues are modelled with the stiffness variation of conical spring. Experimental results show that the proposed method can describe different tissue deformation patterns using one single equation and also exhibit the typical mechanical behaviours of soft tissues.

Computer Simulations of Bottle Brushes: From Melts to Soft Networks

DOE PAGES

Cao, Zhen; Carrillo, Jan-Michael Y.; Sheiko, Sergei S.; ...

2015-07-13

We use a combination of Molecular dynamics simulations and analytical calculations, and study dens bottle-brush systems in a melt and network State. Analysis of our simulation results shows that bottle-brush macromolecules in melt behave as ideal chains with effective Kuhn length b K. Simulations show that the bottle-brush-induced bending rigidity is due to an entropy decrease caused by redistribution of the side chains upon backbone bending. The Kuhn length of the bottle:brushes increases with increasing the side-chain degree of polymerization n sc as b K proportional to n sc 0.46. Moreover, this model of bottle brush macromolecules is extended tomore » describe mechanical properties of bottle brush networks in linear and nonlinear deformation regimes. In the linear deformation regime, the network shear modulus scales with the degree of polymerization of the side chains as G 0 proportional to (n sc + 1) -1 as long as the ratio of the Kuhn length, b K, to the size of the fully extended bottle-brush backbone between cross-links, R-max, is smaller than unity, b K/R max << 1. Bottle-brush networks With b K/R max proportional to 1 demonstrate behavior similar to that of networks Of semiflexible chains with G 0 proportional to n sc -0.5. Finally, in the nonlinear network deformation regime, the deformation-dependent shear modulus is a universal function of the first strain invariant I 1 and bottle-brush backbone deformation ratio beta describing stretching ability of the bottle-brush backbone between cross-links.« less

Nonlinear image registration with bidirectional metric and reciprocal regularization

PubMed Central

Ying, Shihui; Li, Dan; Xiao, Bin; Peng, Yaxin; Du, Shaoyi; Xu, Meifeng

2017-01-01

Nonlinear registration is an important technique to align two different images and widely applied in medical image analysis. In this paper, we develop a novel nonlinear registration framework based on the diffeomorphic demons, where a reciprocal regularizer is introduced to assume that the deformation between two images is an exact diffeomorphism. In detail, first, we adopt a bidirectional metric to improve the symmetry of the energy functional, whose variables are two reciprocal deformations. Secondly, we slack these two deformations into two independent variables and introduce a reciprocal regularizer to assure the deformations being the exact diffeomorphism. Then, we utilize an alternating iterative strategy to decouple the model into two minimizing subproblems, where a new closed form for the approximate velocity of deformation is calculated. Finally, we compare our proposed algorithm on two data sets of real brain MR images with two relative and conventional methods. The results validate that our proposed method improves accuracy and robustness of registration, as well as the gained bidirectional deformations are actually reciprocal. PMID:28231342

Experimental and analytical analysis of stress-strain behavior in a (90/0 deg)2s, SiC/Ti-15-3 laminate

NASA Technical Reports Server (NTRS)

Lerch, Bradley A.; Melis, Matthew E.; Tong, Mike

1991-01-01

The nonlinear stress strain behavior of 90 degree/0 degree sub 2s, SiC/Ti-15-3 composite laminate was numerically investigated with a finite element, unit cell approach. Tensile stress-strain curves from room temperature experiments depicted three distinct regions of deformation, and these regions were predicted by finite element analysis. The first region of behavior, which was linear elastic, occurred at low applied stresses. As applied stresses increased, fiber/matrix debonding in the 90 degree plies caused a break in the stress-strain curve and initiated a second linear region. In this second region, matrix plasticity in the 90 degree plies developed. The third region, which was typified by nonlinear, stress-strain behavior occr red at high stresses. In this region, the onset of matrix plasticity in the 0 degree plies stiffened the laminate in the direction transverse to the applied load. Metallographic sections confirmed the existence of matrix plasticity in specific areas of the structure. Finite element analysis also predicted these locations of matrix slip.

Laboratory determination of effective stress laws for deformation and permeability of chalk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Teufel, L W; Warpinski, N R

1990-01-01

Laboratory deformation and permeability measurements have been made on chalk samples from Ekofisk area fields as a function of confining stress and pore pressure to determine the effective stress laws for chalk. An understanding of the effective stress law is essential to obtain correct reservoir-property data from core analysis and is critical for reservoir management studies and reservoir compaction models. A powerful statistical technique known as the response surface method has been used to analyze our laboratory data determine the form of the effective stress law for deformation and permeability. Experiments were conducted on chalk samples that had a rangemore » of porosities from 15% to 36%, because porosity is the dominant intrinsic property that effects deformation and permeability behavior of chalk. Deformation of a 36% porosity chalk was highly nonlinear, but the effective stress law was linear, with {alpha} equal to about unity. Lower-porosity samples showed linear strain behavior and a linear effective stress law with {alpha} as low as 0.74. Analysis of the effective stress law for permeability is presented only for the lowest porosity chalk sample because changes in permeability in the higher-porosity chalk samples due to increasing confining stress or pore pressure were not were large enough, to deduce meaningful effective stress relationships. 15 refs., 8 figs., 2 tabs.« less

Techniques for Single System Integration of Elastic Simulation Features

NASA Astrophysics Data System (ADS)

Mitchell, Nathan M.

Techniques for simulating the behavior of elastic objects have matured considerably over the last several decades, tackling diverse problems from non-linear models for incompressibility to accurate self-collisions. Alongside these contributions, advances in parallel hardware design and algorithms have made simulation more efficient and affordable than ever before. However, prior research often has had to commit to design choices that compromise certain simulation features to better optimize others, resulting in a fragmented landscape of solutions. For complex, real-world tasks, such as virtual surgery, a holistic approach is desirable, where complex behavior, performance, and ease of modeling are supported equally. This dissertation caters to this goal in the form of several interconnected threads of investigation, each of which contributes a piece of an unified solution. First, it will be demonstrated how various non-linear materials can be combined with lattice deformers to yield simulations with behavioral richness and a high potential for parallelism. This potential will be exploited to show how a hybrid solver approach based on large macroblocks can accelerate the convergence of these deformers. Further extensions of the lattice concept with non-manifold topology will allow for efficient processing of self-collisions and topology change. Finally, these concepts will be explored in the context of a case study on virtual plastic surgery, demonstrating a real-world problem space where these ideas can be combined to build an expressive authoring tool, allowing surgeons to record procedures digitally for future reference or education.

Buckling of Carbon Nanotubes: A State of the Art Review

PubMed Central

Shima, Hiroyuki

2011-01-01

The nonlinear mechanical response of carbon nanotubes, referred to as their “buckling" behavior, is a major topic in the nanotube research community. Buckling means a deformation process in which a large strain beyond a threshold causes an abrupt change in the strain energy vs. deformation profile. Thus far, much effort has been devoted to analysis of the buckling of nanotubes under various loading conditions: compression, bending, torsion, and their certain combinations. Such extensive studies have been motivated by (i) the structural resilience of nanotubes against buckling and (ii) the substantial influence of buckling on their physical properties. In this contribution, I review the dramatic progress in nanotube buckling research during the past few years. PMID:28817032

Mechanical characterization and modeling of non-linear deformation and fracture of a fiber reinforced metal matrix composite

NASA Technical Reports Server (NTRS)

Jansson, S.

1991-01-01

The nonlinear anisotropic mechanical behavior of an aluminum alloy metal matrix composite reinforced with continuous alumina fibers was determined experimentally. The mechanical behavior of the composite were modeled by assuming that the composite has a periodical microstructure. The resulting unit cell problem was solved with the finite element method. Excellent agreement was found between theoretically predicted and measured stress-strain responses for various tensile and shear loadings. The stress-strain responses for transverse and inplane shear were found to be identical and this will provide a simplification of the constitutive equations for the composite. The composite has a very low ductility in transverse tension and a limited ductility in transverse shear that was correlated to high hydrostatic stresses that develop in the matrix. The shape of the initial yield surface was calculated and good agreement was found between the calculated shape and the experimentally determined shape.

Characterization and modeling of tensile behavior of ceramic woven fabric composites

NASA Technical Reports Server (NTRS)

Kuo, Wen-Shyong; Chen, Wennei Y.; Parvizi-Majidi, Azar; Chou, Tsu-Wei

1991-01-01

This paper examines the tensile behavior of SiC/SiC fabric composites. In the characterization effort, the stress-strain relation and damage evolution are studied with a series of loading and unloading tensile test experiments. The stress-strain relation is linear in response to the initial loading and becomes nonlinear when loading exceeds the proportional limit. Transverse cracking has been observed to be a dominant damage mode governing the nonlinear deformation. The damage is initiated at the inter-tow pores where fiber yarns cross over each other. In the modeling work, the analysis is based upon a fiber bundle model, in which fiber undulation in the warp and fill directions and gaps among fiber yarns have been taken into account. Two limiting cases of fabric stacking arrangements are studied. Closed form solutions are obtained for the composite stiffness and Poisson's ratio. Transverse cracking in the composite is discussed by applying a constant failure strain criterion.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

PubMed

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2006-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

Composite Beam Theory with Material Nonlinearities and Progressive Damage

NASA Astrophysics Data System (ADS)

Jiang, Fang

Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping functions, and the 3D spatial gradients of these warping functions. Asymptotic analysis of the extended Hamiltonian's principle suggests dropping the terms of axial gradients of the warping functions. As a result, the solid mechanics problem resolved into a 3D continuum is dimensionally reduced to a problem of solving the warping functions on a 2D cross-sectional field by minimizing the information loss. The present theory is implemented using the finite element method (FEM) in Variational Asymptotic Beam Sectional Analysis (VABS), a general-purpose cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model in the form of the Euler-Bernoulli beam theory. The deformation gradient tensor is directly used to enable the capability of dealing with finite deformation, various strain definitions, and several types of material constitutive laws regarding the nonlinear elasticity and progressive damage. Analytical and numerical examples are given for various problems including the trapeze effect, Poynting effect, Brazier effect, extension-bending coupling effect, and free edge damage. By comparison with the predictions from 3D finite element analyses (FEA), 2D FEA based on plane stress assumptions, and experimental data, the structural and material responses are proven to be rigorously captured by the present theory and the computational cost is significantly reduced. Due to the semi-analytical feature of the code developed, the unrealistic numerical issues widely seen in the conventional FEA with strain softening material behaviors are prevented by VABS. In light of these intrinsic features, the nonlinear elastic and inelastic 3D material models can be economically calibrated by data-matching the VABS predictions directly with the experimental measurements from slender coupons. Furthermore, the global behavior of slender composite structures in meters can also be effectively characterized by VABS without unnecessary loss of important information of its local laminae in micrometers.

Parameter determination of hereditary models of deformation of composite materials based on identification method

NASA Astrophysics Data System (ADS)

Kayumov, R. A.; Muhamedova, I. Z.; Tazyukov, B. F.; Shakirzjanov, F. R.

2018-03-01

In this paper, based on the analysis of some experimental data, a study and selection of hereditary models of deformation of reinforced polymeric composite materials, such as organic plastic, carbon plastic and a matrix of film-fabric composite, was pursued. On the basis of an analysis of a series of experiments it has been established that organo-plastic samples behave like viscoelastic bodies. It is shown that for sufficiently large load levels, the behavior of the material in question should be described by the relations of the nonlinear theory of heredity. An attempt to describe the process of deformation by means of linear relations of the theory of heredity leads to large discrepancies between the experimental and calculated deformation values. The use of the theory of accumulation of micro-damages leads to much better description of the experimental results. With the help of the hierarchical approach, a good approximation of the experimental values was successful only in the first three sections of loading.

Time-Dependent Reversible-Irreversible Deformation Threshold Determined Explicitly by Experimental Technique

NASA Technical Reports Server (NTRS)

Castelli, Michael G.; Arnold, Steven M.

2000-01-01

Structural materials for the design of advanced aeropropulsion components are usually subject to loading under elevated temperatures, where a material's viscosity (resistance to flow) is greatly reduced in comparison to its viscosity under low-temperature conditions. As a result, the propensity for the material to exhibit time-dependent deformation is significantly enhanced, even when loading is limited to a quasi-linear stress-strain regime as an effort to avoid permanent (irreversible) nonlinear deformation. An understanding and assessment of such time-dependent effects in the context of combined reversible and irreversible deformation is critical to the development of constitutive models that can accurately predict the general hereditary behavior of material deformation. To this end, researchers at the NASA Glenn Research Center at Lewis Field developed a unique experimental technique that identifies the existence of and explicitly determines a threshold stress k, below which the time-dependent material deformation is wholly reversible, and above which irreversible deformation is incurred. This technique is unique in the sense that it allows, for the first time, an objective, explicit, experimental measurement of k. The underlying concept for the experiment is based on the assumption that the material s time-dependent reversible response is invariable, even in the presence of irreversible deformation.

Nonlinear Elasticity

NASA Astrophysics Data System (ADS)

Fu, Y. B.; Ogden, R. W.

2001-05-01

This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.

Pressure induced ageing of polymers

NASA Technical Reports Server (NTRS)

Emri, I.; Knauss, W. G.

1988-01-01

The nonlinearly viscoelastic response of an amorphous homopolymer is considered under aspects of time dependent free volume behavior. In contrast to linearly viscoelastic solids, this model couples shear and volume deformation through a shift function which influences the rate of molecular relaxation or creep. Sample computations produce all those qualitative features one observes normally in uniaxial tension including the rate dependent formation of a yield point as a consequence of the history of an imposed pressure.

Creep analysis of silicone for podiatry applications.

PubMed

Janeiro-Arocas, Julia; Tarrío-Saavedra, Javier; López-Beceiro, Jorge; Naya, Salvador; López-Canosa, Adrián; Heredia-García, Nicolás; Artiaga, Ramón

2016-10-01

This work shows an effective methodology to characterize the creep-recovery behavior of silicones before their application in podiatry. The aim is to characterize, model and compare the creep-recovery properties of different types of silicone used in podiatry orthotics. Creep-recovery phenomena of silicones used in podiatry orthotics is characterized by dynamic mechanical analysis (DMA). Silicones provided by Herbitas are compared by observing their viscoelastic properties by Functional Data Analysis (FDA) and nonlinear regression. The relationship between strain and time is modeled by fixed and mixed effects nonlinear regression to compare easily and intuitively podiatry silicones. Functional ANOVA and Kohlrausch-Willians-Watts (KWW) model with fixed and mixed effects allows us to compare different silicones observing the values of fitting parameters and their physical meaning. The differences between silicones are related to the variations of breadth of creep-recovery time distribution and instantaneous deformation-permanent strain. Nevertheless, the mean creep-relaxation time is the same for all the studied silicones. Silicones used in palliative orthoses have higher instantaneous deformation-permanent strain and narrower creep-recovery distribution. The proposed methodology based on DMA, FDA and nonlinear regression is an useful tool to characterize and choose the proper silicone for each podiatry application according to their viscoelastic properties. Copyright © 2016 Elsevier Ltd. All rights reserved.

A nonlinear theory for spinning anisotropic beams using restrained warping functions

NASA Technical Reports Server (NTRS)

Ie, C. A.; Kosmatka, J. B.

1993-01-01

A geometrically nonlinear theory is developed for spinning anisotropic beams having arbitrary cross sections. An assumed displacement field is developed using the standard 3D kinematics relations to describe the global beam behavior supplemented with an additional field that represents the local deformation within the cross section and warping out of the cross section plane. It is assumed that the magnitude of this additional field is directly proportional to the local stress resultants. In order to take into account the effects of boundary conditions, a restraining function is introduced. This function plays the role of reducing the amount of free warping deformation throughout the field due to the restraint of the cross section(s) at the end(s) of the beam, e.g., in the case of a cantilever beam. Using a developed ordering scheme, the nonlinear strains are calculated to the third order. The FEM is developed using the weak form variational formulation. Preliminary interesting numerical results have been obtained that indicate the role of the restraining function in the case of a cantilever beam with circular cross section. These results are for the cases of a tip displacement (static) and free vibration studies for both isotropic and anisotropic materials with varied fiber orientations.

An efficient strongly coupled immersed boundary method for deforming bodies

NASA Astrophysics Data System (ADS)

Goza, Andres; Colonius, Tim

2016-11-01

Immersed boundary methods treat the fluid and immersed solid with separate domains. As a result, a nonlinear interface constraint must be satisfied when these methods are applied to flow-structure interaction problems. This typically results in a large nonlinear system of equations that is difficult to solve efficiently. Often, this system is solved with a block Gauss-Seidel procedure, which is easy to implement but can require many iterations to converge for small solid-to-fluid mass ratios. Alternatively, a Newton-Raphson procedure can be used to solve the nonlinear system. This typically leads to convergence in a small number of iterations for arbitrary mass ratios, but involves the use of large Jacobian matrices. We present an immersed boundary formulation that, like the Newton-Raphson approach, uses a linearization of the system to perform iterations. It therefore inherits the same favorable convergence behavior. However, we avoid large Jacobian matrices by using a block LU factorization of the linearized system. We derive our method for general deforming surfaces and perform verification on 2D test problems of flow past beams. These test problems involve large amplitude flapping and a wide range of mass ratios. This work was partially supported by the Jet Propulsion Laboratory and Air Force Office of Scientific Research.

Towards the stabilization of the low density elements in topology optimization with large deformation

NASA Astrophysics Data System (ADS)

Lahuerta, Ricardo Doll; Simões, Eduardo T.; Campello, Eduardo M. B.; Pimenta, Paulo M.; Silva, Emilio C. N.

2013-10-01

This work addresses the treatment of lower density regions of structures undergoing large deformations during the design process by the topology optimization method (TOM) based on the finite element method. During the design process the nonlinear elastic behavior of the structure is based on exact kinematics. The material model applied in the TOM is based on the solid isotropic microstructure with penalization approach. No void elements are deleted and all internal forces of the nodes surrounding the void elements are considered during the nonlinear equilibrium solution. The distribution of design variables is solved through the method of moving asymptotes, in which the sensitivity of the objective function is obtained directly. In addition, a continuation function and a nonlinear projection function are invoked to obtain a checkerboard free and mesh independent design. 2D examples with both plane strain and plane stress conditions hypothesis are presented and compared. The problem of instability is overcome by adopting a polyconvex constitutive model in conjunction with a suggested relaxation function to stabilize the excessive distorted elements. The exact tangent stiffness matrix is used. The optimal topology results are compared to the results obtained by using the classical Saint Venant-Kirchhoff constitutive law, and strong differences are found.

Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations

NASA Technical Reports Server (NTRS)

Hodges, D. H.

1985-01-01

Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.

Nonlinear vibration of a traveling belt with non-homogeneous boundaries

NASA Astrophysics Data System (ADS)

Ding, Hu; Lim, C. W.; Chen, Li-Qun

2018-06-01

Free and forced nonlinear vibrations of a traveling belt with non-homogeneous boundary conditions are studied. The axially moving materials in operation are always externally excited and produce strong vibrations. The moving materials with the homogeneous boundary condition are usually considered. In this paper, the non-homogeneous boundaries are introduced by the support wheels. Equilibrium deformation of the belt is produced by the non-homogeneous boundaries. In order to solve the equilibrium deformation, the differential and integral quadrature methods (DIQMs) are utilized to develop an iterative scheme. The influence of the equilibrium deformation on free and forced nonlinear vibrations of the belt is explored. The DIQMs are applied to solve the natural frequencies and forced resonance responses of transverse vibration around the equilibrium deformation. The Galerkin truncation method (GTM) is utilized to confirm the DIQMs' results. The numerical results demonstrate that the non-homogeneous boundary conditions cause the transverse vibration to deviate from the straight equilibrium, increase the natural frequencies, and lead to coexistence of square nonlinear terms and cubic nonlinear terms. Moreover, the influence of non-homogeneous boundaries can be exacerbated by the axial speed. Therefore, non-homogeneous boundary conditions of axially moving materials especially should be taken into account.

Experimental and Numerical Investigations on Strength and Deformation Behavior of Cataclastic Sandstone

NASA Astrophysics Data System (ADS)

Zhang, Y.; Shao, J. F.; Xu, W. Y.; Zhao, H. B.; Wang, W.

2015-05-01

This work is devoted to characterization of the deformation and strength properties of cataclastic sandstones. Before conducting mechanical tests, the physical properties were first examined. These sandstones are characterized by a loose damaged microstructure and poorly cemented contacts. Then, a series of mechanical tests including hydrostatic, uniaxial, and triaxial compression tests were performed to study the mechanical strength and deformation of the sandstones. The results obtained show nonlinear stress-strain responses. The initial microcracks are closed at hydrostatic stress of 2.6 MPa, and the uniaxial compressive strength is about 0.98 MPa. Under triaxial compression, there is a clear transition from volumetric compressibility to dilatancy and a strong dependency on confining pressure. Based on the experimental evidence, an elastoplastic model is proposed using a linear yield function and a nonassociated plastic potential. There is good agreement between numerical results and experimental data.

A combined dynamic analysis method for geometrically nonlinear vibration isolators with elastic rings

NASA Astrophysics Data System (ADS)

Hu, Zhan; Zheng, Gangtie

2016-08-01

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

Nonlinear Viscoelastic Rheology and the Occurrence of Aftershocks

NASA Astrophysics Data System (ADS)

Shcherbakov, R.; Zhang, X.

2017-12-01

Aftershocks are ubiquitous in nature. They are the manifestation of relaxation phenomena observed in various physical systems. In one prominent example, they typically occur after large earthquakes. The observed aftershock sequences usually obey several well defined non-trivial empirical laws in magnitude, temporal, and spatial domains. In many cases their characteristics follow scale-invariant distributions. The occurrence of aftershocks displays a prominent temporal behavior due to time-dependent mechanisms of stress and/or energy transfer. There are compelling evidences that the lower continental crust and upper mantle are governed by various solid state creep mechanisms. Among those mechanisms a power-law viscous flow was suggested to explain the postseismic surface deformation after large earthquakes. In this work, we consider a slider-block model to mimic the behavior of a seismogenic fault. In the model, we introduce a nonlinear viscoelastic coupling mechanism to capture the essential characteristics of crustal rheology and stress interaction between the blocks and the medium. For this purpose we employ nonlinear Kelvin-Voigt elements consisting of an elastic spring and a dashpot assembled in parallel to introduce viscoelastic coupling between the blocks and the driving plate. By mapping the model into a cellular automaton we derive the functional form of the stress transfer mechanism in the model. We show that the nonlinear viscoelasticity plays a critical role in triggering of aftershocks. It explains the functional form of the Omori-Utsu law and gives physical interpretation of its parameters. The proposed model also suggests that the power-law rheology of the fault gauge and underlying lower crust and upper mantle controls the decay rate of aftershocks. To verify this, we analyze several prominent aftershock sequences to estimate their decay rates and correlate with the rheological properties of the underlying lower crust and mantle, which were estimated from the postseismic surface deformation. Our modelling suggests that the power-law rheology exponent n controls the decay rate of aftershocks and is related to the parameter p of the Omori-Utsu law.

Nonlinear elasticity in resonance experiments

NASA Astrophysics Data System (ADS)

Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel

2018-04-01

Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.

Investigating physical field effects on the size-dependent dynamic behavior of inhomogeneous nanoscale plates

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Reza Barati, Mohammad

2017-02-01

This article investigates the thermo-mechanical vibration frequencies of magneto-electro-thermo-elastic functionally graded (METE-FG) nanoplates in the framework of refined four-unknown shear deformation plate theory. The present nanoplate is subjected to various kinds of thermal loads with uniform, linear and nonlinear distributions. The nonlinear distribution is considered as heat conduction and sinusoidal temperature rise. The present refined theory captures the influences of shear deformations without the need for shear correction factors. Thermo-magneto-electro-elastic coefficients of the FG nanoplate vary gradually along the thickness according to the power-law form. The scale coefficient is taken into consideration implementing the nonlocal elasticity of Eringen. The governing equations are derived through Hamilton's principle and are solved analytically. The frequency response is compared with those of previously published data. The obtained results are presented for the thermo-mechanical vibrations of the FG nanobeams to investigate the effects of material graduation, nonlocal parameter, mode number, slenderness ratio and thermal loading in detail. The present study is associated to aerospace, mechanical and nuclear engineering structures which are under thermal loads.

[Research on adaptive quasi-linear viscoelastic model for nonlinear viscoelastic properties of in vivo soft tissues].

PubMed

Wang, Heng; Sang, Yuanjun

2017-10-01

The mechanical behavior modeling of human soft biological tissues is a key issue for a large number of medical applications, such as surgery simulation, surgery planning, diagnosis, etc. To develop a biomechanical model of human soft tissues under large deformation for surgery simulation, the adaptive quasi-linear viscoelastic (AQLV) model was proposed and applied in human forearm soft tissues by indentation tests. An incremental ramp-and-hold test was carried out to calibrate the model parameters. To verify the predictive ability of the AQLV model, the incremental ramp-and-hold test, a single large amplitude ramp-and-hold test and a sinusoidal cyclic test at large strain amplitude were adopted in this study. Results showed that the AQLV model could predict the test results under the three kinds of load conditions. It is concluded that the AQLV model is feasible to describe the nonlinear viscoelastic properties of in vivo soft tissues under large deformation. It is promising that this model can be selected as one of the soft tissues models in the software design for surgery simulation or diagnosis.

Extensions of the Ferry shear wave model for active linear and nonlinear microrheology

PubMed Central

Mitran, Sorin M.; Forest, M. Gregory; Yao, Lingxing; Lindley, Brandon; Hill, David B.

2009-01-01

The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior. PMID:20011614

Nonlinear Dynamic Behavior of Impact Damage in a Composite Skin-Stiffener Structure

NASA Technical Reports Server (NTRS)

Ooijevaar, T. H.; Rogge, M. D.; Loendersloot, R.; Warnet, L.; Akkerman, R.; deBoer, A.

2013-01-01

One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage, like delaminations. A wide range of technologies, comprising global vibration and local wave propagation methods can be employed for health monitoring purposes. Traditional low frequency modal analysis based methods are linear methods. The effectiveness of these methods is often limited since they rely on a stationary and linear approximation of the system. The nonlinear interaction between a low frequency wave field and a local impact induced skin-stiffener failure is experimentally demonstrated in this paper. The different mechanisms that are responsible for the nonlinearities (opening, closing and contact) of the distorted harmonic waveforms are separated with the help of phase portraits. A basic analytical model is employed to support the observations.

A new physical model with multilayer architecture for facial expression animation using dynamic adaptive mesh.

PubMed

Zhang, Yu; Prakash, Edmond C; Sung, Eric

2004-01-01

This paper presents a new physically-based 3D facial model based on anatomical knowledge which provides high fidelity for facial expression animation while optimizing the computation. Our facial model has a multilayer biomechanical structure, incorporating a physically-based approximation to facial skin tissue, a set of anatomically-motivated facial muscle actuators, and underlying skull structure. In contrast to existing mass-spring-damper (MSD) facial models, our dynamic skin model uses the nonlinear springs to directly simulate the nonlinear visco-elastic behavior of soft tissue and a new kind of edge repulsion spring is developed to prevent collapse of the skin model. Different types of muscle models have been developed to simulate distribution of the muscle force applied on the skin due to muscle contraction. The presence of the skull advantageously constrain the skin movements, resulting in more accurate facial deformation and also guides the interactive placement of facial muscles. The governing dynamics are computed using a local semi-implicit ODE solver. In the dynamic simulation, an adaptive refinement automatically adapts the local resolution at which potential inaccuracies are detected depending on local deformation. The method, in effect, ensures the required speedup by concentrating computational time only where needed while ensuring realistic behavior within a predefined error threshold. This mechanism allows more pleasing animation results to be produced at a reduced computational cost.

Multi-functional surface acoustic wave sensor for monitoring enviromental and structural condition

NASA Astrophysics Data System (ADS)

Furuya, Y.; Kon, T.; Okazaki, T.; Saigusa, Y.; Nomura, T.

2006-03-01

As a first step to develop a health monitoring system with active and embedded nondestructive evaluation devices for the machineries and structures, multi-functional SAW (surface acoustic wave) device was developed. A piezoelectric LiNbO3(x-y cut) materials were used as a SAW substrate on which IDT(20μm pitch) was produced by lithography. On the surface of a path of SAW between IDTs, environmentally active material films of shape memory Ti50Ni41Cu(at%) with non-linear hysteresis and superelastic Ti48Ni43Cu(at%) with linear deformation behavior were formed by magnetron-sputtering technique. In this study, these two kinds of shape memory alloys SMA) system were used to measure 1) loading level, 2) phase transformation and 3)stress-strain hysteresis under cyclic loading by utilizing their linearity and non-linearity deformation behaviors. Temperature and stress dependencies of SAW signal were also investigated in the non-sputtered film state. Signal amplitude and phase change of SAW were chosen to measure as the sensing parameters. As a result, temperature, stress level, phase transformation in SMA depending on temperature and mechanical damage accumulation could be measured by the proposed multi-functional SAW sensor. Moreover, the wireless SAW sensing system which has a unique feature of no supplying electric battery was constructed, and the same characteristic evaluation is confirmed in comparison with wired case.

Numerical simulation of magmatic hydrothermal systems

USGS Publications Warehouse

Ingebritsen, S.E.; Geiger, S.; Hurwitz, S.; Driesner, T.

2010-01-01

The dynamic behavior of magmatic hydrothermal systems entails coupled and nonlinear multiphase flow, heat and solute transport, and deformation in highly heterogeneous media. Thus, quantitative analysis of these systems depends mainly on numerical solution of coupled partial differential equations and complementary equations of state (EOS). The past 2 decades have seen steady growth of computational power and the development of numerical models that have eliminated or minimized the need for various simplifying assumptions. Considerable heuristic insight has been gained from process-oriented numerical modeling. Recent modeling efforts employing relatively complete EOS and accurate transport calculations have revealed dynamic behavior that was damped by linearized, less accurate models, including fluid property control of hydrothermal plume temperatures and three-dimensional geometries. Other recent modeling results have further elucidated the controlling role of permeability structure and revealed the potential for significant hydrothermally driven deformation. Key areas for future reSearch include incorporation of accurate EOS for the complete H2O-NaCl-CO2 system, more realistic treatment of material heterogeneity in space and time, realistic description of large-scale relative permeability behavior, and intercode benchmarking comparisons. Copyright 2010 by the American Geophysical Union.

Indentation mapping revealed poroelastic, but not viscoelastic, properties spanning native zonal articular cartilage.

PubMed

Wahlquist, Joseph A; DelRio, Frank W; Randolph, Mark A; Aziz, Aaron H; Heveran, Chelsea M; Bryant, Stephanie J; Neu, Corey P; Ferguson, Virginia L

2017-12-01

Osteoarthrosis is a debilitating disease affecting millions, yet engineering materials for cartilage regeneration has proven difficult because of the complex microstructure of this tissue. Articular cartilage, like many biological tissues, produces a time-dependent response to mechanical load that is critical to cell's physiological function in part due to solid and fluid phase interactions and property variations across multiple length scales. Recreating the time-dependent strain and fluid flow may be critical for successfully engineering replacement tissues but thus far has largely been neglected. Here, microindentation is used to accomplish three objectives: (1) quantify a material's time-dependent mechanical response, (2) map material properties at a cellular relevant length scale throughout zonal articular cartilage and (3) elucidate the underlying viscoelastic, poroelastic, and nonlinear poroelastic causes of deformation in articular cartilage. Untreated and trypsin-treated cartilage was sectioned perpendicular to the articular surface and indentation was used to evaluate properties throughout zonal cartilage on the cut surface. The experimental results demonstrated that within all cartilage zones, the mechanical response was well represented by a model assuming nonlinear biphasic behavior and did not follow conventional viscoelastic or linear poroelastic models. Additionally, 10% (w/w) agarose was tested and, as anticipated, behaved as a linear poroelastic material. The approach outlined here provides a method, applicable to many tissues and biomaterials, which reveals and quantifies the underlying causes of time-dependent deformation, elucidates key aspects of material structure and function, and that can be used to provide important inputs for computational models and targets for tissue engineering. Elucidating the time-dependent mechanical behavior of cartilage, and other biological materials, is critical to adequately recapitulate native mechanosensory cues for cells. We used microindentation to map the time-dependent properties of untreated and trypsin treated cartilage throughout each cartilage zone. Unlike conventional approaches that combine viscoelastic and poroelastic behaviors into a single framework, we deconvoluted the mechanical response into separate contributions to time-dependent behavior. Poroelastic effects in all cartilage zones dominated the time-dependent behavior of articular cartilage, and a model that incorporates tension-compression nonlinearity best represented cartilage mechanical behavior. These results can be used to assess the success of regeneration and repair approaches, as design targets for tissue engineering, and for development of accurate computational models. Copyright © 2017 Acta Materialia Inc. All rights reserved.

Prediction of water loss and viscoelastic deformation of apple tissue using a multiscale model.

PubMed

Aregawi, Wondwosen A; Abera, Metadel K; Fanta, Solomon W; Verboven, Pieter; Nicolai, Bart

2014-11-19

A two-dimensional multiscale water transport and mechanical model was developed to predict the water loss and deformation of apple tissue (Malus × domestica Borkh. cv. 'Jonagold') during dehydration. At the macroscopic level, a continuum approach was used to construct a coupled water transport and mechanical model. Water transport in the tissue was simulated using a phenomenological approach using Fick's second law of diffusion. Mechanical deformation due to shrinkage was based on a structural mechanics model consisting of two parts: Yeoh strain energy functions to account for non-linearity and Maxwell's rheological model of visco-elasticity. Apparent parameters of the macroscale model were computed from a microscale model. The latter accounted for water exchange between different microscopic structures of the tissue (intercellular space, the cell wall network and cytoplasm) using transport laws with the water potential as the driving force for water exchange between different compartments of tissue. The microscale deformation mechanics were computed using a model where the cells were represented as a closed thin walled structure. The predicted apparent water transport properties of apple cortex tissue from the microscale model showed good agreement with the experimentally measured values. Deviations between calculated and measured mechanical properties of apple tissue were observed at strains larger than 3%, and were attributed to differences in water transport behavior between the experimental compression tests and the simulated dehydration-deformation behavior. Tissue dehydration and deformation in the high relative humidity range ( > 97% RH) could, however, be accurately predicted by the multiscale model. The multiscale model helped to understand the dynamics of the dehydration process and the importance of the different microstructural compartments (intercellular space, cell wall, membrane and cytoplasm) for water transport and mechanical deformation.

Possibilities and limitations of rod-beam theories. [nonlinear distortion tensor and nonlinear stress tensors

NASA Technical Reports Server (NTRS)

Peterson, D.

1979-01-01

Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.

Study on the Unsteady Creep of Composite Beams with an Irregular Laminar Fibrous Structure Made from Nonlinear Hereditary Materials

NASA Astrophysics Data System (ADS)

Yankovskii, A. P.

2017-09-01

The creep of homogenous and hybrid composite beams of an irregular laminar fibrous structure is investigated. The beams consist of thin walls and flanges (load-carrying layers). The walls may be reinforced longitudinally or crosswise in the plane, and the load-carrying layers are reinforced in the longitudinal direction. The mechanical behavior of phase materials is described by the Rabotnov nonlinear hereditary theory of creep taking into account their possible different resistance to tension and compression. On the basis of hypotheses of the Timoshenko theory, with using the method of time steps, a problem is formulated for the inelastic bending deformation of such beams with account of the weakened resistance of their walls to the transverse shear. It is shown that, at discrete instants of time, the mechanical behavior of such structures can formally be described by the governing relations for composite beams made of nonlinear elastic anisotropic materials with a known initial stress state. The method of successive iterations, similar to the method of variable parameters of elasticity, is used to linearize the boundary-value problem at each instant of time. The bending deformation is investigated for homogeneous and reinforced cantilever and simply supported beams in creep under the action of a uniformly distributed transverse load. The cross sections of the beams considered are I-shaped. It is found that the use of the classical theory for such beams leads to the prediction of indefensibly underestimated flexibility, especially in long-term loading. It is shown that, in beams with reinforced load-carrying layers, the creep mainly develops due to the shear strains of walls. It is found that, in short- and long-term loadings of composite beams, the reinforcement structures rational by the criterion of minimum flexibility are different.

Creep and shrinkage effects on integral abutment bridges

NASA Astrophysics Data System (ADS)

Munuswamy, Sivakumar

Integral abutment bridges provide bridge engineers an economical design alternative to traditional bridges with expansion joints owing to the benefits, arising from elimination of expensive joints installation and reduced maintenance cost. The superstructure for integral abutment bridges is cast integrally with abutments. Time-dependent effects of creep, shrinkage of concrete, relaxation of prestressing steel, temperature gradient, restraints provided by abutment foundation and backfill and statical indeterminacy of the structure introduce time-dependent variations in the redundant forces. An analytical model and numerical procedure to predict instantaneous linear behavior and non-linear time dependent long-term behavior of continuous composite superstructure are developed in which the redundant forces in the integral abutment bridges are derived considering the time-dependent effects. The redistributions of moments due to time-dependent effects have been considered in the analysis. The analysis includes nonlinearity due to cracking of the concrete, as well as the time-dependent deformations. American Concrete Institute (ACI) and American Association of State Highway and Transportation Officials (AASHTO) models for creep and shrinkage are considered in modeling the time dependent material behavior. The variations in the material property of the cross-section corresponding to the constituent materials are incorporated and age-adjusted effective modulus method with relaxation procedure is followed to include the creep behavior of concrete. The partial restraint provided by the abutment-pile-soil system is modeled using discrete spring stiffness as translational and rotational degrees of freedom. Numerical simulation of the behavior is carried out on continuous composite integral abutment bridges and the deformations and stresses due to time-dependent effects due to typical sustained loads are computed. The results from the analytical model are compared with the published laboratory experimental and field data. The behavior of the laterally loaded piles supporting the integral abutments is evaluated and presented in terms of the lateral deflection, bending moment, shear force and stress along the pile depth.

Bubble deformations and segmented flows in corrugated microchannels at large capillary numbers

NASA Astrophysics Data System (ADS)

Sauzade, Martin; Cubaud, Thomas

2018-03-01

We experimentally investigate the interaction between individual bubble deformations and collective distortions of segmented flows in nonlinear microfluidic geometries. Using highly viscous carrier fluids, we study the evolution of monodisperse trains of gas bubbles from a square to a smoothly corrugated microchannel characterized with a series of extensions and constrictions along the flow path. The hysteresis in the bubble shape between accelerating and decelerating flow fields is shown to increase with the capillary number. Measurements of instantaneous bubble velocities reveal the presence of a capillary pull that produces a nonmonotonic behavior for the front velocity in accelerating flow regions. Functional relationships are developed for predicting the morphology and dynamics of viscous multiphase flow patterns at the pore scale.

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time: application to non-rigid neuroimage registration.

PubMed

Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol

2010-12-01

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peryshkin, A. Yu., E-mail: alexb700@yandex.ru; Makarov, P. V., E-mail: bacardi@ispms.ru; Eremin, M. O., E-mail: bacardi@ispms.ru

An evolutionary approach proposed in [1, 2] combining the achievements of traditional macroscopic theory of solid mechanics and basic ideas of nonlinear dynamics is applied in a numerical simulation of present-day tectonic plates motion and seismic process in Central Asia. Relative values of strength parameters of rigid blocks with respect to the soft zones were characterized by the δ parameter that was varied in the numerical experiments within δ = 1.1–1.8 for different groups of the zonal-block divisibility. In general, the numerical simulations of tectonic block motion and accompanying seismic process in the model geomedium indicate that the numerical solutionsmore » of the solid mechanics equations characterize its deformation as a typical behavior of a nonlinear dynamic system under conditions of self-organized criticality.« less

Dynamics of Geometrically Nonlinear Elastic Nonthin Anisotropic Shells of Variable Thickness

NASA Astrophysics Data System (ADS)

Marchuk, M. V.; Tuchapskii, R. I.

2017-11-01

A theory of dynamic elastic geometrically nonlinear deformation of nonthin anisotropic shells with variable thickness is constructed. Shells are assumed asymmetric about the reference surface. Functions are expanded into Legendre series. The basic equations are written in a coordinate system aligned with the lines of curvature of the reference surface. The equations of motion and appropriate boundary conditions are obtained using the Hamilton-Ostrogradsky variational principle. The change in metric across the thickness is taken into account. The theory assumes that the refinement process is regular and allows deriving equations including products of terms of Legendre series of unknown functions of arbitrary order. The behavior of a square metallic plate acted upon by a pressure pulse distributed over its face is studied.

LS-DYNA Implementation of Polymer Matrix Composite Model Under High Strain Rate Impact

NASA Technical Reports Server (NTRS)

Zheng, Xia-Hua; Goldberg, Robert K.; Binienda, Wieslaw K.; Roberts, Gary D.

2003-01-01

A recently developed constitutive model is implemented into LS-DYNA as a user defined material model (UMAT) to characterize the nonlinear strain rate dependent behavior of polymers. By utilizing this model within a micromechanics technique based on a laminate analogy, an algorithm to analyze the strain rate dependent, nonlinear deformation of a fiber reinforced polymer matrix composite is then developed as a UMAT to simulate the response of these composites under high strain rate impact. The models are designed for shell elements in order to ensure computational efficiency. Experimental and numerical stress-strain curves are compared for two representative polymers and a representative polymer matrix composite, with the analytical model predicting the experimental response reasonably well.

A Study on Flexural Properties of Sandwich Structures with Fiber/Metal Laminate Face Sheets

NASA Astrophysics Data System (ADS)

Dariushi, S.; Sadighi, M.

2013-10-01

In this work, a new family of sandwich structures with fiber metal laminate (FML) faces is investigated. FMLs have benefits over both metal and fiber reinforced composites. To investigate the bending properties of sandwich beams with FML faces and compare with similar sandwich beams with fibrous composite faces, 6 groups of specimen with different layer arrangements were made and tested. Results show that FML faces have good resistance against transverse local loads and minimize stress concentration and local deformations of skin and core under the loading tip. In addition, FML faces have a good integrity even after plateau region of foam cores and prevent from catastrophic failures, which cannot be seen in fibrous composite faces. Also, FML faces are lighter than metal faces and have better connection with foam cores. Sandwich beams with FML faces have a larger elastic region because of simultaneous deformation of top and bottom faces and larger failure strain thanks to good durability of FMLs. A geometrical nonlinear classical theory is used to predict force-deflection behavior. In this model an explicit formula between symmetrical sandwich beams deflections and applied force which can be useful for designers, is derived. Good agreement is obtained between the analytical predictions and experimental results. Also, analytical results are compared with small deformation solution in a parametric study, and the effects of geometric parameters on difference between linear and nonlinear results are discussed.

Nonlinear mesomechanics of composites with periodic microstructure

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Jordan, Eric H.; Freed, Alan D.

1989-01-01

This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.

A Physics-driven Neural Networks-based Simulation System (PhyNNeSS) for multimodal interactive virtual environments involving nonlinear deformable objects

PubMed Central

De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S.

2012-01-01

Background While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics. Physics-based modeling of deformable objects, especially when large nonlinear deformations and complex nonlinear material properties are involved, at these very high rates is one of the most challenging tasks in the development of real time simulation systems. While some specialized solutions exist, there is no general solution for arbitrary nonlinearities. Methods In this work we present PhyNNeSS - a Physics-driven Neural Networks-based Simulation System - to address this long-standing technical challenge. The first step is an off-line pre-computation step in which a database is generated by applying carefully prescribed displacements to each node of the finite element models of the deformable objects. In the next step, the data is condensed into a set of coefficients describing neurons of a Radial Basis Function network (RBFN). During real-time computation, these neural networks are used to reconstruct the deformation fields as well as the interaction forces. Results We present realistic simulation examples from interactive surgical simulation with real time force feedback. As an example, we have developed a deformable human stomach model and a Penrose-drain model used in the Fundamentals of Laparoscopic Surgery (FLS) training tool box. Conclusions A unique computational modeling system has been developed that is capable of simulating the response of nonlinear deformable objects in real time. The method distinguishes itself from previous efforts in that a systematic physics-based pre-computational step allows training of neural networks which may be used in real time simulations. We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation. PhyNNeSS has been integrated into SoFMIS (Software Framework for Multimodal Interactive Simulation) for general use. PMID:22629108

Vacua and walls of mass-deformed Kähler nonlinear sigma models on S p (N )/U (N )

NASA Astrophysics Data System (ADS)

Arai, Masato; Golubtsova, Anastasia; Park, Chanyong; Shin, Sunyoung

2018-05-01

We study vacua and walls of mass-deformed Kähler nonlinear sigma models on S p (N )/U (N ). We identify elementary walls with the simple roots of U S p (2 N ) and discuss compressed walls, penetrable walls, and multiwalls by using the moduli matrix formalism.

Identifying traction-separation behavior of self-adhesive polymeric films from in situ digital images under T-peeling

NASA Astrophysics Data System (ADS)

Nase, Michael; Rennert, Mirko; Naumenko, Konstantin; Eremeyev, Victor A.

2016-06-01

In this paper procedures are developed to identify traction-separation curves from digital images of the deformed flexible films during peeling. T-peel tests were performed for self-adhesive polymeric films. High quality photographs of the deformed shape within and outside the zone of adhesive interaction were made in situ by the digital light microscope. The deformed line is approximated by a power series with coefficients computed by minimizing a least squares functional. Two approaches to identify the traction-separation curve for the given deformation line are proposed. The first one is based on the energy integral of the non-linear theory of rods and allows the direct evaluation of the adhesion force potential. The second one utilizes the complementary energy type variational equation and the Ritz method to compute the adhesion force. The accuracy of both approaches is analyzed with respect to different approximations for the deformed line and the force of interaction. The obtained traction vs. axial coordinate and the traction-separation curves provide several properties of the adhesive system including the maximum adhesion force, the length of the adhesive zone and the equilibrium position, where the adhesive force is zero while the separation is positive.

Experimental Investigation of Stiffness Characteristics and Damping Properties of a Metallic Rubber Material

NASA Astrophysics Data System (ADS)

Lu, Ch. Zh.; Li, Jingyuan; Zhou, Bangyang; Li, Shuang

2017-09-01

The static stiffness and dynamic damping properties of a metallic rubber material (MR) were investigated, which exhibited a nonlinear deformation behavior. Its static stiffness is analyzed and discussed. The effects of structural parameters of MR and experimental conditions on its shock absorption capacity were examined by dynamic tests. Results revealed excellent elastic and damping properties of the material. Its stiffness increased with density, but decreased with thickness. The damping property of MR varied with its density, thickness, loading frequency, and amplitude.

Structural analysis of cylindrical thrust chambers, volume 3

NASA Technical Reports Server (NTRS)

Pearson, M. L.

1981-01-01

A system of three computer programs is described for use in conjunction with the BOPAGE finite element program. The programs are demonstrated by analyzing cumulative plastic deformation in a regeneratively cooled rocket thrust chamber. The codes provide the capability to predict geometric and material nonlinear behavior of cyclically loaded structures without performing a cycle-by-cycle analysis over the life of the structure. The program set consists of a BOPACE restart tape reader routine, and extrapolation program and a plot package.

Coupled multi-disciplinary simulation of composite engine structures in propulsion environment

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Singhal, Surendra N.

1992-01-01

A computational simulation procedure is described for the coupled response of multi-layered multi-material composite engine structural components which are subjected to simultaneous multi-disciplinary thermal, structural, vibration, and acoustic loadings including the effect of hostile environments. The simulation is based on a three dimensional finite element analysis technique in conjunction with structural mechanics codes and with acoustic analysis methods. The composite material behavior is assessed at the various composite scales, i.e., the laminate/ply/constituents (fiber/matrix), via a nonlinear material characterization model. Sample cases exhibiting nonlinear geometrical, material, loading, and environmental behavior of aircraft engine fan blades, are presented. Results for deformed shape, vibration frequency, mode shapes, and acoustic noise emitted from the fan blade, are discussed for their coupled effect in hot and humid environments. Results such as acoustic noise for coupled composite-mechanics/heat transfer/structural/vibration/acoustic analyses demonstrate the effectiveness of coupled multi-disciplinary computational simulation and the various advantages of composite materials compared to metals.

A q-deformation of the Bogoliubov transformations

NASA Astrophysics Data System (ADS)

Arraut, Ivan; Segovia, Carlos

2018-02-01

An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Finally, we introduce a Hopf structure when q is a root of unity.

Solving nonlinear equilibrium equations of deformable systems by method of embedded polygons

NASA Astrophysics Data System (ADS)

Razdolsky, A. G.

2017-09-01

Solving of nonlinear algebraic equations is an obligatory stage of studying the equilibrium paths of nonlinear deformable systems. The iterative method for solving a system of nonlinear algebraic equations stated in an explicit or implicit form is developed in the present work. The method consists of constructing a sequence of polygons in Euclidean space that converge into a single point that displays the solution of the system. Polygon vertices are determined on the assumption that individual equations of the system are independent from each other and each of them is a function of only one variable. Initial positions of vertices for each subsequent polygon are specified at the midpoints of certain straight segments determined at the previous iteration. The present algorithm is applied for analytical investigation of the behavior of biaxially compressed nonlinear-elastic beam-column with an open thin-walled cross-section. Numerical examples are made for the I-beam-column on the assumption that its material follows a bilinear stress-strain diagram. A computer program based on the shooting method is developed for solving the problem. The method is reduced to numerical integration of a system of differential equations and to the solution of a system of nonlinear algebraic equations between the boundary values of displacements at the ends of the beam-column. A stress distribution at the beam-column cross-sections is determined by subdividing the cross-section area into many small cells. The equilibrium path for the twisting angle and the lateral displacements tend to the stationary point when the load is increased. Configuration of the path curves reveals that the ultimate load is reached shortly once the maximal normal stresses at the beam-column fall outside the limit of the elastic region. The beam-column has a unique equilibrium state for each value of the load, that is, there are no equilibrium states once the maximum load is reached.

A Reformulation of Nonlinear Anisotropic Elasticity for Impact Physics

DTIC Science & Technology

2014-02-01

aluminum, copper, and magnesium . 15. SUBJECT TERMS impact physics, shock compression, elasticity, plasticity 16. SECURITY CLASSIFICATION OF: 17... deformation wave propagation code accounting for dissipative inelastic mechanisms. • Accuracy of the new nonlinear elastic- plastic model(s) will be...gradient and its transpose. A new general thermomechanical theory accounting for both elastic and plastic deformations has been briefly outlined in

Segmentation of deformable organs from medical images using particle swarm optimization and nonlinear shape priors

NASA Astrophysics Data System (ADS)

Afifi, Ahmed; Nakaguchi, Toshiya; Tsumura, Norimichi

2010-03-01

In many medical applications, the automatic segmentation of deformable organs from medical images is indispensable and its accuracy is of a special interest. However, the automatic segmentation of these organs is a challenging task according to its complex shape. Moreover, the medical images usually have noise, clutter, or occlusion and considering the image information only often leads to meager image segmentation. In this paper, we propose a fully automated technique for the segmentation of deformable organs from medical images. In this technique, the segmentation is performed by fitting a nonlinear shape model with pre-segmented images. The kernel principle component analysis (KPCA) is utilized to capture the complex organs deformation and to construct the nonlinear shape model. The presegmentation is carried out by labeling each pixel according to its high level texture features extracted using the overcomplete wavelet packet decomposition. Furthermore, to guarantee an accurate fitting between the nonlinear model and the pre-segmented images, the particle swarm optimization (PSO) algorithm is employed to adapt the model parameters for the novel images. In this paper, we demonstrate the competence of proposed technique by implementing it to the liver segmentation from computed tomography (CT) scans of different patients.

Remote optoelectronic sensors for monitoring of nonlinear surfaces

NASA Astrophysics Data System (ADS)

Petrochenko, Andrew V.; Konyakhin, Igor A.

2015-05-01

Actually during construction of the high building actively are used objects of various nonlinear surface, for example, sinuous (parabolic or hyperbolic) roofs of the sport complexes that require automatic deformation control [1]. This type of deformation has character of deflection that is impossible to monitor objectively with just one optoelectronic sensor (which is fixed on this surface). In this article is described structure of remote optoelectronic sensor, which is part of the optoelectronic monitoring system of nonlinear surface, and mathematical transformation of exterior orientation sensor elements in the coordinates of control points.

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

Matar, O. K.; Craster, R. V.; Kumar, S.

2007-11-01

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.

Iterative and variational homogenization methods for filled elastomers

NASA Astrophysics Data System (ADS)

Goudarzi, Taha

Elastomeric composites have increasingly proved invaluable in commercial technological applications due to their unique mechanical properties, especially their ability to undergo large reversible deformation in response to a variety of stimuli (e.g., mechanical forces, electric and magnetic fields, changes in temperature). Modern advances in organic materials science have revealed that elastomeric composites hold also tremendous potential to enable new high-end technologies, especially as the next generation of sensors and actuators featured by their low cost together with their biocompatibility, and processability into arbitrary shapes. This potential calls for an in-depth investigation of the macroscopic mechanical/physical behavior of elastomeric composites directly in terms of their microscopic behavior with the objective of creating the knowledge base needed to guide their bottom-up design. The purpose of this thesis is to generate a mathematical framework to describe, explain, and predict the macroscopic nonlinear elastic behavior of filled elastomers, arguably the most prominent class of elastomeric composites, directly in terms of the behavior of their constituents --- i.e., the elastomeric matrix and the filler particles --- and their microstructure --- i.e., the content, size, shape, and spatial distribution of the filler particles. This will be accomplished via a combination of novel iterative and variational homogenization techniques capable of accounting for interphasial phenomena and finite deformations. Exact and approximate analytical solutions for the fundamental nonlinear elastic response of dilute suspensions of rigid spherical particles (either firmly bonded or bonded through finite size interphases) in Gaussian rubber are first generated. These results are in turn utilized to construct approximate solutions for the nonlinear elastic response of non-Gaussian elastomers filled with a random distribution of rigid particles (again, either firmly bonded or bonded through finite size interphases) at finite concentrations. Three-dimensional finite element simulations are also carried out to gain further insight into the proposed theoretical solutions. Inter alia, we make use of these solutions to examine the effects of particle concentration, mono- and poly-dispersity of the filler particle size, and the presence of finite size interphases on the macroscopic response of filled elastomers. The solutions are found able to explain and describe experimental results that to date have been understood only in part. More generally, the solutions provide a robust tool to efficiently guide the design of filled elastomers with desired macroscopic properties. The homogenization techniques developed in this work are not limited to nonlinear elasticity, but can be readily utilized to study multi-functional properties as well. For demonstration purposes, we work out a novel exact solution for the macroscopic dielectric response of filled elastomers with interphasial space charges.

A Nonlinear Elasticity Model of Macromolecular Conformational Change Induced by Electrostatic Forces

PubMed Central

Zhou, Y. C.; Holst, Michael; McCammon, J. Andrew

2008-01-01

In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic potential is analyzed in a domain varying with the elastic deformation of molecules, and a new continuous model of the electrostatic forces is developed to ensure solvability of the nonlinear elasticity equations. We derive the estimates of electrostatic forces corresponding to four types of perturbations to an electrostatic potential field, and establish the existance of an equilibrium configuration using a fixed-point argument, under the assumption that the change in the ionic strength and charges due to the additional molecules causing the deformation are sufficiently small. The results are valid for elastic models with arbitrarily complex dielectric interfaces and cavities, and can be generalized to large elastic deformation caused by high ionic strength, large charges, and strong external fields by using continuation methods. PMID:19461946

Novel silicon microchannels device for use in red blood cell deformability studies

NASA Astrophysics Data System (ADS)

Zheng, Xiao-Lin; Liao, Yan-Jian; Zhang, Wen-Xian

2001-10-01

Currently, a number of techniques are used to access cell deformability. We study a novel silicon microchannels device for use in red blood cell deformability. The channels are produced in silicon substrate using microengineering technology. The microgrooves formed in the surface of a single-crystal silicon substrate. They were converted to channels by tightly covering them with an optical flat glass plate. An array of flow channels (number 950 in parallel) have typical dimensions of 5 micrometers width X 5.5 Xm depth, and 30 micrometers length. There the RBC's are forced to pass through channels. Thus, the microchannels are used to simulate human blood capillaries. It provides a specific measurement of individual cell in terms of both flow velocity profile and an index of cell volume while the cell flow through the channels. It dominates the complex cellular flow behavior, such as, the viscosity of whole blood is a nonlinear function of shear rate, index of filtration, etc.

Microhydrodynamics of deformable particles: surprising responses of drops and vesicles to uniform electric field or shear flow

NASA Astrophysics Data System (ADS)

Vlahovska, Petia

2015-11-01

Particle motion in a viscous fluid is a classic problem that continues to surprise researchers. In this talk, I will discuss some intriguing, experimentally-observed behaviors of droplets and giant vesicles (cell-size lipid membrane sacs) in electric or flow fields. In a uniform electric field, a droplet deforms into an ellipsoid that can either be steadily tilted relative to the applied field direction or undergo unsteady motions (periodic shape oscillations or irregular flipping); a spherical vesicle can adopt a transient square shape or reversibly porate. In a steady shear flow, a vesicle can tank-tread, tumble or swing. Theoretical models show that the nonlinear drop dynamics originates from the interplay of Quincke rotation and interface deformation, while the vesicle dynamics stems from the membrane inextensibility. The practical motivation for this research lies in an improved understanding of technologies that rely on the manipulation of drops and cells by flow or electric fields.

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Swafford, Timothy W.; Reddy, T. S. R.

1991-01-01

A compressible flow code that can predict the nonlinear unsteady aerodynamics associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

Behavior of a nuclear steel containment equipment hatch at large strain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fanous, F.; Greimann, L.

1988-05-01

During a severe accident, buckling of a steel containment hatch door, large deformation and ovaling of the hatch sleeve are potential causes of mismatch at the sealing surface which can result in a leakage path. A three-dimensional nonlinear finite element analysis of a typical steel containment/sleeve/hatch assembly that includes containment stiffeners, pretensioned swing bolts, and hatch door geometric imperfection is presented. The analysis was carried out to the nonlinear range up to large strains. The results indicated that the buckling load occurs at pressure, far above that which causes gross yielding of the shell plate. Although buckling of the hatchmore » door increased the relative motions of the hatch sleeve and the hatch door, the motions remained sufficiently small to prevent leakage.« less

Vector form Intrinsic Finite Element Method for the Two-Dimensional Analysis of Marine Risers with Large Deformations

NASA Astrophysics Data System (ADS)

Li, Xiaomin; Guo, Xueli; Guo, Haiyan

2018-06-01

Robust numerical models that describe the complex behaviors of risers are needed because these constitute dynamically sensitive systems. This paper presents a simple and efficient algorithm for the nonlinear static and dynamic analyses of marine risers. The proposed approach uses the vector form intrinsic finite element (VFIFE) method, which is based on vector mechanics theory and numerical calculation. In this method, the risers are described by a set of particles directly governed by Newton's second law and are connected by weightless elements that can only resist internal forces. The method does not require the integration of the stiffness matrix, nor does it need iterations to solve the governing equations. Due to these advantages, the method can easily increase or decrease the element and change the boundary conditions, thus representing an innovative concept of solving nonlinear behaviors, such as large deformation and large displacement. To prove the feasibility of the VFIFE method in the analysis of the risers, rigid and flexible risers belonging to two different categories of marine risers, which usually have differences in modeling and solving methods, are employed in the present study. In the analysis, the plane beam element is adopted in the simulation of interaction forces between the particles and the axial force, shear force, and bending moment are also considered. The results are compared with the conventional finite element method (FEM) and those reported in the related literature. The findings revealed that both the rigid and flexible risers could be modeled in a similar unified analysis model and that the VFIFE method is feasible for solving problems related to the complex behaviors of marine risers.

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.; Gilat, Amos

2003-01-01

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

An Exposition on the Nonlinear Kinematics of Shells, Including Transverse Shearing Deformations

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2013-01-01

An in-depth exposition on the nonlinear deformations of shells with "small" initial geometric imperfections, is presented without the use of tensors. First, the mathematical descriptions of an undeformed-shell reference surface, and its deformed image, are given in general nonorthogonal coordinates. The two-dimensional Green-Lagrange strains of the reference surface derived and simplified for the case of "small" strains. Linearized reference-surface strains, rotations, curvatures, and torsions are then derived and used to obtain the "small" Green-Lagrange strains in terms of linear deformation measures. Next, the geometry of the deformed shell is described mathematically and the "small" three-dimensional Green-Lagrange strains are given. The deformations of the shell and its reference surface are related by introducing a kinematic hypothesis that includes transverse shearing deformations and contains the classical Love-Kirchhoff kinematic hypothesis as a proper, explicit subset. Lastly, summaries of the essential equations are given for general nonorthogonal and orthogonal coordinates, and the basis for further simplification of the equations is discussed.

A combined experimental and finite element study to predict the failure mechanisms in SiC coated carbon/carbon composites at room and elevated temperatures under flexural loading

NASA Technical Reports Server (NTRS)

Mahfuz, Hassan; Das, Partha S.; Xue, Dongwei; Krishnagopalan, Jaya; Jeelani, Shaik

1993-01-01

Response of quasi-isotropic laminates of SiC coated Carbon/Carbon (C/C) composites have been investigated under flexural loading at various temperatures. Variation of load-deflection behavior with temperatures are studied. Increase in flexural strength and stiffness are observed with the rise in temperature. Extensive analyses through Optical Microscope (OM) and Non-Destructive Evaluation (NDE) have been performed to understand the failure mechanisms. Damage zone is found only within the neighborhood of the loading plane. Isoparametric layered shell elements developed on the basis of the first order shear deformation theory have been used to model the thin laminates of C/C under flexural loading. Large deformation behavior has been considered in the finite element analysis to account for the non-linearities encountered during the actual test. Data generated using finite element analysis are presented to corroborate the experimental findings, and a comparison in respect of displacement and stress-strain behavior are given to check the accuracy of the finite element analysis. Reasonable correlation between the experimental and finite element results have been established.

A Nonlinear Modal Aeroelastic Solver for FUN3D

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.

2016-01-01

A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.

Multiscale mechanical integrity of human supraspinatus tendon in shear after elastin depletion.

PubMed

Fang, Fei; Lake, Spencer P

2016-10-01

Human supraspinatus tendon (SST) exhibits region-specific nonlinear mechanical properties under tension, which have been attributed to its complex multiaxial physiological loading environment. However, the mechanical response and underlying multiscale mechanism regulating SST behavior under other loading scenarios are poorly understood. Furthermore, little is known about the contribution of elastin to tendon mechanics. We hypothesized that (1) SST exhibits region-specific shear mechanical properties, (2) fiber sliding is the predominant mode of local matrix deformation in SST in shear, and (3) elastin helps maintain SST mechanical integrity by facilitating force transfer among collagen fibers. Through the use of biomechanical testing and multiphoton microscopy, we measured the multiscale mechanical behavior of human SST in shear before and after elastase treatment. Three distinct SST regions showed similar stresses and microscale deformation. Collagen fiber reorganization and sliding were physical mechanisms observed as the SST response to shear loading. Measures of microscale deformation were highly variable, likely due to a high degree of extracellular matrix heterogeneity. After elastase treatment, tendon exhibited significantly decreased stresses under shear loading, particularly at low strains. These results show that elastin contributes to tendon mechanics in shear, further complementing our understanding of multiscale tendon structure-function relationships. Copyright © 2016 Elsevier Ltd. All rights reserved.

Mechanical instability and percolation of deformable particles through porous networks

NASA Astrophysics Data System (ADS)

Benet, Eduard; Lostec, Guillaume; Pellegrino, John; Vernerey, Franck

2018-04-01

The transport of micron-sized particles such as bacteria, cells, or synthetic lipid vesicles through porous spaces is a process relevant to drug delivery, separation systems, or sensors, to cite a few examples. Often, the motion of these particles depends on their ability to squeeze through small constrictions, making their capacity to deform an important factor for their permeation. However, it is still unclear how the mechanical behavior of these particles affects collective transport through porous networks. To address this issue, we present a method to reconcile the pore-scale mechanics of the particles with the Darcy scale to understand the motion of a deformable particle through a porous network. We first show that particle transport is governed by a mechanical instability occurring at the pore scale, which leads to a binary permeation response on each pore. Then, using the principles of directed bond percolation, we are able to link this microscopic behavior to the probability of permeating through a random porous network. We show that this instability, together with network uniformity, are key to understanding the nonlinear permeation of particles at a given pressure gradient. The results are then summarized by a phase diagram that predicts three distinct permeation regimes based on particle properties and the randomness of the pore network.

Calculation of load-bearing capacity of prestressed reinforced concrete trusses by the finite element method

NASA Astrophysics Data System (ADS)

Agapov, Vladimir; Golovanov, Roman; Aidemirov, Kurban

2017-10-01

The technique of calculation of prestressed reinforced concrete trusses with taking into account geometrical and physical nonlinearity is considered. As a tool for solving the problem, the finite element method has been chosen. Basic design equations and methods for their solution are given. It is assumed that there are both a prestressed and nonprestressed reinforcement in the bars of the trusses. The prestress is modeled by setting the temperature effect on the reinforcement. The ways of taking into account the physical and geometrical nonlinearity for bars of reinforced concrete trusses are considered. An example of the analysis of a flat truss is given and the behavior of the truss on various stages of its loading up to destruction is analyzed. A program for the analysis of flat and spatial concrete trusses taking into account the nonlinear deformation is developed. The program is adapted to the computational complex PRINS. As a part of this complex it is available to a wide range of engineering, scientific and technical workers

TRUST84. Sat-Unsat Flow in Deformable Media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narasimhan, T.N.

1984-11-01

TRUST84 solves for transient and steady-state flow in variably saturated deformable media in one, two, or three dimensions. It can handle porous media, fractured media, or fractured-porous media. Boundary conditions may be an arbitrary function of time. Sources or sinks may be a function of time or of potential. The theoretical model considers a general three-dimensional field of flow in conjunction with a one-dimensional vertical deformation field. The governing equation expresses the conservation of fluid mass in an elemental volume that has a constant volume of solids. Deformation of the porous medium may be nonelastic. Permeability and the compressibility coefficientsmore » may be nonlinearly related to effective stress. Relationships between permeability and saturation with pore water pressure in the unsaturated zone may be characterized by hysteresis. The relation between pore pressure change and effective stress change may be a function of saturation. The basic calculational model of the conductive heat transfer code TRUMP is applied in TRUST84 to the flow of fluids in porous media. The model combines an integrated finite difference algorithm for numerically solving the governing equation with a mixed explicit-implicit iterative scheme in which the explicit changes in potential are first computed for all elements in the system, after which implicit corrections are made only for those elements for which the stable time-step is less than the time-step being used. Time-step sizes are automatically controlled to optimize the number of iterations, to control maximum change to potential during a time-step, and to obtain desired output information. Time derivatives, estimated on the basis of system behavior during the two previous time-steps, are used to start the iteration process and to evaluate nonlinear coefficients. Both heterogeneity and anisotropy can be handled.« less

Rheological behavior of the crust and mantle in subduction zones in the time-scale range from earthquake (minute) to mln years inferred from thermomechanical model and geodetic observations

NASA Astrophysics Data System (ADS)

Sobolev, Stephan; Muldashev, Iskander

2016-04-01

The key achievement of the geodynamic modelling community greatly contributed by the work of Evgenii Burov and his students is application of "realistic" mineral-physics based non-linear rheological models to simulate deformation processes in crust and mantle. Subduction being a type example of such process is an essentially multi-scale phenomenon with the time-scales spanning from geological to earthquake scale with the seismic cycle in-between. In this study we test the possibility to simulate the entire subduction process from rupture (1 min) to geological time (Mln yr) with the single cross-scale thermomechanical model that employs elasticity, mineral-physics constrained non-linear transient viscous rheology and rate-and-state friction plasticity. First we generate a thermo-mechanical model of subduction zone at geological time-scale including a narrow subduction channel with "wet-quartz" visco-elasto-plastic rheology and low static friction. We next introduce in the same model classic rate-and state friction law in subduction channel, leading to stick-slip instability. This model generates spontaneous earthquake sequence. In order to follow in details deformation process during the entire seismic cycle and multiple seismic cycles we use adaptive time-step algorithm changing step from 40 sec during the earthquake to minute-5 year during postseismic and interseismic processes. We observe many interesting deformation patterns and demonstrate that contrary to the conventional ideas, this model predicts that postseismic deformation is controlled by visco-elastic relaxation in the mantle wedge already since hour to day after the great (M>9) earthquakes. We demonstrate that our results are consistent with the postseismic surface displacement after the Great Tohoku Earthquake for the day-to-4year time range.

Dual-phase steel sheets under cyclic tension-compression to large strains: Experiments and crystal plasticity modeling

NASA Astrophysics Data System (ADS)

Zecevic, Milovan; Korkolis, Yannis P.; Kuwabara, Toshihiko; Knezevic, Marko

2016-11-01

In this work, we develop a physically-based crystal plasticity model for the prediction of cyclic tension-compression deformation of multi-phase materials, specifically dual-phase (DP) steels. The model is elasto-plastic in nature and integrates a hardening law based on statistically stored dislocation density, localized hardening due to geometrically necessary dislocations (GNDs), slip-system-level kinematic backstresses, and annihilation of dislocations. The model further features a two level homogenization scheme where the first level is the overall response of a two-phase polycrystalline aggregate and the second level is the homogenized response of the martensite polycrystalline regions. The model is applied to simulate a cyclic tension-compression-tension deformation behavior of DP590 steel sheets. From experiments, we observe that the material exhibits a typical decreasing hardening rate during forward loading, followed by a linear and then a non-linear unloading upon the load reversal, the Bauschinger effect, and changes in hardening rate during strain reversals. To predict these effects, we identify the model parameters using a portion of the measured data and validate and verify them using the remaining data. The developed model is capable of predicting all the particular features of the cyclic deformation of DP590 steel, with great accuracy. From the predictions, we infer and discuss the effects of GNDs, the backstresses, dislocation annihilation, and the two-level homogenization scheme on capturing the cyclic deformation behavior of the material.

Investigation of a mathematical model of the system of electro-optical sensors for monitoring nonlinear surfaces

NASA Astrophysics Data System (ADS)

Petrochenko, Andrew V.; Konyakhin, Igor A.

2015-06-01

Actually during construction of the high building actively are used objects of various nonlinear surface, for example, sinuous (parabolic or hyperbolic) roofs of the sport complexes that require automatic deformation control [1,2,3,4]. This type of deformation has character of deflection that is impossible to monitor objectively with just one optoelectronic sensor (which is fixed on this surface). In this article is described structure of remote optoelectronic sensor, which is part of the optoelectronic monitoring system of nonlinear surface, and mathematical transformation of exterior orientation sensor elements in the coordinates of control points.

A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

NASA Technical Reports Server (NTRS)

Shay, R. M., Jr.; Caruthers, J. M.

1987-01-01

Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.

Mechanical Behavior of AZ31B Mg Alloy Sheets under Monotonic and Cyclic Loadings at Room and Moderately Elevated Temperatures

PubMed Central

Nguyen, Ngoc-Trung; Seo, Oh Suk; Lee, Chung An; Lee, Myoung-Gyu; Kim, Ji-hoon; Kim, Heon Young

2014-01-01

Large-strain monotonic and cyclic loading tests of AZ31B magnesium alloy sheets were performed with a newly developed testing system, at different temperatures, ranging from room temperature to 250 °C. Behaviors showing significant twinning during initial in-plane compression and untwinning in subsequent tension at and slightly above room temperature were recorded. Strong yielding asymmetry and nonlinear hardening behavior were also revealed. Considerable Bauschinger effects, transient behavior, and variable permanent softening responses were observed near room temperature, but these were reduced and almost disappeared as the temperature increased. Different stress–strain responses were inherent to the activation of twinning at lower temperatures and non-basal slip systems at elevated temperatures. A critical temperature was identified to account for the transition between the twinning-dominant and slip-dominant deformation mechanisms. Accordingly, below the transition point, stress–strain curves of cyclic loading tests exhibited concave-up shapes for compression or compression following tension, and an unusual S-shape for tension following compression. This unusual shape disappeared when the temperature was above the transition point. Shrinkage of the elastic range and variation in Young’s modulus due to plastic strain deformation during stress reversals were also observed. The texture-induced anisotropy of both the elastic and plastic behaviors was characterized experimentally. PMID:28788514

DYCAST: A finite element program for the crash analysis of structures

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Winter, R.; Ogilvie, P.

1987-01-01

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

Buckling and postbuckling behavior of square compression-loaded graphite-epoxy plates with circular cutouts

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

1990-01-01

Results are presented for unidirectional (0, 10)(sub s) and (90,10)(sub s) plates, ((0/90)(sub 5)(sub s)) plates, and for aluminum plates. Results are also presented for ((+/- theta)(sub 6)(sub s)) angle-ply plates for values of theta = 30, 45, and 60 degrees. The results indicate that the change in axial stiffness of a plate at buckling is strongly dependent upon cutout size and plate orthotropy. The presence of a cutout gives rise to an internal load distribution that changes, sometimes dramatically, as a function of cutout size coupled with the plate orthotropy. In the buckled state, the role of orthotropy becomes more significant since bending in addition to membrane orthotropy is present. Most of the plates with cutouts exhibited less postbuckling stiffness than the corresponding plate without a cutout, and the postbuckling stiffness decreased with increasing cutout size. However, some of the highly orthotropic plates with cutouts exhibited more postbuckling stiffness than the corresponding plate without a cutout. These results suggest the possibility of tailoring the cutout size and the stacking sequence of a composite plate to optimize postbuckling stiffness. It was found that plates with large radius cutouts do exhibit some postbuckling strength. The results also indicate that a cutout can influence modal interaction in a plate. Specifically, results are presented that show a plate with a relatively small cutout buckling at a higher load than the corresponding plate without a cutout, due to modal interaction. Other results are presented that indicate the presence of nonlinear prebuckling deformations, due to material nonlinearity, in the angle-ply plates with theta = 45 and 60 degrees. The nonlinear prebuckling deformations are more pronounced in the plates with theta = 45 degrees and become even more pronounced as the cutout size increases. Results are also presented that show how load-path eccentricity due to improper machining of the test specimens affects the buckling behavior. Some of the plates with cutouts and eccentricity exhibited a snap-through type of buckling behavior.

Adagio 4.20 User’s Guide

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spencer, Benjamin Whiting; Crane, Nathan K.; Heinstein, Martin W.

2011-03-01

Adagio is a Lagrangian, three-dimensional, implicit code for the analysis of solids and structures. It uses a multi-level iterative solver, which enables it to solve problems with large deformations, nonlinear material behavior, and contact. It also has a versatile library of continuum and structural elements, and an extensive library of material models. Adagio is written for parallel computing environments, and its solvers allow for scalable solutions of very large problems. Adagio uses the SIERRA Framework, which allows for coupling with other SIERRA mechanics codes. This document describes the functionality and input structure for Adagio.

Analysis of knitted fabric reinforced flexible composites and applications in thermoforming

NASA Astrophysics Data System (ADS)

Bekisli, Burak

In this study, large deformation behavior of knitted fabric reinforced composites is investigated. In order to fully utilize the unique stretchability of knitted fabric reinforcements, elastomeric materials are used as the matrix material, resulting in "flexible composites" capable of reaching several hundred percent stretch before failing. These non-traditional composites are ideal candidates for many engineering applications where large deformation is desired, including energy/impact absorption and novel forming processes. A multi-level nonlinear finite element (FE) procedure is developed to analyze the deformation behavior of plain weft-knitted fabrics and the composites derived from these materials. The hierarchy of the model is composed of a 3D unit cell analysis (micro/meso-scale) and a 2D global analysis (macro scale). Using results from different numerical experiments performed in the micro/meso scale, a mechanical behavior database of knit fabric geometries is constructed, both for the uniaxial and biaxial stretch cases. Through an optimization procedure, these results are used to determine the mechanical properties of nonlinear truss elements needed for modeling in the macro scale. A hexagonal honeycomb structure, which closely resembles the knit fabric architecture, is formed using these nonlinear trusses. This truss structure is then used to efficiently model a large number of loops generally found in a fabric. Results from uniaxial experimental measurements are presented for knitted fabrics to validate the FE model. Appropriate hyperelastic material models are determined for the elastomeric matrix, using a curve fit to experimental data. Examples of raw fabric and composite deformation simulations in the global scale are presented in this study. Two types of composites are studied experimentally and numerically: (1) knitted fabric embedded in an elastomeric medium, and (2) the sandwich type composites with elastomeric skins and fabric core. The strain energy dissipation is found to be superior in the latter case, since yarns are not restricted by the elastomer. In addition, yarns used in this type of composite move to effectively align along the load direction, yielding a better utilization of the fibers' high axial stiffness. Fabrication methods, including novel techniques involving twin-sheet thermoforming, for both types of composites are discussed. Tensile test results for glassfiber reinforced, TPE/polyurea based specimens are also presented. Innovative concepts related to the thermoforming process are also investigated using the developed numerical model. It is shown that some of the most critical problems in this forming process, such as non-uniform thickness distribution in the final part and the sensitivity of part quality to minor thermal variations, can be beneficially addressed using carefully "tailored" knit fabrics. Common thermoformed part geometries, such as a 3D box corner and a long U-shaped channel, are studied in numerical simulations to illustrate the effects of knitted fabric reinforcements on the stabilization of the forming process.

Compression behavior of delaminated composite plates

NASA Technical Reports Server (NTRS)

Peck, Scott O.; Springer, George S.

1989-01-01

The response of delaminated composite plates to compressive in-plane loads was investigated. The delaminated region may be either circular or elliptical, and may be located between any two plies of the laminate. For elliptical delaminations, the axes of the ellipse may be arbitrarily oriented with respect to the applied loads. A model was developed that describes the stresses, strains, and deformation of the sublaminate created by the delamination. The mathematical model is based on a two dimensional nonlinear plate theory that includes the effects of transverse shear deformation. The model takes into account thermal and moisture induced strains, transverse pressures acting on the sublaminate, and contact between the sublaminate and plate. The solution technique used is the Ritz method. A computationally efficient computer implementation of the model was developed. The code can be used to predict the nonlinear-load-strain behavior of the sublaminate including the buckling load, postbuckling behavior, and the onset of delamination growth. The accuracy of the code was evaluated by comparing the model results to benchmark analytical solutions. A series of experiments was conducted on Fiberite T300/976 graphite/epoxy laminates bonded to an aluminum honeycomb core forming a sandwich panel. Either circles or ellipses made from Teflon film were embedded in the laminates, simulating the presence of a delamination. Each specimen was loaded in compression and the strain history of the sublaminate was recorded far into the postbuckling regime. The extent of delamination growth was evaluated by C-scan examination of each specimen. The experimental data were compared to code predictions. The code was found to describe the data with reasonable accuracy. A sensitivity study examined the relative importance of various material properties, the delamination dimensions, the contact model, the transverse pressure differential, the critical strain energy release rate, and the relative growth direction on the buckling load, the postbuckling behavior, and the growth load of the sublaminate.

Compressive deformation of a single microcapsule

NASA Astrophysics Data System (ADS)

Liu, K. K.; Williams, D. R.; Briscoe, B. J.

1996-12-01

This paper reports an experimental and theoretical study of the compressive behavior of single microcapsules; that is, liquid-filled cellular entities (approximately 65 μm in diameter) with a thin polymeric membrane wall. An experimental technique which allows the simultaneous measurement of both the compressive displacement and the reaction forces of individual microcapsules deformed between two parallel plates up to a dimensionless approach [(compressive displacement)/(initial particle diameter)] of 60% is described. The corresponding major geometric parameters of the deformed microcapsule, such as central lateral extension as well as the failure phenomena, are reported and recorded through a microscopic visualization system. The elastic modulus, the bursting strength of the membrane, and the pressure difference across the membrane are computed by using a theoretical analysis which is also presented in this paper. This theoretical model, which was developed by Feng and Yang [

New intrinsic mechanism on gum-like superelasticity of multifunctional alloys

PubMed Central

Liu, Jia-Peng; Wang, Yan-Dong; Hao, Yu-Lin; Wang, Yunzhi; Nie, Zhi-Hua; Wang, Dong; Ren, Yang; Lu, Zhao-Ping; Wang, Jinguo; Wang, Haoliang; Hui, Xidong; Lu, Ning; Kim, Moon J.; Yang, Rui

2013-01-01

Ti-Nb-based Gum Metals exhibit extraordinary superelasticity with ultralow elastic modulus, superior strength and ductility, and a peculiar dislocation-free deformation behavior, most of which challenge existing theories of crystal strength. Additionally, this kind of alloys actually displays even more anomalous mechanical properties, such as the non-linear superelastic behavior, accompanied by a pronounced tension-to-compression asymmetry, and large ductility with a low Poisson's ratio. Two main contradictory arguments exist concerning the deformation mechanisms of those alloys, i.e., formation of reversible nanodisturbance and reversible martensitic transformation. Herein we used the in-situ synchrotron high-energy X-ray scattering technique to reveal the novel intrinsic physical origin of all anomalous mechanical properties of the Ti-24Nb-4Zr-8Sn-0.10O alloy, a typical gum-like metal. Our experiments provide direct evidence on two different kinds of interesting, stress-induced, reversible nanoscale martensitic transitions, i.e., the austenitic regions with B2 structure transform to α″ martensite and those with BCC structure transform to δ martensite. PMID:23831664

TWO-LAYER MODEL FOR PULL-OUT BEHAVIOR OF POST-INSTALLED ANCHOR

NASA Astrophysics Data System (ADS)

Saleem, Muhammad; Tsubaki, Tatsuya

A new two-layer anchor-infill assembly structure for the post-installed anchor is introduced with the analytical model to simulate its pull-out deformational response. The post-installed anchor is such that used in strengthening techniques for reinforced concrete structures. The properties of the infill material used for post-installed anchor are characterized by nonlinear interfaces. Because of the mechanical properties of the infill layer the existing pull-out model of deformed bars is not applicable in this case. Interfacial de-bonding is examined using energy criterion and strength criterion. The effect of the interface properties such as stiffness and strength on the pull-out behavior of a post-installed anchor is investigated. Using sensitivity analysis, the effect of these parameters on load-displacement curve, shear stress distribution, de-bonded length and damage to the surrounding concrete is clarified. Then, the optimum combination of these parameters is presented. It is confirmed that the elastic modulus of infill should be large to reduce the pull-out displacement and the increase of the shear strength of infill makes the pull-out load larger.

Twinning-detwinning behavior during cyclic deformation of magnesium alloy

DOE PAGES

Lee, Soo Yeol; Wang, Huamiao; Gharghouri, Michael A.

2015-05-26

In situ neutron diffraction has been used to examine the deformation mechanisms of a precipitation-hardened and extruded Mg-8.5wt.%Al alloy subjected to (i) compression followed by reverse tension (texture T1) and (ii) tension followed by reverse compression (texture T2). Two starting textures are used: (1) as-extruded texture, T1, in which the basal pole of most grains is normal to the extrusion axis and a small portion of grains are oriented with the basal pole parallel to the extrusion axis; (2) a reoriented texture, T2, in which the basal pole of most grains is parallel to the extrusion axis. For texture T1,more » the onset of extension twinning corresponds well with the macroscopic elastic-plastic transition during the initial compression stage. The non-linear macroscopic stress/strain behavior during unloading after compression is more significant than during unloading after tension. For texture T2, little detwinning occurs after the initial tension stage, but almost all of the twinned volumes are detwinned during loading in reverse compression.« less

A review on shape memory alloys with applications to morphing aircraft

NASA Astrophysics Data System (ADS)

Barbarino, S.; Saavedra Flores, E. I.; Ajaj, R. M.; Dayyani, I.; Friswell, M. I.

2014-06-01

Shape memory alloys (SMAs) are a unique class of metallic materials with the ability to recover their original shape at certain characteristic temperatures (shape memory effect), even under high applied loads and large inelastic deformations, or to undergo large strains without plastic deformation or failure (super-elasticity). In this review, we describe the main features of SMAs, their constitutive models and their properties. We also review the fatigue behavior of SMAs and some methods adopted to remove or reduce its undesirable effects. SMAs have been used in a wide variety of applications in different fields. In this review, we focus on the use of shape memory alloys in the context of morphing aircraft, with particular emphasis on variable twist and camber, and also on actuation bandwidth and reduction of power consumption. These applications prove particularly challenging because novel configurations are adopted to maximize integration and effectiveness of SMAs, which play the role of an actuator (using the shape memory effect), often combined with structural, load-carrying capabilities. Iterative and multi-disciplinary modeling is therefore necessary due to the fluid-structure interaction combined with the nonlinear behavior of SMAs.

Spheroidal and conical shapes of ferrofluid-filled capsules in magnetic fields

NASA Astrophysics Data System (ADS)

Wischnewski, Christian; Kierfeld, Jan

2018-04-01

We investigate the deformation of soft spherical elastic capsules filled with a ferrofluid in external uniform magnetic fields at fixed volume by a combination of numerical and analytical approaches. We develop a numerical iterative solution strategy based on nonlinear elastic shape equations to calculate the stretched capsule shape numerically and a coupled finite element and boundary element method to solve the corresponding magnetostatic problem and employ analytical linear response theory, approximative energy minimization, and slender-body theory. The observed deformation behavior is qualitatively similar to the deformation of ferrofluid droplets in uniform magnetic fields. Homogeneous magnetic fields elongate the capsule and a discontinuous shape transition from a spheroidal shape to a conical shape takes place at a critical field strength. We investigate how capsule elasticity modifies this hysteretic shape transition. We show that conical capsule shapes are possible but involve diverging stretch factors at the tips, which gives rise to rupture for real capsule materials. In a slender-body approximation we find that the critical susceptibility above which conical shapes occur for ferrofluid capsules is the same as for droplets. At small fields capsules remain spheroidal and we characterize the deformation of spheroidal capsules both analytically and numerically. Finally, we determine whether wrinkling of a spheroidal capsule occurs during elongation in a magnetic field and how it modifies the stretching behavior. We find the nontrivial dependence between the extent of the wrinkled region and capsule elongation. Our results can be helpful in quantitatively determining capsule or ferrofluid material properties from magnetic deformation experiments. All results also apply to elastic capsules filled with a dielectric liquid in an external uniform electric field.

NASA/FAA general aviation crash dynamics program - An update

NASA Technical Reports Server (NTRS)

Hayduk, R. J.; Thomson, R. G.; Carden, H. D.

1979-01-01

Work in progress in the NASA/FAA General Aviation Crash Dynamics Program for the development of technology for increased crash-worthiness and occupant survivability of general aviation aircraft is presented. Full-scale crash testing facilities and procedures are outlined, and a chronological summary of full-scale tests conducted and planned is presented. The Plastic and Large Deflection Analysis of Nonlinear Structures and Modified Seat Occupant Model for Light Aircraft computer programs which form part of the effort to predict nonlinear geometric and material behavior of sheet-stringer aircraft structures subjected to large deformations are described, and excellent agreement between simulations and experiments is noted. The development of structural concepts to attenuate the load transmitted to the passenger through the seats and subfloor structure is discussed, and an apparatus built to test emergency locator transmitters in a realistic environment is presented.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Nonlinear dynamic modeling of rotor system supported by angular contact ball bearings

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Zhou, Daning

2017-02-01

In current bearing dynamic models, the displacement coordinate relations are usually utilized to approximately obtain the contact deformations between the rolling element and raceways, and then the nonlinear restoring forces of the rolling bearing could be calculated accordingly. Although the calculation efficiency is relatively higher, the accuracy is lower as the contact deformations should be solved through iterative analysis. Thus, an improved nonlinear dynamic model is presented in this paper. Considering the preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication, load distribution analysis is solved iteratively to more accurately obtain the contact deformations and angles between the rolling balls and raceways. The bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. Dynamic tests upon a typical rotor system supported by two angular contact ball bearings are conducted to verify the model. Through comparisons, the differences between the nonlinear dynamic model and current models are also pointed out. The effects of axial preload, rotor eccentricity and inner/outer waviness amplitudes on the dynamic response are discussed in detail.

Nonlinear Phase Field Theory for Fracture and Twinning with Analysis of Simple Shear

DTIC Science & Technology

2015-09-01

elasticity; crystal; shear deformation 1. Introduction Cleavage fracture and deformation twinning are two fundamental inelastic deformation mechanisms that...stress [2,3]. Both of these anisotropic mechanisms involve deformation on specific planes (the cleavage plane for fracture or the habit plane for...be the first phase field theory accounting for both fracture and deformation twinning wherein each mechanism is repre- sented by a distinct-order

Hysteresis modeling and identification of a dielectric electro-active polymer actuator using an APSO-based nonlinear Preisach NARX fuzzy model

NASA Astrophysics Data System (ADS)

Truong, Bui Ngoc Minh; Nam, Doan Ngoc Chi; Ahn, Kyoung Kwan

2013-09-01

Dielectric electro-active polymer (DEAP) materials are attractive since they are low cost, lightweight and have a large deformation capability. They have no operating noise, very low electric power consumption and higher performance and efficiency than competing technologies. However, DEAP materials generally have strong hysteresis as well as uncertain and nonlinear characteristics. These disadvantages can limit the efficiency in the use of DEAP materials. To address these limitations, this research will present the combination of the Preisach model and the dynamic nonlinear autoregressive exogenous (NARX) fuzzy model-based adaptive particle swarm optimization (APSO) identification algorithm for modeling and identification of the nonlinear behavior of one typical type of DEAP actuator. Firstly, open loop input signals are applied to obtain nonlinear features and to investigate the responses of the DEAP actuator system. Then, a Preisach model can be combined with a dynamic NARX fuzzy structure to estimate the tip displacement of a DEAP actuator. To optimize all unknown parameters of the designed combination, an identification scheme based on a least squares method and an APSO algorithm is carried out. Finally, experimental validation research is carefully completed, and the effectiveness of the proposed model is evaluated by employing various input signals.

An Investigation of a Vertical Test Method for Large Deformation Bending of High Strain Composite Laminates

NASA Astrophysics Data System (ADS)

Herrmann, Kelsey M.

Research to date indicates that traditional composite material failure analysis methods are not appropriate for thin laminates in flexure. Thin composite structures subjected to large bending deformations often attain significantly higher strain-to-failure than previously anticipated tensile and compression coupon test data and linear material model assumption predict. At NASA Langley Research Center, a new bend test method is being developed for High Strain Composite (HSC) structures. This method provides an adequate approximation of a pure moment, large deformation bend test for thin-ply, high strain composites to analyze the large strain flexure response of the laminates. The objective of this research was to further develop this new test method to measure the true bending stiffness and strain-to-failure of high strain composite materials. Of primary importance is the ability to characterize composite laminates that are of interest for current NASA deployable structures in both materials and layups. Two separate testing campaigns were performed for the development of the testing procedure. Initially six laminates were bend tested in three different fiber orientations. These laminates were some combination of unidirectional intermediate modulus (IM) carbon, high tenacity (HT) carbon plain weave, and astroquartz plain weave composite materials. The second test campaign was performed as a more detailed look into the simplest composite laminates at thicknesses that better represented deployable boom structures. The second campaign tested three basic, thinner laminates, again in three different fiber orientations. All testing was monotonic loading to failure. The thickness of the laminates tested ranged from 0.166mm (campaign 2) to 0.45mm (campaign 1). The measured strains at failure for the unidirectional material were approximately 2.1% and 1.4% at the compression and tension sides, respectively, failing as fiber tensile fracture. Both of these values differ from what would be expected from considering much thicker coupons tested under pure compression and tension, that show a strain-to-failure of 1.0-1.1% and 1.6-1.7%, respectively. The significant differences in strain values obtained at the outer surfaces of the coupon is thought to be related to the shift in neutral axis that the specimen experiences during the large deformation bending test as a result of fiber material nonlinearities at higher strains. The vertical test nature of the CBT when compared to other test methods proves to be helpful for visually capturing with Digital Image Correlation the distinct behavior of the flexure on both the compressive and tensile sides. It was found that the thinner the laminate tested, the more confirmation of a nonlinear response of this classification of composites. The moment versus curvature curves were predominantly nonlinear resulting in a near linear bending stiffness versus curvature response. At these large strains, carbon fibers are highly nonlinear resulting in the laminate flexure modulus increasing by up to 5x. The theoretical bending stiffness values calculated using Classical Lamination Theory analysis are within small differences with respect to the experimentally measured values: errors of approximately 5-10% for both D11 and D22. The error between the finite element model computed strain response and the experimental values was on average around 22%, with 35% of the laminates and orientation having errors less than 7%. Comparison between CLT, FEA, and experimentation show that the Column Bend Test appears to be a promising candidate for characterization of large deformation bending behavior of thin-ply high strain composite laminates.

Nonlinear microrheology and molecular imaging to map microscale deformations of entangled DNA networks

NASA Astrophysics Data System (ADS)

Wu, Tsai-Chin; Anderson, Rae

We use active microrheology coupled to single-molecule fluorescence imaging to elucidate the microscale dynamics of entangled DNA. DNA naturally exists in a wide range of lengths and topologies, and is often confined in cell nucleui, forming highly concentrated and entangled biopolymer networks. Thus, DNA is the model polymer for understanding entangled polymer dynamics as well as the crowded environment of cells. These networks display complex viscoelastic properties that are not well understood, especially at the molecular-level and in response to nonlinear perturbations. Specifically, how microscopic stresses and strains propagate through entangled networks, and what molecular deformations lead to the network stress responses are unknown. To answer these important questions, we optically drive a microsphere through entangled DNA, perturbing the system far from equilibrium, while measuring the resistive force the DNA exerts on the bead during and after bead motion. We simultaneously image single fluorescent-labeled DNA molecules throughout the network to directly link the microscale stress response to molecular deformations. We characterize the deformation of the network from the molecular-level to the mesoscale, and map the stress propagation throughout the network. We further study the impact of DNA length (11 - 115 kbp) and topology (linear vs ring DNA) on deformation and propagation dynamics, exploring key nonlinear features such as tube dilation and power-law relaxation.

Brain tissue deforms similarly to filled elastomers and follows consolidation theory

NASA Astrophysics Data System (ADS)

Franceschini, G.; Bigoni, D.; Regitnig, P.; Holzapfel, G. A.

2006-12-01

Slow, large deformations of human brain tissue—accompanying cranial vault deformation induced by positional plagiocephaly, occurring during hydrocephalus, and in the convolutional development—has surprisingly received scarce mechanical investigation. Since the effects of these deformations may be important, we performed a systematic series of in vitro experiments on human brain tissue, revealing the following features. (i) Under uniaxial (quasi-static), cyclic loading, brain tissue exhibits a peculiar nonlinear mechanical behaviour, exhibiting hysteresis, Mullins effect and residual strain, qualitatively similar to that observed in filled elastomers. As a consequence, the loading and unloading uniaxial curves have been found to follow the Ogden nonlinear elastic theory of rubber (and its variants to include Mullins effect and permanent strain). (ii) Loaded up to failure, the "shape" of the stress/strain curve qualitatively changes, evidencing softening related to local failure. (iii) Uniaxial (quasi-static) strain experiments under controlled drainage conditions provide the first direct evidence that the tissue obeys consolidation theory involving fluid migration, with properties similar to fine soils, but having much smaller volumetric compressibility. (iv) Our experimental findings also support the existence of a viscous component of the solid phase deformation. Brain tissue should, therefore, be modelled as a porous, fluid-saturated, nonlinear solid with very small volumetric (drained) compressibility.

How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

PubMed Central

2017-01-01

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales. PMID:29225507

Modeling and control of a dielectric elastomer actuator

NASA Astrophysics Data System (ADS)

Gupta, Ujjaval; Gu, Guo-Ying; Zhu, Jian

2016-04-01

The emerging field of soft robotics offers the prospect of applying soft actuators as artificial muscles in the robots, replacing traditional actuators based on hard materials, such as electric motors, piezoceramic actuators, etc. Dielectric elastomers are one class of soft actuators, which can deform in response to voltage and can resemble biological muscles in the aspects of large deformation, high energy density and fast response. Recent research into dielectric elastomers has mainly focused on issues regarding mechanics, physics, material designs and mechanical designs, whereas less importance is given to the control of these soft actuators. Strong nonlinearities due to large deformation and electromechanical coupling make control of the dielectric elastomer actuators challenging. This paper investigates feed-forward control of a dielectric elastomer actuator by using a nonlinear dynamic model. The material and physical parameters in the model are identified by quasi-static and dynamic experiments. A feed-forward controller is developed based on this nonlinear dynamic model. Experimental evidence shows that this controller can control the soft actuator to track the desired trajectories effectively. The present study confirms that dielectric elastomer actuators are capable of being precisely controlled with the nonlinear dynamic model despite the presence of material nonlinearity and electromechanical coupling. It is expected that the reported results can promote the applications of dielectric elastomer actuators to soft robots or biomimetic robots.

Hydrostatic Stress Effects Incorporated Into the Analysis of the High-Strain-Rate Deformation of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.

2003-01-01

Procedures for modeling the effect of high strain rate on composite materials are needed for designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and strain rate dependence of the composite response is primarily due to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. An experimental program has been carried out through a university grant with the Ohio State University to obtain tensile and shear deformation data for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. This information has been used at the NASA Glenn Research Center to develop, characterize, and correlate a material model in which the strain rate dependence and nonlinearity (including hydrostatic stress effects) of the polymer are correctly analyzed. To obtain the material data, Glenn s researchers designed and fabricated test specimens of a representative toughened epoxy resin. Quasi-static tests at low strain rates and split Hopkinson bar tests at high strain rates were then conducted at the Ohio State University. The experimental data confirmed the strong effects of strain rate on both the tensile and shear deformation of the polymer. For the analytical model, Glenn researchers modified state variable constitutive equations previously used for the viscoplastic analysis of metals to allow for the analysis of the nonlinear, strain-rate-dependent polymer deformation. Specifically, we accounted for the effects of hydrostatic stresses. An important discovery in the course of this work was that the hydrostatic stress effects varied during the loading process, which needed to be accounted for within the constitutive equations. The model is characterized primarily by shear data, with tensile data used to characterize the hydrostatic stress effects.

Studies on Stress-Strain Relationships of Polymeric Materials Used in Space Applications

NASA Technical Reports Server (NTRS)

Jana, Sadhan C.; Freed, Alan

2002-01-01

A two-year research plan was undertaken in association with Polymers Branch, NASA Glenn Research Center, to carry out experimental and modeling work relating stress and strain behavior of polymeric materials, especially elastomers and vulcanized rubber. An experimental system based on MTS (Mechanical Testing and Simulation) A/T-4 test facility environment has been developed for a broader range of polymeric materials in addition to a design of laser compatible temperature control chamber for online measurements of various strains. Necessary material processing has been accomplished including rubber compounding and thermoplastic elastomer processing via injection molding. A broad suite of testing methodologies has been identified to reveal the complex non-linear mechanical behaviors of rubbery materials when subjected to complex modes of deformation. This suite of tests required the conceptualization, design and development of new specimen geometries, test fixtures, and test systems including development of a new laser based technique to measure large multi-axial deformations. Test data has been generated for some of these new fixtures and has revealed some complex coupling effects generated during multi-axial deformations. In addition, fundamental research has been conducted concerning the foundation principles of rubber thermodynamics and resulting theories of rubber elasticity. Studies have been completed on morphological properties of several thermoplastic elastomers. Finally, a series of steps have been identified to further advance the goals of NASA's ongoing effort.

Multiaxial mechanical properties and constitutive modeling of human adipose tissue: a basis for preoperative simulations in plastic and reconstructive surgery.

PubMed

Sommer, Gerhard; Eder, Maximilian; Kovacs, Laszlo; Pathak, Heramb; Bonitz, Lars; Mueller, Christoph; Regitnig, Peter; Holzapfel, Gerhard A

2013-11-01

A preoperative simulation of soft tissue deformations during plastic and reconstructive surgery is desirable to support the surgeon's planning and to improve surgical outcomes. The current development of constitutive adipose tissue models, for the implementation in multilayer computational frameworks for the simulation of human soft tissue deformations, has proved difficult because knowledge of the required mechanical parameters of fat tissue is limited. Therefore, for the first time, human abdominal adipose tissues were mechanically investigated by biaxial tensile and triaxial shear tests. The results of this study suggest that human abdominal adipose tissues under quasi-static and dynamic multiaxial loadings can be characterized as a nonlinear, anisotropic and viscoelastic soft biological material. The nonlinear and anisotropic features are consequences of the material's collagenous microstructure. The aligned collagenous septa observed in histological investigations causes the anisotropy of the tissue. A hyperelastic model used in this study was appropriate to represent the quasi-static multiaxial mechanical behavior of fat tissue. The constitutive parameters are intended to serve as a basis for soft tissue simulations using the finite element method, which is an apparent method for obtaining promising results in the field of plastic and reconstructive surgery. Copyright © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Three-dimensional Sponges with Super Mechanical Stability: Harnessing True Elasticity of Individual Carbon Nanotubes in Macroscopic Architectures

PubMed Central

Dai, Zhaohe; Liu, Luqi; Qi, Xiaoying; Kuang, Jun; Wei, Yueguang; Zhu, Hongwei; Zhang, Zhong

2016-01-01

Efficient assembly of carbon nanotube (CNT) based cellular solids with appropriate structure is the key to fully realize the potential of individual nanotubes in macroscopic architecture. In this work, the macroscopic CNT sponge consisting of randomly interconnected individual carbon nanotubes was grown by CVD, exhibiting a combination of super-elasticity, high strength to weight ratio, fatigue resistance, thermo-mechanical stability and electro-mechanical stability. To deeply understand such extraordinary mechanical performance compared to that of conventional cellular materials and other nanostructured cellular architectures, a thorough study on the response of this CNT-based spongy structure to compression is conducted based on classic elastic theory. The strong inter-tube bonding between neighboring nanotubes is examined, believed to play a critical role in the reversible deformation such as bending and buckling without structural collapse under compression. Based on in-situ scanning electron microscopy observation and nanotube deformation analysis, structural evolution (completely elastic bending-buckling transition) of the carbon nanotubes sponges to deformation is proposed to clarify their mechanical properties and nonlinear electromechanical coupling behavior. PMID:26732143

Viscoelastic effects on the actuation performance of a dielectric elastomer actuator under different equal, un-equal biaxial pre-stretches

NASA Astrophysics Data System (ADS)

Quang Tran, Danh; Li, Jin; Xuan, Fuzhen; Xiao, Ting

2018-06-01

Dielectric elastomers (DEs) are belonged to a group of polymers which cause a time-dependence deformation due to the effect of viscoelastic. In recent years, viscoelasticity has been accounted in the modeling in order to understand the complete electromechanical behavior of dielectric elastomer actuators (DEAs). In this paper, we investigate the actuation performance of a circular DEA under different equal, un-equal biaxial pre-stretches, based on a nonlinear rheological model. The theoretical results are validated by experiments, which verify the electromechanical constitutive equation of the DEs. The viscoelastic mechanical characteristic is analyzed by modeling simulation analysis and experimental to describe the influence of frequency, voltage, pre-stretch, and waveform on the actuation response of the actuator. Our study indicates that: The DEA with different equal or un-equal biaxial pre-stretches undergoes different actuation performance when subject to high voltage. Under an un-equal biaxial pre-stretch, the DEA deforms unequally and shows different deformation abilities in two directions. The relative creep strain behavior of the DEA due to the effect of viscoelasticity can be reduced by increasing pre-stretch ratio. Higher equal biaxial pre-stretch obtains larger deformation strain, improves actuation response time, and reduces the drifting of the equilibrium position in the dynamic response of the DEA when activated by step and period voltage, while increasing the frequency will inhibit the output stretch amplitude. The results in this paper can provide theoretical guidance and application reference for design and control of the viscoelastic DEAs.

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

NASA Technical Reports Server (NTRS)

Rodal, J. J. A.; Witmer, E. A.

1979-01-01

A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.

Introduction of non-linear elasticity models for characterization of shape and deformation statistics: application to contractility assessment of isolated adult cardiocytes.

PubMed

Bazan, Carlos; Hawkins, Trevor; Torres-Barba, David; Blomgren, Peter; Paolini, Paul

2011-08-22

We are exploring the viability of a novel approach to cardiocyte contractility assessment based on biomechanical properties of the cardiac cells, energy conservation principles, and information content measures. We define our measure of cell contraction as being the distance between the shapes of the contracting cell, assessed by the minimum total energy of the domain deformation (warping) of one cell shape into another. To guarantee a meaningful vis-à-vis correspondence between the two shapes, we employ both a data fidelity term and a regularization term. The data fidelity term is based on nonlinear features of the shapes while the regularization term enforces the compatibility between the shape deformations and that of a hyper-elastic material. We tested the proposed approach by assessing the contractile responses in isolated adult rat cardiocytes and contrasted these measurements against two different methods for contractility assessment in the literature. Our results show good qualitative and quantitative agreements with these methods as far as frequency, pacing, and overall behavior of the contractions are concerned. We hypothesize that the proposed methodology, once appropriately developed and customized, can provide a framework for computational cardiac cell biomechanics that can be used to integrate both theory and experiment. For example, besides giving a good assessment of contractile response of the cardiocyte, since the excitation process of the cell is a closed system, this methodology can be employed in an attempt to infer statistically significant model parameters for the constitutive equations of the cardiocytes.

Associative Flow Rule Used to Include Hydrostatic Stress Effects in Analysis of Strain-Rate-Dependent Deformation of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.

2004-01-01

designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and the strain-rate dependence of the composite response are due primarily to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. By applying micromechanics techniques along with given fiber properties, one can also determine the effects of the hydrostatic stresses in the polymer on the overall composite deformation response. First efforts to account for the hydrostatic stress effects in the composite deformation applied purely empirical methods that relied on composite-level data. In later efforts, to allow polymer properties to be characterized solely on the basis of polymer data, researchers at the NASA Glenn Research Center developed equations to model the polymers that were based on a non-associative flow rule, and efforts to use these equations to simulate the deformation of representative polymer materials were reasonably successful. However, these equations were found to have difficulty in correctly analyzing the multiaxial stress states found in the polymer matrix constituent of a composite material. To correct these difficulties, and to allow for the accurate simulation of the nonlinear strain-rate-dependent deformation analysis of polymer matrix composites, in the efforts reported here Glenn researchers reformulated the polymer constitutive equations from basic principles using the concept of an associative flow rule. These revised equations were characterized and validated in an experimental program carried out through a university grant with the Ohio State University, wherein tensile and shear deformation data were obtained for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. Tensile deformation data also were obtained over a variety of strain rates and fiber orientation angles for a representative polymer matrix composite composed using the polymer.

Prediction of bead area contact load at the tire-wheel interface using NASTRAN

NASA Technical Reports Server (NTRS)

Chen, C. H. S.

1982-01-01

The theoretical prediction of the bead area contact load at the tire wheel interface using NASTRAN is reported. The application of the linear code to a basically nonlinear problem results in excessive deformation of the structure and the tire-wheel contact conditions become impossible to achieve. A psuedo-nonlinear approach was adopted in which the moduli of the cord reinforced composite are increased so that the computed key deformations matched that of the experiment. Numerical results presented are discussed.

Free-vibration acoustic resonance of a nonlinear elastic bar

NASA Astrophysics Data System (ADS)

Tarumi, Ryuichi; Oshita, Yoshihito

2011-02-01

Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.

Loads and Deformations of Buckled Rectangular Plates. Degree awarded by Virginia Polytechnic Inst., Jun. 1958

NASA Technical Reports Server (NTRS)

Stein, Manuel

1959-01-01

The nonlinear large-deflection equations of von Karman for plates are converted into a set of linear equations by expanding the displacements Into a power series in terms of an arbitrary parameter. The postbuckling behavior of simply supported rectangular plates subjected to longitudinal compression and subject to a uniform temperature rise is investigated in detail by solving the first few of the equations. Experimental data are presented for the compression problem. Comparisons are made for total shortening and local strains and deflections which indicate good agreement between experimental and theoretical results.

Fermion localization on a split brane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chumbes, A. E. R.; Vasquez, A. E. O.; Hott, M. B.

2011-05-15

In this work we analyze the localization of fermions on a brane embedded in five-dimensional, warped and nonwarped, space-time. In both cases we use the same nonlinear theoretical model with a nonpolynomial potential featuring a self-interacting scalar field whose minimum energy solution is a soliton (a kink) which can be continuously deformed into a two-kink. Thus a single brane splits into two branes. The behavior of spin 1/2 fermions wave functions on the split brane depends on the coupling of fermions to the scalar field and on the geometry of the space-time.

Pretest predictions for the response of a 1:8-scale steel LWR containment building model to static overpressurization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clauss, D.B.

The analyses used to predict the behavior of a 1:8-scale model of a steel LWR containment building to static overpressurization are described and results are presented. Finite strain, large displacement, and nonlinear material properties were accounted for using finite element methods. Three-dimensional models were needed to analyze the penetrations, which included operable equipment hatches, personnel lock representations, and a constrained pipe. It was concluded that the scale model would fail due to leakage caused by large deformations of the equipment hatch sleeves. 13 refs., 34 figs., 1 tab.

Equilibrium softening of an enzyme explored with the DNA spring

NASA Astrophysics Data System (ADS)

Tseng, Chiao-Yu; Zocchi, Giovanni

2014-04-01

We explore enzyme mechanics using a system of two mechanically coupled biomolecules. Measurements of the mechanical modulation of enzymatic activity in a Luciferase—DNA chimera are presented. These are molecules where the enzyme is deformed by the action of a DNA spring. The response of the enzyme for different states of stress is examined. It is found that small changes in the stress cause large changes in activity. This nonlinear behavior is qualitatively interpreted as arising from a soft regime of the enzyme beyond linear elasticity. This soft regime may enable large conformational motion in enzymes.

Non-isothermal elastoviscoplastic analysis of planar curved beams

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1988-01-01

The development of a general mathematical model and solution methodologies, to examine the behavior of thin structural elements such as beams, rings, and arches, subjected to large nonisothermal elastoviscoplastic deformations is presented. Thus, geometric as well as material type nonlinearities of higher order are present in the analysis. For this purpose a complete true abinito rate theory of kinematics and kinetics for thin bodies, without any restriction on the magnitude of the transformation is presented. A previously formulated elasto-thermo-viscoplastic material constitutive law is employed in the analysis. The methodology is demonstrated through three different straight and curved beams problems.

Mechanics of inter-modal tunneling in nonlinear waveguides

NASA Astrophysics Data System (ADS)

Jiao, Weijian; Gonella, Stefano

2018-02-01

In this article, we investigate the mechanics of nonlinearly induced inter-modal energy tunneling between flexurally-dominated and axially-dominated modes in phononic waveguides. Special attention is devoted to elucidating the role played by the coupling between axial and flexural degrees of freedom in the determination of the available mode hopping conditions and the associated mechanisms of deformation. Waveguides offer an ideal test bed to investigate the mechanics of nonlinear energy tunneling, due to the fact that they naturally feature, even at low frequencies, families of modes (flexural and axial) that are intrinsically characterized by extreme complementarity. Moreover, thanks to their geometric simplicity, their behavior can be explained by resorting to intuitive structural mechanics models that effectively capture the dichotomy and interplay between flexural and axial mechanisms. After having delineated the fundamental mechanics of flexural-to-axial hopping using the benchmark example of a homogeneous structure, we adapt the analysis to the case of periodic waveguides, in which the complex dispersive behavior due to periodicity results in additional richness of mode hopping mechanisms. We finally extend the analysis to periodic waveguides with internal resonators, in which the availability of locally-resonant bandgaps implies the possibility to activate the resonators even at relatively low frequencies, thus increasing the degree of modal complementarity that is available in the acoustic range. In this context, inter-modal tunneling provides an unprecedented mechanism to transfer conspicuous packets of energy to the resonating microstructure.

Nonlinear probabilistic finite element models of laminated composite shells

NASA Technical Reports Server (NTRS)

Engelstad, S. P.; Reddy, J. N.

1993-01-01

A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.

Evaluation of on-line pulse control for vibration suppression in flexible spacecraft

NASA Technical Reports Server (NTRS)

Masri, Sami F.

1987-01-01

A numerical simulation was performed, by means of a large-scale finite element code capable of handling large deformations and/or nonlinear behavior, to investigate the suitability of the nonlinear pulse-control algorithm to suppress the vibrations induced in the Spacecraft Control Laboratory Experiment (SCOLE) components under realistic maneuvers. Among the topics investigated were the effects of various control parameters on the efficiency and robustness of the vibration control algorithm. Advanced nonlinear control techniques were applied to an idealized model of some of the SCOLE components to develop an efficient algorithm to determine the optimal locations of point actuators, considering the hardware on the SCOLE project as distributed in nature. The control was obtained from a quadratic optimization criterion, given in terms of the state variables of the distributed system. An experimental investigation was performed on a model flexible structure resembling the essential features of the SCOLE components, and electrodynamic and electrohydraulic actuators were used to investigate the applicability of the control algorithm with such devices in addition to mass-ejection pulse generators using compressed air.

Deforming black hole and cosmological solutions by quasiperiodic and/or pattern forming structures in modified and Einstein gravity

NASA Astrophysics Data System (ADS)

Bubuianu, Laurenţiu; Vacaru, Sergiu I.

2018-05-01

We elaborate on the anholonomic frame deformation method, AFDM, for constructing exact solutions with quasiperiodic structure in modified gravity theories, MGTs, and general relativity, GR. Such solutions are described by generic off-diagonal metrics, nonlinear and linear connections and (effective) matter sources with coefficients depending on all spacetime coordinates via corresponding classes of generation and integration functions and (effective) matter sources. There are studied effective free energy functionals and nonlinear evolution equations for generating off-diagonal quasiperiodic deformations of black hole and/or homogeneous cosmological metrics. The physical data for such functionals are stated by different values of constants and prescribed symmetries for defining quasiperiodic structures at cosmological scales, or astrophysical objects in nontrivial gravitational backgrounds some similar forms as in condensed matter physics. It is shown how quasiperiodic structures determined by general nonlinear, or additive, functionals for generating functions and (effective) sources may transform black hole like configurations into cosmological metrics and inversely. We speculate on possible implications of quasiperiodic solutions in dark energy and dark matter physics. Finally, it is concluded that geometric methods for constructing exact solutions consist an important alternative tool to numerical relativity for investigating nonlinear effects in astrophysics and cosmology.

Nonlinear flow response of soft hair beds

NASA Astrophysics Data System (ADS)

Alvarado, José; Comtet, Jean; de Langre, Emmanuel; Hosoi, A. E.

2017-10-01

We are `hairy' on the inside: beds of passive fibres anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. These hairs are soft enough to deform in response to stresses from fluid flows. Yet fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem that is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear-driven Stokes flows. We characterize this system with a theoretical model that accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers towards the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter that controls nonlinear behaviour. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps.

Study of non-linear deformation of vocal folds in simulations of human phonation

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Bodony, Daniel

2014-11-01

Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).

Geometrically Nonlinear Transient Analysis of Laminated Composite Plates.

DTIC Science & Technology

1982-03-01

theory (CPT), in which normals to the midsurface before deformation are assumed to remain straight and normal to the midsurface after deformation (i.e...the plate are negligible when compared to the inplane stresses, and normals to the plate midsurface before deformation remain straight but not...necessarily normal to the midsurface after deformation. $ Equations of motion The plate under consideration is composed of a finite number of orthotropic

Multi-temporal InSAR analysis to reduce uncertainties and assess time-dependence of deformation in the northern Chilean forearc

NASA Astrophysics Data System (ADS)

Manjunath, D.; Gomez, F.; Loveless, J.

2005-12-01

Interferometric Synthetic Aperture Radar (InSAR) provides unprecedented spatial imaging of crustal deformation. However, for small deformations, such as those due to interseismic strain accumulation, potentially significant uncertainty may result from other sources of interferometric phase, such as atmospheric effects, errors in satellite baseline, and height errors in the reference digital elevation model (DEM). We aim to constrain spatial and temporal variations in crustal deformation of the northern Chilean forearc region of the Andean subduction zone (19° - 22°S) using multiple interferograms spanning 1995 - 2000. The study area includes the region of the 1995 Mw 8.1 Antofagasta earthquake and the region to the north. In contrast to previous InSAR-based studies of the Chilean forearc, we seek to distinguish interferometric phase contributions from linear and nonlinear deformation, height errors in the DEM, and atmospheric effects. Understanding these phase contributions reduces the uncertainties on the deformation rates and provides a view of the time-dependence of deformation. The inteferograms cover a 150 km-wide swath spanning two adjacent orbital tracks. Our study involves the analysis of more than 28 inteferograms along each track. Coherent interferograms in the hyper-arid Atacama Desert permit spatial phase unwrapping. Initial estimates of topographic phase were determined using 3'' DEM data from the SRTM mission. We perform a pixel-by-pixel analysis of the unwrapped phase to identify time- and baseline-dependent phase contributions, using the Gamma Remote Sensing radar software. Atmospheric phase, non-linear deformation, and phase noise were further distinguished using a combination of spatial and temporal filters. Non-linear deformation is evident for up to 2.5 years following the 1995 earthquake, followed by a return to time-linear, interseismic strain accumulation. The regional trend of linear deformation, characterized by coastal subsidence and relative uplift inland, is consistent with the displacement field expected for a locked subduction zone. Our improved determination of deformation rates is used to formulate a new elastic model of interseismic strain in the Chilean forearc.

Preliminary Development of a Unified Viscoplastic Constitutive Model for Alloy 617 with Special Reference to Long Term Creep Behavior

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sham, Sam; Walker, Kevin P.

The expected service life of the Next Generation Nuclear Plant is 60 years. Structural analyses of the Intermediate Heat Exchanger (IHX) will require the development of unified viscoplastic constitutive models that address the material behavior of Alloy 617, a construction material of choice, over a wide range of strain rates. Many unified constitutive models employ a yield stress state variable which is used to account for cyclic hardening and softening of the material. For low stress values below the yield stress state variable these constitutive models predict that no inelastic deformation takes place which is contrary to experimental results. Themore » ability to model creep deformation at low stresses for the IHX application is very important as the IHX operational stresses are restricted to very small values due to the low creep strengths at elevated temperatures and long design lifetime. This paper presents some preliminary work in modeling the unified viscoplastic constitutive behavior of Alloy 617 which accounts for the long term, low stress, creep behavior and the hysteretic behavior of the material at elevated temperatures. The preliminary model is presented in one-dimensional form for ease of understanding, but the intent of the present work is to produce a three-dimensional model suitable for inclusion in the user subroutines UMAT and USERPL of the ABAQUS and ANSYS nonlinear finite element codes. Further experiments and constitutive modeling efforts are planned to model the material behavior of Alloy 617 in more detail.« less

Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models

NASA Astrophysics Data System (ADS)

González, C.; Segurado, J.; LLorca, J.

2004-07-01

The deformation of a composite made up of a random and homogeneous dispersion of elastic spheres in an elasto-plastic matrix was simulated by the finite element analysis of three-dimensional multiparticle cubic cells with periodic boundary conditions. "Exact" results (to a few percent) in tension and shear were determined by averaging 12 stress-strain curves obtained from cells containing 30 spheres, and they were compared with the predictions of secant homogenization models. In addition, the numerical simulations supplied detailed information of the stress microfields, which was used to ascertain the accuracy and the limitations of the homogenization models to include the nonlinear deformation of the matrix. It was found that secant approximations based on the volume-averaged second-order moment of the matrix stress tensor, combined with a highly accurate linear homogenization model, provided excellent predictions of the composite response when the matrix strain hardening rate was high. This was not the case, however, in composites which exhibited marked plastic strain localization in the matrix. The analysis of the evolution of the matrix stresses revealed that better predictions of the composite behavior can be obtained with new homogenization models which capture the essential differences in the stress carried by the elastic and plastic regions in the matrix at the onset of plastic deformation.

Prestressed F-actin networks cross-linked by hinged filamins replicate mechanical properties of cells

NASA Astrophysics Data System (ADS)

Gardel, M. L.; Nakamura, F.; Hartwig, J. H.; Crocker, J. C.; Stossel, T. P.; Weitz, D. A.

2006-02-01

We show that actin filaments, shortened to physiological lengths by gelsolin and cross-linked with recombinant human filamins (FLNs), exhibit dynamic elastic properties similar to those reported for live cells. To achieve elasticity values of comparable magnitude to those of cells, the in vitro network must be subjected to external prestress, which directly controls network elasticity. A molecular requirement for the strain-related behavior at physiological conditionsis a flexible hinge found in FLNa and some FLNb molecules. Basic physical properties of the in vitro filamin-F-actin network replicate the essential mechanical properties of living cells. This physical behavior could accommodate passive deformation and internal organelle trafficking at low strains yet resist externally or internally generated high shear forces. cytoskeleton | cell mechanics | nonlinear rheology

Innovative energy absorbing devices based on composite tubes

NASA Astrophysics Data System (ADS)

Tiwari, Chandrashekhar

Analytical and experimental study of innovative load limiting and energy absorbing devices are presented here. The devices are based on composite tubes and can be categorized in to two groups based upon the energy absorbing mechanisms exhibited by them, namely: foam crushing and foam fracturing. The device based on foam crushing as the energy absorbing mechanism is composed of light weight elastic-plastic foam filling inside an angle ply composite tube. The tube is tailored to have a high Poisson’s ratio (>20). Upon being loaded the device experiences large transverse contraction resulting in rapid decrease in diameter. At a certain axial load the foam core begins to crush and energy is dissipated. This device is termed as crush tube device. The device based upon foam shear fracture as the energy absorbing mechanism involves an elastic-plastic core foam in annulus of two concentric extension-twist coupled composite tubes with opposite angles of fibers. The core foam is bonded to the inner and outer tube walls. Upon being loaded axially, the tubes twist in opposite directions and fracture the core foam in out of plane shear and thus dissipate the energy stored. The device is termed as sandwich core device (SCD). The devices exhibit variations in force-displacement characteristics with changes in design and material parameters, resulting in wide range of energy absorption capabilities. A flexible matrix composite system was selected, which was composed of high stiffness carbon fibers as reinforcements in relatively low stiffness polyurethane matrix, based upon large strain to failure capabilities and large beneficial elastic couplings. Linear and non-linear analytical models were developed encapsulating large deformation theory of the laminated composite shells (using non-linear strain energy formulation) to the fracture mechanics of core foam and elastic-plastic deformation theory of the foam filling. The non-linear model is capable of including material and geometric nonlinearities that arise from large deformation and fiber reorientation. Developed non-linear analysis predicts the behavior of extension-twist coupled and angle ply flexible matrix composite tubes under multi-axial loadings. The predicted results show close correlation with experimental findings. It was also found that these devices exhibit variations with respect to rate of loading. It was found that the novel energy absorbing devices are capable of providing 4-5 times higher specific energy absorption (SEA) than currently used devices for similar purposes (such as wire bender which has SEA of 3.6 J/g).

Finite stretching of a circular plate of neo-Hookean material.

NASA Technical Reports Server (NTRS)

Biricikoglu, V.

1971-01-01

The analytical solution presented is based on the assumption that the deformed thickness of the plate is approximately constant. The nonlinear equations governing finite axisymmetric deformations of a circular plate made of neo-Hookean material are used in the analysis. The variation of circumferential extension ratio and the variation of deformed thickness are shown in graphs.

Internal resonance of an elastic body levitated above high-Tc superconducting bulks

NASA Astrophysics Data System (ADS)

Kokuzawa, T.; Toshihiko, S.; Yoshizawa, M.

2010-06-01

In high-Tc superconducting magnetic levitation systems, levitated bodies can keep stable levitation with no contact and no control and thus their damping is very small. Thanks to these features, their applications to various apparatus are expected. However, on account of their small damping, the nonlinearity of electromagnetic levitation force can give notable effects upon motion of the levitated bodies. Therefore this nonlinearity must be taken into account to accurately analyze the dynamical behavior of the levitated bodies. Structures of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Therefore, we need to deal with the model as an elastic body. As mentioned above, nonlinear characteristics easily appear in this elastic vibration on account of the small damping. Especially when the ratio of the natural frequencies of the eigenmodes is integer, internal resonance can occur. This nonlinear resonance is derived from nonlinear interactions among the eigenmodes of the elastic levitated body. This kind of internal resonance of an elastic body appearing in high-Tc superconducting levitation systems has not been studied so far. This research especially deals with internal resonance of a beam supported at both its ends by electromagnetic forces acting on permanent magnets. The governing equation with the nonlinear boundary conditions for the dynamics of a levitated beam has been derived. Numerical results show internal resonance of the 1st mode and the 3rd mode. Experimental results are qualitatively in good agreement with numerical ones.

Modeling nonlinear dynamic properties of dielectric elastomers with various crosslinks, entanglements, and finite deformations

NASA Astrophysics Data System (ADS)

Zhang, Junshi; Chen, Hualing; Li, Dichen

2018-02-01

Subject to an AC voltage, dielectric elastomers (DEs) behave as a nonlinear vibration, implying potential applications as soft dynamical actuators and robots. In this article, by utilizing the Lagrange's equation, a theoretical model is deduced to investigate the dynamic performances of DEs by considering three internal properties, including crosslinks, entanglements, and finite deformations of polymer chains. Numerical calculations are employed to describe the dynamic response, stability, periodicity, and resonance properties of DEs. It is observed that the frequency and nonlinearity of dynamic response are tuned by the internal properties of DEs. Phase paths and Poincaré maps are utilized to detect the stability and periodicity of the nonlinear vibrations of DEs, which demonstrate that transitions between aperiodic and quasi-periodic vibrations may occur when the three internal properties vary. The resonance of DEs involving the three internal properties of polymer chains is also investigated.

Simulation of finite-strain inelastic phenomena governed by creep and plasticity

NASA Astrophysics Data System (ADS)

Li, Zhen; Bloomfield, Max O.; Oberai, Assad A.

2017-11-01

Inelastic mechanical behavior plays an important role in many applications in science and engineering. Phenomenologically, this behavior is often modeled as plasticity or creep. Plasticity is used to represent the rate-independent component of inelastic deformation and creep is used to represent the rate-dependent component. In several applications, especially those at elevated temperatures and stresses, these processes occur simultaneously. In order to model these process, we develop a rate-objective, finite-deformation constitutive model for plasticity and creep. The plastic component of this model is based on rate-independent J_2 plasticity, and the creep component is based on a thermally activated Norton model. We describe the implementation of this model within a finite element formulation, and present a radial return mapping algorithm for it. This approach reduces the additional complexity of modeling plasticity and creep, over thermoelasticity, to just solving one nonlinear scalar equation at each quadrature point. We implement this algorithm within a multiphysics finite element code and evaluate the consistent tangent through automatic differentiation. We verify and validate the implementation, apply it to modeling the evolution of stresses in the flip chip manufacturing process, and test its parallel strong-scaling performance.

Nonlinear pressure-flow relationships for passive microfluidic valves.

PubMed

Seker, Erkin; Leslie, Daniel C; Haj-Hariri, Hossein; Landers, James P; Utz, Marcel; Begley, Matthew R

2009-09-21

An analytical solution is presented for the nonlinear pressure-flow relationship of deformable passive valves, which are formed by bonding a deformable film over etched channels separated by a weir. A fluidic pathway connecting the channels is opened when the upstream pressure creates a tunnel along a predefined narrow strip where the film is not bonded to the weir. When the width of the strip is comparable to the inlet channel width, the predicted closed-form pressure-flow rate relationship is in excellent agreement with experiments, which determine pressures by measuring film deflections for prescribed flow rates. The validated closed-form models involve no fitting parameters, and provide the foundation to design passive diodes with specific nonlinear pressure-flow characteristics.

Deformation behavior of carbon-fiber reinforced shape-memory-polymer composites used for deployable structures (Conference Presentation)

NASA Astrophysics Data System (ADS)

Lan, Xin; Liu, Liwu; Li, Fengfeng; Pan, Chengtong; Liu, Yanju; Leng, Jinsong

2017-04-01

Shape memory polymers (SMPs) are a new type of smart material, they perform large reversible deformation with a certain external stimulus (e.g., heat and electricity). The properties (e.g., stiffness, strength and other mechanically static or quasi-static load-bearing capacity) are primarily considered for conventional resin-based composite materials which are mainly used for structural materials. By contrast, the mechanical actuating performance with finite deformation is considered for the shape memory polymers and their composites which can be used for both structural materials and functional materials. For shape memory polymers and their composites, the performance of active deformation is expected to further promote the development in smart active deformation structures, such as deployable space structures and morphing wing aircraft. The shape memory polymer composites (SMPCs) are also one type of High Strain Composite (HSC). The space deployable structures based on carbon fiber reinforced shape memory polymer composites (SMPCs) show great prospects. Considering the problems that SMPCs are difficult to meet the practical applications in space deployable structures in the recent ten years, this paper aims to research the mechanics of deformation, actuation and failure of SMPCs. In the overall view of the shape memory polymer material's nonlinearity (nonlinearity and stress softening in the process of pre-deformation and recovery, relaxation in storage process, irreversible deformation), by the multiple verifications among theory, finite element and experiments, one obtains the deformation and actuation mechanism for the process of "pre-deformation, energy storage and actuation" and its non-fracture constraint domain. Then, the parameters of SMPCs will be optimized. Theoretical analysis is realized by the strain energy function, additionally considering the interaction strain energy between the fiber and the matrix. For the common resin-based or soft-material-based composites under pure bending deformation, we expect to uniformly explain the whole process of buckling occurrence, evolution and finally failure, especially for the early evolution characteristics of fiber microbuckling inside the microstructures. The research results are meaningful for the practical applications for SMPC deployable structures in space. Considering the deformation mechanisms of SMPCs, the local post-microbuckling is required for the unidirectional fiber reinforced composite materials, at the conditions of its large geometrical deflection. The cross section of SMPC is divided into three areas: non-buckling stretching area, non-buckling compressive area, and buckling compressive area. Three variables are considered: critical buckling position, and neutral plane, the fiber buckling half-wavelength. Considering the condition of the small strain and large displacement, the strain energy expression of the SMP/fiber system was derived, which contains two types, e.g., strain energy of SMP and fiber. According to the minimum energy principle, the expression for all key parameters were derived, including the critical buckling curvature, neutral plane position, the buckling half-wavelength, fiber buckling amplitude, and strain.

Hierarchical nonlinear behavior of hot composite structures

NASA Technical Reports Server (NTRS)

Murthy, P. L. N.; Chamis, C. C.; Singhal, S. N.

1993-01-01

Hierarchical computational procedures are described to simulate the multiple scale thermal/mechanical behavior of high temperature metal matrix composites (HT-MMC) in the following three broad areas: (1) behavior of HT-MMC's from micromechanics to laminate via METCAN (Metal Matrix Composite Analyzer), (2) tailoring of HT-MMC behavior for optimum specific performance via MMLT (Metal Matrix Laminate Tailoring), and (3) HT-MMC structural response for hot structural components via HITCAN (High Temperature Composite Analyzer). Representative results from each area are presented to illustrate the effectiveness of computational simulation procedures and accompanying computer codes. The sample case results show that METCAN can be used to simulate material behavior such as the entire creep span; MMLT can be used to concurrently tailor the fabrication process and the interphase layer for optimum performance such as minimum residual stresses; and HITCAN can be used to predict the structural behavior such as the deformed shape due to component fabrication. These codes constitute virtual portable desk-top test laboratories for characterizing HT-MMC laminates, tailoring the fabrication process, and qualifying structural components made from them.

Nonlinear Dynamics of Electroelastic Dielectric Elastomers

DTIC Science & Technology

2018-01-30

research will significantly advance the basic science and fundamental understanding of how rate- dependent material response couples to large, nonlinear...experimental studies of constrained dielectric elastomer films, a transition in the surface instability mechanism depending on the elastocapillary number...fundamental understanding of how rate- dependent material response couples to large, nonlinear material deformation under applied electrostatic loading to

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

NASA Technical Reports Server (NTRS)

Murthy, V. R.; Shultz, Louis A.

1994-01-01

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

Nonlinear dynamic modeling of surface defects in rolling element bearing systems

NASA Astrophysics Data System (ADS)

Rafsanjani, Ahmad; Abbasion, Saeed; Farshidianfar, Anoushiravan; Moeenfard, Hamid

2009-01-01

In this paper an analytical model is proposed to study the nonlinear dynamic behavior of rolling element bearing systems including surface defects. Various surface defects due to local imperfections on raceways and rolling elements are introduced to the proposed model. The contact force of each rolling element described according to nonlinear Hertzian contact deformation and the effect of internal radial clearance has been taken into account. Mathematical expressions were derived for inner race, outer race and rolling element local defects. To overcome the strong nonlinearity of the governing equations of motion, a modified Newmark time integration technique was used to solve the equations of motion numerically. The results were obtained in the form of time series, frequency responses and phase trajectories. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The classical Floquet theory has been applied to the proposed model to investigate the linear stability of the defective bearing rotor systems as the parameters of the system changes. The peak-to-peak frequency response of the system for each case is obtained and the basic routes to periodic, quasi-periodic and chaotic motions for different internal radial clearances are determined. The current study provides a powerful tool for design and health monitoring of machine systems.

A Numerical Model of Unsteady, Subsonic Aeroelastic Behavior. Ph.D Thesis

NASA Technical Reports Server (NTRS)

Strganac, Thomas W.

1987-01-01

A method for predicting unsteady, subsonic aeroelastic responses was developed. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The fluid and the wing together are treated as a single dynamical system, and the equations of motion for the structure and flow field are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a predictor-corrector technique. The aerodynamic loads are computed by the general unsteady vortex-lattice method and are determined simultaneously with the motion of the wing. Because the unsteady vortex-lattice method predicts the wake as part of the solution, the history of the motion is taken into account; hysteresis is predicted. Two models are used to demonstrate the technique: a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis, and an elastic wing rigidly supported at the root chord experiencing spanwise bending and twisting. The method can be readily extended to account for structural nonlinearities and/or substitute aerodynamic load models. The time domain solution coupled with the unsteady vortex-lattice method provides the capability of graphically depicting wing and wake motion.

Failure Behavior and Strength of Composite I-Section Beam with Double Cutouts and Stiffener Reinforcement

NASA Astrophysics Data System (ADS)

Zhang, Jian; Liu, Wei; Gao, Weicheng

2018-02-01

This work is carried out to study the influence of double cutouts and stiffener reinforcements on the performance of I-section Carbon Fibre/Epoxy composites beam, including buckling, post-buckling behavior and the ultimate failure. The cantilever I-section beam with two diamond-shaped cutouts in the web and three longitudinal L-shaped stiffeners bonded to one side is subjected to a shear load at free end. Both numerical modelling and Experiment of I-section CFRP beam are performed. In numerical analysis, Tsai-Wu failure criterion is utilized to detect the first-ply-failure load in nonlinear analysis by predicting the load-deflection response. Good agreements are obtained from comparison between the numerical simulations and test results. For the double-hole beam web, the two cutouts show close surface deformation amplitude, which indicates that the stiffeners make the force transformation more effective. Comparing to the numerical result of corresponding beam with single cutout and stiffener reinforcement, the longitudinal stiffeners can not only play a significant role in improving the structural stability (increase about 30%), but also take effects to improve the deformation compatibility of structure. Local buckling happened within the sub-webs partioned by the stiffener and the buckling load is different but close. With post-buckling regime, the two areas show similar deformation characteristic, while the sub-web close to fixed end bears more shear load than the sub-web close to loading end with the increase of normal deformation of structure. The catastrophic failure load is approximate 75.6% higher comparing to buckling load. Results illustrate that the tensile fracture of the fiber is the immediate cause of the ultimate failure of the structure.

Superelastic stress-strain behavior in ferrogels with different types of magneto-elastic coupling

NASA Astrophysics Data System (ADS)

Cremer, Peet; Löwen, Hartmut; Menzel, Andreas M.

Colloidal magnetic particles embedded in an elastic polymer matrix constitute a smart material called ferrogel. It responds to an applied external magnetic field by changes in elastic properties, which can be exploited for various applications like dampers, vibration absorbers, or actuators. Under appropriate conditions, the stress-strain behavior of a ferrogel can display a fascinating feature: superelasticity, the capability to reversibly deform by a huge amount while barely altering the applied load. In a previous work, using numerical simulations, we investigated this behavior assuming that the magnetic moments carried by the embedded particles can freely reorient to minimize their magnetic interaction energy. Here, we extend the analysis to ferrogels where restoring torques by the surrounding matrix hinder rotations towards a magnetically favored configuration. For example, the particles can be chemically cross-linked into the polymer matrix and the magnetic moments can be fixed to the particle axes. We demonstrate that these systems still feature a superelastic regime. As before, the nonlinear stress-strain behavior can be reversibly tailored during operation by external magnetic fields. Yet, the different coupling of the magnetic moments causes different types of response to external stimuli. For instance, an external magnetic field applied parallel to the stretching axis hardly affects the superelastic regime but stiffens the system beyond it. Other smart materials featuring superelasticity, e.g. metallic shape-memory alloys, have already found widespread applications. Our soft polymer systems offer many additional advantages like a typically higher deformability and enhanced biocompatibility combined with high tunability.

Determination of Anand parameters for SnAgCuCe solder

NASA Astrophysics Data System (ADS)

Zhang, Liang; Xue, Songbai; Gao, Lili; Zeng, Guang; Sheng, Zhong; Chen, Yan; Yu, Shenglin

2009-10-01

A unified viscoplastic constitutive model, Anand equations, was used to represent the inelastic deformation behavior for Sn3.8Ag0.7Cu/Sn3.8Ag0.7 Cu0.03Ce solders in surface mount technology. The Anand parameters of the constitutive equations for the SnAgCu and SnAgCuCe solders were determined from separated constitutive relations and experimental results. Non-linear least-squares fitting was selected to determine the model constants. Comparisons were then made with experimental measurements of the stress-inelastic strain curves: excellent agreement was found. The model accurately predicted the overall trend of steady-state stress-strain behavior of SnAgCu and SnAgCuCe solders for the temperature ranges from -55 to 125 °C and for the strain rate range from 1% s-1 to 0.01% s-1. It is concluded that the Anand model can be applied to represent the inelastic deformation behavior of solders at high homologous temperatures and can be recommended for finite element simulation of the stress-strain response of lead-free soldered joints. Based on the Anand model, the investigations of thermo-mechanical behavior of SnAgCu and SnAgCuCe soldered joints in fine pitch quad flat package by the finite element code have been done under thermal cyclic loading, and it is found that the reliability of the SnAgCuCe soldered joints is better than that of the SnAgCu soldered joints.

Optimizing Cubature for Efficient Integration of Subspace Deformations

PubMed Central

An, Steven S.; Kim, Theodore; James, Doug L.

2009-01-01

We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration. CR Categories: I.6.8 [Simulation and Modeling]: Types of Simulation—Animation, I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling G.1.4 [Mathematics of Computing]: Numerical Analysis—Quadrature and Numerical Differentiation PMID:19956777

Inelastic deformation of metal matrix composites

NASA Technical Reports Server (NTRS)

Lissenden, C. J.; Herakovich, C. T.; Pindera, M-J.

1993-01-01

A theoretical model capable of predicting the thermomechanical response of continuously reinforced metal matrix composite laminates subjected to multiaxial loading was developed. A micromechanical model is used in conjunction with nonlinear lamination theory to determine inelastic laminae response. Matrix viscoplasticity, residual stresses, and damage to the fiber/matrix interfacial zone are explicitly included in the model. The representative cell of the micromechanical model is considered to be in a state of generalized plane strain, enabling a quasi two-dimensional analysis to be performed. Constant strain finite elements are formulated with elastic-viscoplastic constitutive equations. Interfacial debonding is incorporated into the model through interface elements based on the interfacial debonding theory originally presented by Needleman, and modified by Tvergaard. Nonlinear interfacial constitutive equations relate interfacial tractions to displacement discontinuities at the interface. Theoretical predictions are compared with the results of an experimental program conducted on silicon carbide/titanium (SiC/Ti) unidirectional, (O4), and angle-ply, (+34)(sub s), tubular specimens. Multiaxial loading included increments of axial tension, compression, torque, and internal pressure. Loadings were chosen in an effort to distinguish inelastic deformation due to damage from matrix plasticity and separate time-dependent effects from time-independent effects. Results show that fiber/matrix debonding is nonuniform throughout the composite and is a major factor in the effective response. Also, significant creep behavior occurs at relatively low applied stress levels at room temperature.

Numerical study on the electromechanical behavior of dielectric elastomer with the influence of surrounding medium

NASA Astrophysics Data System (ADS)

Jia; Lu

2016-01-01

The considerable electric-induced shape change, together with the attributes of lightweight, high efficiency, and inexpensive cost, makes dielectric elastomer, a promising soft active material for the realization of actuators in broad applications. Although, a number of prototype devices have been demonstrated in the past few years, the further development of this technology necessitates adequate analytical and numerical tools. Especially, previous theoretical studies always neglect the influence of surrounding medium. Due to the large deformation and nonlinear equations of states involved in dielectric elastomer, finite element method (FEM) is anticipated; however, the few available formulations employ homemade codes, which are inconvenient to implement. The aim of this work is to present a numerical approach with the commercial FEM package COMSOL to investigate the nonlinear response of dielectric elastomer under electric stimulation. The influence of surrounding free space on the electric field is analyzed and the corresponding electric force is taken into account through an electric surface traction on the circumstances edge. By employing Maxwell stress tensor as actuation pressure, the mechanical and electric governing equations for dielectric elastomer are coupled, and then solved simultaneously with the Gent model of stain energy to derive the electric induced large deformation as well as the electromechanical instability. The finite element implementation presented here may provide a powerful computational tool to help design and optimize the engineering applications of dielectric elastomer.

Nonlinear Finite Element Analysis of a Composite Non-Cylindrical Pressurized Aircraft Fuselage Structure

NASA Technical Reports Server (NTRS)

Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter

2014-01-01

The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously published preliminary linear analysis, it is demonstrated in the present paper that neglecting nonlinear effects for the structure and loads of interest can lead to appreciable loss in analysis fidelity.

Mechanical deformation of carbon nanotube nano-rings on flat substrate

NASA Astrophysics Data System (ADS)

Zheng, Meng; Ke, Changhong

2011-04-01

We present a numerical analysis of the mechanical deformation of carbon nanotube (CNT) nano-rings on flat graphite substrates, which is motivated by our recent experimental findings on the elastic deformation of CNT nano-rings. Our analysis considers a perfectly circular CNT ring formed by bending a straight individual or bundled single-walled nanotube to connect its two ends. The seamless CNT ring is placed vertically on a flat graphite substrate and its respective deformation curvatures under zero external force, compressive, and tensile forces are determined using a continuum model based on nonlinear elastica theory. Our results show that the van der Waals interaction between the CNT ring and the substrate has profound effects on the deformation of the CNT ring, and that the interfacial binding interaction between the CNT ring and the substrate is strongly modulated by the ring deformation. Our results demonstrate that the CNT ring in force-free conditions has a flat ring segment in contact with the substrate if the ring radius R ≥√EI/2Wvdw , in which EI is the flexural rigidity of the nanotube and Wvdw is the per-unit-length van der Waals energy between the flat ring segment and the substrate. Our results reveal that the load-deformation profiles of the CNT ring under tensile loadings exhibit bifurcation behavior, which is ascribed to its van der Waals interaction with the substrate and is dependent on its relaxed conformation on the substrate. Our work suggests that CNT nano-rings are promising for a number of applications, such as ultrasensitive force sensors and stretchable and flexible structural components in nanoscale mechanical and electromechanical systems.

Modeling coupled Thermo-Hydro-Mechanical processes including plastic deformation in geological porous media

NASA Astrophysics Data System (ADS)

Kelkar, S.; Karra, S.; Pawar, R. J.; Zyvoloski, G.

2012-12-01

There has been an increasing interest in the recent years in developing computational tools for analyzing coupled thermal, hydrological and mechanical (THM) processes that occur in geological porous media. This is mainly due to their importance in applications including carbon sequestration, enhanced geothermal systems, oil and gas production from unconventional sources, degradation of Arctic permafrost, and nuclear waste isolation. Large changes in pressures, temperatures and saturation can result due to injection/withdrawal of fluids or emplaced heat sources. These can potentially lead to large changes in the fluid flow and mechanical behavior of the formation, including shear and tensile failure on pre-existing or induced fractures and the associated permeability changes. Due to this, plastic deformation and large changes in material properties such as permeability and porosity can be expected to play an important role in these processes. We describe a general purpose computational code FEHM that has been developed for the purpose of modeling coupled THM processes during multi-phase fluid flow and transport in fractured porous media. The code uses a continuum mechanics approach, based on control volume - finite element method. It is designed to address spatial scales on the order of tens of centimeters to tens of kilometers. While large deformations are important in many situations, we have adapted the small strain formulation as useful insight can be obtained in many problems of practical interest with this approach while remaining computationally manageable. Nonlinearities in the equations and the material properties are handled using a full Jacobian Newton-Raphson technique. Stress-strain relationships are assumed to follow linear elastic/plastic behavior. The code incorporates several plasticity models such as von Mises, Drucker-Prager, and also a large suite of models for coupling flow and mechanical deformation via permeability and stresses/deformations. In this work we present several example applications of such models.

Optomechanics of two- and three-dimensional soft photonic crystals

NASA Astrophysics Data System (ADS)

Krishnan, Dwarak

Soft photonic crystals are a class of periodic dielectric structures that undergo highly nonlinear deformation due to strain or other external stimulus such as temperature, pH etc. This can in turn dramatically affect optical properties such as light transmittance. Moreover certain classes of lithographically fabricated structures undergo some structural distortion due to the effects of processing, eventually affecting the optical properties of the final photonic crystal. In this work, we study the deformation mechanics of soft photonic crystal structures using realistic physics-based models and leverage that understanding to explain the optomechanics of actual 2-D and 3-D soft photonic crystals undergoing similar symmetry breaking nonlinear deformations. We first study the optomechanics of two classes of 3-D soft photonic crystals: (1) hydrogel and (2) elastomer based material systems. The hydrogel based inverse face-centered-cubic structure undergoes swelling with change in pH of the surrounding fluid. The inverse structure is a network of bulky domains with thin ligament-like connections, and it undergoes a pattern transformation from FCC to L11 as a result of swelling. A continuum scale poroelasticity based coupled fluid-diffusion FEM model is developed to accurately predict this mechanical behavior. Light transmittance simulation results qualitatively explain the experimentally observed trends in the optical behavior with pH change. The elastomer based, lithographically fabricated material experiences shrinkage induced distortion upon processing. This behavior is modeled using FEM with the material represented by a neo-Hookean constitutive law. The light transmittance calculations for normal incidence are carried out using the transfer matrix method and a good comparison is obtained for the positions of first and second order reflectance peaks. A unit cell based approach is taken to compute the photonic bandstructure to estimate light propagation through the structure for other angles of light incidence. To obtain a detailed picture of the change in optical properties due to a pattern transformation, we study simple 2-D elastomer photonic crystals which undergo an interesting structural pattern transformation from simple circular holes to alternately oriented ellipses in a square lattice due to uniaxial compression. The incident light does not have any effect on the properties of the elastomer material. A decomposition of the deformation gradient quickly shows that the pattern transformation is induced by alternating rotations of the interstitial regions and the bending of interconnecting ligaments. Numerical simulations of light transmittance using vector element based FEM analysis of Maxwells equations shows changes in the light energy localization within the material especially in the high energy/low wavelength regions of the spectra. Additionally, with bandstructure calculations on a unit cell of the structure, the optomechanical behavior is completely explained. Finally, computational evidence is provided for a hypothetical 2-D photonic crystal made of a light-sensitive material, which undergoes a structural pattern transformation primarily due to the effect of incident light. The model takes into account the order kinetics of optically induced isomerization (of trans to cis configuration) in the azobenzene-liquid crystal elastomer to compute the transformational strain. This strain, in turn, deforms the structure and hence changes its periodicity and dielectric properties and thus affects the manner in which light gets localized within the material system. This consequently changes the profile of the imposed transformational strain on the deformed structure. The macroscopic strain history shows that prior to the mechanical instability that causes the pattern transformation, there is a period of structural relaxation which initiates the pattern transformation. After the symmetry breaking pattern transformation, the photonic bandstructure is altered significantly. Light does not get localized in the spot regions anymore and stress relaxation dominates. Due to this, the compressive macroscopic strain of the pattern transformed structure starts to decrease indicating a possible cyclical behavior.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oleinikov, A. I., E-mail: a.i.oleinikov@mail.ru; Bormotin, K. S., E-mail: cvmi@knastu.ru

It is shown that inverse problems of steady-state creep bending of plates in both the geometrically linear and nonlinear formulations can be represented in a variational formulation. Steady-state values of the obtained functionals corresponding to the solutions of the problems of inelastic deformation and springback are determined by applying a finite element procedure to the functionals. Optimal laws of creep deformation are formulated using the criterion of minimizing damage in the functionals of the inverse problems. The formulated problems are reduced to the problems solved by the finite element method using MSC.Marc software. Currently, forming of light metals poses tremendousmore » challenges due to their low ductility at room temperature and their unusual deformation characteristics at hot-cold work: strong asymmetry between tensile and compressive behavior, and a very pronounced anisotropy. We used the constitutive models of steady-state creep of initially transverse isotropy structural materials the kind of the stress state has influence. The paper gives basics of the developed computer-aided system of design, modeling, and electronic simulation targeting the processes of manufacture of wing integral panels. The modeling results can be used to calculate the die tooling, determine the panel processibility, and control panel rejection in the course of forming.« less

Deformation and electrical properties of magnetic and vertically conductive composites with a chain-of-spheres structure

NASA Astrophysics Data System (ADS)

Choi, Chulmin; Hong, Soonkook; Chen, Li-Han; Liu, Chin-Hung; Choi, Duyoung; Kuru, Cihan; Jin, Sungho

2014-05-01

Vertically anisotropically conductive composites with aligned chain-of-spheres of 20-75 mm Ni particles in an elastomer matrix have been prepared by curing the mixture at 100°C-150°C under an applied magnetic field of ˜300-1000 Oe. The particles are coated with a ˜120 nm thick Au layer for enhanced electrical conductivity. The resultant vertically aligned but laterally isolated columns of conductive particles extend through the whole composite thickness and the end of the Ni columns protrude from the surface, contributing to enhanced electrical contact on the composite surface. The stress-strain curve on compressive deformation exhibits a nonlinear behavior with a rapidly increasing Young's modulus with stress (or pressure). The electrical contact resistance Rc decreases rapidly when the applied pressure is small and then more gradually after the applied pressure reaches 500 psi (˜3.4 MPa), corresponding to a 30% deformation. The directionally conductive elastomer composite material with metal pads and conductive electrodes on the substrate surface can be used as a convenient tactile shear sensor for applications involving artificial limbs, robotic devices, and other visual communication devices such as touch sensitive screens.

The inverse problems of wing panel manufacture processes

NASA Astrophysics Data System (ADS)

Oleinikov, A. I.; Bormotin, K. S.

2013-12-01

It is shown that inverse problems of steady-state creep bending of plates in both the geometrically linear and nonlinear formulations can be represented in a variational formulation. Steady-state values of the obtained functionals corresponding to the solutions of the problems of inelastic deformation and springback are determined by applying a finite element procedure to the functionals. Optimal laws of creep deformation are formulated using the criterion of minimizing damage in the functionals of the inverse problems. The formulated problems are reduced to the problems solved by the finite element method using MSC.Marc software. Currently, forming of light metals poses tremendous challenges due to their low ductility at room temperature and their unusual deformation characteristics at hot-cold work: strong asymmetry between tensile and compressive behavior, and a very pronounced anisotropy. We used the constitutive models of steady-state creep of initially transverse isotropy structural materials the kind of the stress state has influence. The paper gives basics of the developed computer-aided system of design, modeling, and electronic simulation targeting the processes of manufacture of wing integral panels. The modeling results can be used to calculate the die tooling, determine the panel processibility, and control panel rejection in the course of forming.

Integrating viscoelastic mass spring dampers into position-based dynamics to simulate soft tissue deformation in real time

PubMed Central

Lu, Yuhua; Liu, Qian

2018-01-01

We propose a novel method to simulate soft tissue deformation for virtual surgery applications. The method considers the mechanical properties of soft tissue, such as its viscoelasticity, nonlinearity and incompressibility; its speed, stability and accuracy also meet the requirements for a surgery simulator. Modifying the traditional equation for mass spring dampers (MSD) introduces nonlinearity and viscoelasticity into the calculation of elastic force. Then, the elastic force is used in the constraint projection step for naturally reducing constraint potential. The node position is enforced by the combined spring force and constraint conservative force through Newton's second law. We conduct a comparison study of conventional MSD and position-based dynamics for our new integrating method. Our approach enables stable, fast and large step simulation by freely controlling visual effects based on nonlinearity, viscoelasticity and incompressibility. We implement a laparoscopic cholecystectomy simulator to demonstrate the practicality of our method, in which liver and gallbladder deformation can be simulated in real time. Our method is an appropriate choice for the development of real-time virtual surgery applications. PMID:29515870

Integrating viscoelastic mass spring dampers into position-based dynamics to simulate soft tissue deformation in real time.

PubMed

Xu, Lang; Lu, Yuhua; Liu, Qian

2018-02-01

We propose a novel method to simulate soft tissue deformation for virtual surgery applications. The method considers the mechanical properties of soft tissue, such as its viscoelasticity, nonlinearity and incompressibility; its speed, stability and accuracy also meet the requirements for a surgery simulator. Modifying the traditional equation for mass spring dampers (MSD) introduces nonlinearity and viscoelasticity into the calculation of elastic force. Then, the elastic force is used in the constraint projection step for naturally reducing constraint potential. The node position is enforced by the combined spring force and constraint conservative force through Newton's second law. We conduct a comparison study of conventional MSD and position-based dynamics for our new integrating method. Our approach enables stable, fast and large step simulation by freely controlling visual effects based on nonlinearity, viscoelasticity and incompressibility. We implement a laparoscopic cholecystectomy simulator to demonstrate the practicality of our method, in which liver and gallbladder deformation can be simulated in real time. Our method is an appropriate choice for the development of real-time virtual surgery applications.

Integral finite element analysis of turntable bearing with flexible rings

NASA Astrophysics Data System (ADS)

Deng, Biao; Liu, Yunfei; Guo, Yuan; Tang, Shengjin; Su, Wenbin; Lei, Zhufeng; Wang, Pengcheng

2018-03-01

This paper suggests a method to calculate the internal load distribution and contact stress of the thrust angular contact ball turntable bearing by FEA. The influence of the stiffness of the bearing structure and the plastic deformation of contact area on the internal load distribution and contact stress of the bearing is considered. In this method, the load-deformation relationship of the rolling elements is determined by the finite element contact analysis of a single rolling element and the raceway. Based on this, the nonlinear contact between the rolling elements and the inner and outer ring raceways is same as a nonlinear compression spring and bearing integral finite element analysis model including support structure was established. The effects of structural deformation and plastic deformation on the built-in stress distribution of slewing bearing are investigated on basis of comparing the consequences of load distribution, inner and outer ring stress, contact stress and other finite element analysis results with the traditional bearing theory, which has guiding function for improving the design of slewing bearing.

Nonlinear analysis of AS4/PEEK thermoplastic composite laminate using a one parameter plasticity model

NASA Technical Reports Server (NTRS)

Sun, C. T.; Yoon, K. J.

1990-01-01

A one-parameter plasticity model was shown to adequately describe the orthotropic plastic deformation of AS4/PEEK (APC-2) unidirectional thermoplastic composite. This model was verified further for unidirectional and laminated composite panels with and without a hole. The nonlinear stress-strain relations were measured and compared with those predicted by the finite element analysis using the one-parameter elastic-plastic constitutive model. The results show that the one-parameter orthotropic plasticity model is suitable for the analysis of elastic-plastic deformation of AS4/PEEK composite laminates.

Dynamics of associative polymer solutions: Capillary break-up, jetting and rheology

NASA Astrophysics Data System (ADS)

Sharma, Vivek; Serdy, James G.; Threfall-Holmes, Phil; McKinley, Gareth H.

2011-11-01

Associative polymer solutions are used in extensively in the formulations for water-borne paints, food, inks, cosmetics, etc to control the rheology and processing behavior of multi-component dispersions. These complex dispersions are processed and used over a broad range of shear and extensional rates. Furthermore, the commercially relevant formulations use dilute solutions of associative polymers, which have low viscosity and short relaxation times, and hence their non-Newtonian response is not apparent in a conventional rheometer. In this talk, we explore several methods for systematically exploring the linear and nonlinear solution rheology of associative polymer dispersions, including: fractional model description of physical gelation, high frequency oscillatory tests at frequencies up to 10 kHz, microfluidic shear rheometry at deformation rates up to 1000000 /s and the influence of transient extensional rheology in the jet breakup. We show that high deformation rates can be obtained in jetting flows, and the growth and evolution of instability during jetting and break-up of these viscoelastic fluids shows the influence of both elasticity and extensibility.

3D Finite Element Analysis of Yixing CFRD Built on Inclined Mountain Slope

NASA Astrophysics Data System (ADS)

Sun, Da Wei; Zhang, Liang; Qing Yao, Hui; Wang, Kang Ping

2018-05-01

There are few CFRDs built on steep slope with dam height more than 50 m. So does the relative design and construction experience. The 75 m-high Yixing CFRD was built on steep mountain slope and the 45.9m-high gravity retaining wall was used to against dam sliding. Since the excessive deformation of dam body and perimetric joints would lead to failure of seal materials and cause water leakage, 3D nonlinear finite element stress-deformation analysis was carried out. 3D finite element mesh with 63875 elements including retaining wall and surrounding mountain was established by use of advanced grid discreteness technique. Large scales of equations solving method were adopted in the computer procedure and the calculation time was greatly reduced from former 40 hours to now 45 minutes. Therefore the behavior of the dam, retaining wall and the joint was obtained in a short time, and the results would be helpful to the design and construction of Yixing dam.

A Novel Model to Simulate Flexural Complements in Compliant Sensor Systems

PubMed Central

Tang, Hongyan; Zhang, Dan; Guo, Sheng; Qu, Haibo

2018-01-01

The main challenge in analyzing compliant sensor systems is how to calculate the large deformation of flexural complements. Our study proposes a new model that is called the spline pseudo-rigid-body model (spline PRBM). It combines dynamic spline and the pseudo-rigid-body model (PRBM) to simulate the flexural complements. The axial deformations of flexural complements are modeled by using dynamic spline. This makes it possible to consider the nonlinear compliance of the system using four control points. Three rigid rods connected by two revolute (R) pins with two torsion springs replace the three lines connecting the four control points. The kinematic behavior of the system is described using Lagrange equations. Both the optimization and the numerical fitting methods are used for resolving the characteristic parameters of the new model. An example is given of a compliant mechanism to modify the accuracy of the model. The spline PRBM is important in expanding the applications of the PRBM to the design and simulation of flexural force sensors. PMID:29596377

Estimation of constitutive parameters for the Belridge Diatomite, South Belridge Diatomite Field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fossum, A.F.; Fredrich, J.T.

1998-06-01

A cooperative national laboratory/industry research program was initiated in 1994 that improved understanding of the geomechanical processes causing well casing damage during oil production from weak, compactible formations. The program focused on the shallow diatomaceous oil reservoirs located in California`s San Joaquin Valley, and combined analyses of historical field data, experimental determination of rock mechanical behavior, and geomechanical simulation of the reservoir and overburden response to production and injection. Sandia National Laboratories` quasi-static, large-deformation structural mechanics finite element code JAS3D was used to perform the three-dimensional geomechanical simulations. One of the material models implemented in JAS3D to simulate the time-independentmore » inelastic (non-linear) deformation of geomaterials is a generalized version of the Sandler and Rubin cap plasticity model (Sandler and Rubin, 1979). This report documents the experimental rock mechanics data and material cap plasticity models that were derived to describe the Belridge Diatomite reservoir rock at the South Belridge Diatomite Field, Section 33.« less

Study of a reinforced concrete beam strengthened using a combination of SMA wire and CFRP plate

NASA Astrophysics Data System (ADS)

Liu, Zhi-qiang; Li, Hui

2006-03-01

Traditional methods used for strengthening of reinforced concrete (RC) structures, such as bonding of steel plates, suffer from inherent disadvantages. In recent years, strengthening of RC structures using carbon fiber reinforced polymer (CFRP) plates has attracted considerable attentions around the world. Most existing research on CFRP plate bonding for flexural strengthening of RC beams has been carried out for the strength enhancement. However, little research is focused on effect of residual deformations on the strengthening. The residual deformations have an important effect on the strengthening by CFRP plates. There exists a very significant challenge how the residual deformations are reduced. Shape memory alloy (SMA) has showed outstanding functional properties as an actuator. It is a possibility that SMA can be used to reduce the residual deformation and make cracks of concrete close by imposing the recovery forces on the concrete in the tensile zone. It is only an emergency damage repair since the SMA wires need to be heated continuously. So, an innovative method of a RC beam strengthened by CFRP plates in combination with SMA wires was first investigated experimentally in this paper. In addition, the nonlinear finite element software of ABAQUS was employed to further simulate the behavior of RC beams strengthened through the new strengthening method. It can be found that this is an excellent and effective strengthening method.

Innovative design of composite structures: Axisymmetric deformations of unsymmetrically laminated cylinders loaded in axial compression

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Paraska, P. J.

1990-01-01

The study focuses on the axisymmetric deformation response of unsymmetrically laminate cylinders loaded in axial compression by known loads. A geometrically nonlinear analysis is used. Though buckling is not studied, the deformations can be considered to be the prebuckling response. Attention is directed at three 16 layer laminates: a (90 sub 8/0 sub 8) sub T; a (0 sub 8/90 sub 8) sub T and a (0/90) sub 4s. The symmetric laminate is used as a basis for comparison, while the two unsymmetric laminates were chosen because they have equal but opposite bending-stretching effects. Particular attention is given to the influence of the thermally-induced preloading deformations that accompany the cool-down of any unsymmetric laminate from the consolidation temperature. Simple support and clamped boundary conditions are considered. It is concluded that: (1) The radial deformations of an unsymmetric laminate are significantly larger than the radial deformations of a symmetric laminate, although for both symmetric and unsymmetric laminates the large deformations are confined to a boundary layer near the ends of the cylinder; (2) For this nonlinear problem the length of the boundary layer is a function of the applied load; (3) The sign of the radial deformations near the supported end of the cylinder depends strongly on the sense (sign) of the laminate asymmetry; (4) For unsymmetric laminates, ignoring the thermally-induced preloading deformations that accompany cool-down results in load-induced deformations that are under predicted; and (5) The support conditions strongly influence the response but the influence of the sense of asymmetry and the influence of the thermally-induced preloading deformations are independent of the support conditions.

Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades

NASA Technical Reports Server (NTRS)

Hodges, D. H.; Dowell, E. H.

1974-01-01

The equations of motion are developed by two complementary methods, Hamilton's principle and the Newtonian method. The resulting equations are valid to second order for long, straight, slender, homogeneous, isotropic beams undergoing moderate displacements. The ordering scheme is based on the restriction that squares of the bending slopes, the torsion deformation, and the chord/radius and thickness/radius ratios are negligible with respect to unity. All remaining nonlinear terms are retained. The equations are valid for beams with mass centroid axis and area centroid (tension) axis offsets from the elastic axis, nonuniform mass and stiffness section properties, variable pretwist, and a small precone angle. The strain-displacement relations are developed from an exact transformation between the deformed and undeformed coordinate systems. These nonlinear relations form an important contribution to the final equations. Several nonlinear structural and inertial terms in the final equations are identified that can substantially influence the aeroelastic stability and response of hingeless helicopter rotor blades.

Optimization of the dynamic behavior of strongly nonlinear heterogeneous materials

NASA Astrophysics Data System (ADS)

Herbold, Eric B.

New aspects of strongly nonlinear wave and structural phenomena in granular media are developed numerically, theoretically and experimentally. One-dimensional chains of particles and compressed powder composites are the two main types of materials considered here. Typical granular assemblies consist of linearly elastic spheres or layers of masses and effective nonlinear springs in one-dimensional columns for dynamic testing. These materials are highly sensitive to initial and boundary conditions, making them useful for acoustic and shock-mitigating applications. One-dimensional assemblies of spherical particles are examples of strongly nonlinear systems with unique properties. For example, if initially uncompressed, these materials have a sound speed equal to zero (sonic vacuum), supporting strongly nonlinear compression solitary waves with a finite width. Different types of assembled metamaterials will be presented with a discussion of the material's response to static compression. The acoustic diode effect will be presented, which may be useful in shock mitigation applications. Systems with controlled dissipation will also be discussed from an experimental and theoretical standpoint emphasizing the critical viscosity that defines the transition from an oscillatory to monotonous shock profile. The dynamic compression of compressed powder composites may lead to self-organizing mesoscale structures in two and three dimensions. A reactive granular material composed of a compressed mixture of polytetrafluoroethylene (PTFE), tungsten (W) and aluminum (Al) fine-grain powders exhibit this behavior. Quasistatic, Hopkinson bar, and drop-weight experiments show that composite materials with a high porosity and fine metallic particles exhibit a higher strength than less porous mixtures with larger particles, given the same mass fraction of constituents. A two-dimensional Eulerian hydrocode is implemented to investigate the mechanical deformation and failure of the compressed powder samples in simulated drop-weight tests. The calculations indicate that the dynamic formation of mesoscale force chains increase the strength of the sample. This is also apparent in three-dimensional finite element calculations of drop-weight test simulations using LS-Dyna despite a higher granular bulk coordination number, and an increased mobility of individual grains.

Review of severe deformation recommended practice through analyses - comparison of two cab car end frame designs

DOT National Transportation Integrated Search

2005-03-16

Non-linear large deformation analyses have been conducted : to evaluate the performance of the cab car corner and collision : posts of the Federal Railroad Administration's (FRA) : sponsored state-of-the-art (SOA) end frame design and the : Bombardie...

Modelling of deformation of underground tunnel lining, interacting with water-saturated soil

NASA Astrophysics Data System (ADS)

Berezhnoi, D. V.; Balafendieva, I. S.; Sachenkov, A. A.; Sekaeva, L. R.

2016-11-01

Built finite element method of calculating the deformation of underground tunnel lining, interacting with dry and water-saturated soils. To simulate the interaction between the lining and soils environments, including physical and non-linear, a special "contact" finite element, which allows to consider all cases of interaction between the contacting surfaces. It solved a number of problems of deformation with the ground subway tunnel lining rings.

Assessment of regional ventilation and deformation using 4D-CT imaging for healthy human lungs during tidal breathing

PubMed Central

Jahani, Nariman; Choi, Jiwoong; Iyer, Krishna; Hoffman, Eric A.

2015-01-01

This study aims to assess regional ventilation, nonlinearity, and hysteresis of human lungs during dynamic breathing via image registration of four-dimensional computed tomography (4D-CT) scans. Six healthy adult humans were studied by spiral multidetector-row CT during controlled tidal breathing as well as during total lung capacity and functional residual capacity breath holds. Static images were utilized to contrast static vs. dynamic (deep vs. tidal) breathing. A rolling-seal piston system was employed to maintain consistent tidal breathing during 4D-CT spiral image acquisition, providing required between-breath consistency for physiologically meaningful reconstructed respiratory motion. Registration-derived variables including local air volume and anisotropic deformation index (ADI, an indicator of preferential deformation in response to local force) were employed to assess regional ventilation and lung deformation. Lobar distributions of air volume change during tidal breathing were correlated with those of deep breathing (R2 ≈ 0.84). Small discrepancies between tidal and deep breathing were shown to be likely due to different distributions of air volume change in the left and the right lungs. We also demonstrated an asymmetric characteristic of flow rate between inhalation and exhalation. With ADI, we were able to quantify nonlinearity and hysteresis of lung deformation that can only be captured in dynamic images. Nonlinearity quantified by ADI is greater during inhalation, and it is stronger in the lower lobes (P < 0.05). Lung hysteresis estimated by the difference of ADI between inhalation and exhalation is more significant in the right lungs than that in the left lungs. PMID:26316512

A higher-order theory for geometrically nonlinear analysis of composite laminates

NASA Technical Reports Server (NTRS)

Reddy, J. N.; Liu, C. F.

1987-01-01

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Buckling Behavior of Compression-Loaded Quasi-Isotropic Curved Panels with a Circular Cutout

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Britt, Vicki O.; Nemeth, Michael P.

1999-01-01

Results from a numerical and experimental study of the response of compression-loaded quasi-isotropic curved panels with a centrally located circular cutout are presented. The numerical results were obtained by using a geometrically nonlinear finite element analysis code. The effects of cutout size, panel curvature and initial geo- metric imperfections on the overall response of compression-loaded panels are described. In addition, results are presented from a numerical parametric study that indicate the effects of elastic circumferential edge restraints on the prebuckling and buckling response of a selected panel and these numerical results are compared to experimentally measured results. These restraints are used to identify the effects of circumferential edge restraints that are introduced by the test fixture that was used in the present study. It is shown that circumferential edge restraints can introduce substantial nonlinear prebuckling deformations into shallow compression-loaded curved panels that can results in a significant increase in buckling load.

A Linearized and Incompressible Constitutive Model for Arteries

PubMed Central

Liu, Y.; Zhang, W.; Wang, C.; Kassab, G. S.

2011-01-01

In many biomechanical studies, blood vessels can be modeled as pseudoelastic orthotropic materials that are incompressible (volume-preserving) under physiological loading. To use a minimum number of elastic constants to describe the constitutive behavior of arteries, we adopt a generalized Hooke’s law for the co-rotational Cauchy stress and a recently proposed logarithmic-exponential strain. This strain tensor absorbs the material nonlinearity and its trace is zero for volume-preserving deformations. Thus, the relationships between model parameters due to the incompressibility constraint are easy to analyze and interpret. In particular, the number of independent elastic constants reduces from ten to seven in the orthotropic model. As an illustratory study, we fit this model to measured data of porcine coronary arteries in inflation-stretch tests. Four parameters, n (material nonlinearity), Young’s moduli E1 (circumferential), E2 (axial), and E3 (radial) are necessary to fit the data. The advantages and limitations of this model are discussed. PMID:21605567

A linearized and incompressible constitutive model for arteries.

PubMed

Liu, Y; Zhang, W; Wang, C; Kassab, G S

2011-10-07

In many biomechanical studies, blood vessels can be modeled as pseudoelastic orthotropic materials that are incompressible (volume-preserving) under physiological loading. To use a minimum number of elastic constants to describe the constitutive behavior of arteries, we adopt a generalized Hooke's law for the co-rotational Cauchy stress and a recently proposed logarithmic-exponential strain. This strain tensor absorbs the material nonlinearity and its trace is zero for volume-preserving deformations. Thus, the relationships between model parameters due to the incompressibility constraint are easy to analyze and interpret. In particular, the number of independent elastic constants reduces from ten to seven in the orthotropic model. As an illustratory study, we fit this model to measured data of porcine coronary arteries in inflation-stretch tests. Four parameters, n (material nonlinearity), Young's moduli E₁ (circumferential), E₂ (axial), and E₃ (radial) are necessary to fit the data. The advantages and limitations of this model are discussed. Copyright © 2011 Elsevier Ltd. All rights reserved.

BOOK REVIEW: Nonlinear Continuum Mechanics for Finite Element Analysis

NASA Astrophysics Data System (ADS)

Bialek, James M.

1998-05-01

Nonlinear continuum mechanics of solids is a fascinating subject. All the assumptions inherited from an overexposure to linear behaviour and analysis must be re-examined. The standard definitions of strain designed for small deformation linear problems may be totally misleading when finite motion or large deformations are considered. Nonlinear behaviour includes phenomena like `snap-through', where bifurcation theory is applied to engineering design. Capabilities in this field are growing at a fantastic speed; for example, modern automobiles are presently being designed to crumple in the most energy absorbing manner in order to protect the occupants. The combination of nonlinear mechanics and the finite element method is a very important field. Most engineering designs encountered in the fusion effort are strictly limited to small deformation linear theory. In fact, fusion devices are usually kept in the low stress, long life regime that avoids large deformations, nonlinearity and any plastic behaviour. The only aspect of nonlinear continuum solid mechanics about which the fusion community now worries is that rare case where details of the metal forming process must be considered. This text is divided into nine sections: introduction, mathematical preliminaries, kinematics, stress and equilibrium, hyperelasticity, linearized equilibrium equations, discretization and solution, computer implementation and an appendix covering an introduction to large inelastic deformations. The authors have decided to use vector and tensor notation almost exclusively. This means that the usual maze of indicial equations is avoided, but most readers will therefore be stretched considerably to follow the presentation, which quickly proceeds to the heart of nonlinear behaviour in solids. With great speed the reader is led through the material (Lagrangian) and spatial (Eulerian) co-ordinates, the deformation gradient tensor (an example of a two point tensor), the right and left Cauchy-Green tensors, the Eulerian or Almansi strain tensor, distortional components, strain rate tensors, rate of deformation tensors, spin tensors and objectivity. The standard Cauchy stress tensor is mentioned in passing, and then virtual work and work conjugacy lead to alternative stress representations such as the Piola-Kirchoff representation. Chapter 5 concentrates on hyperelasticity (where stresses are derived from a stored energy function) and its subvarieties. Chapter 6 proceeds by linearizing the virtual work statement prior to discretization and Chapter 7 deals with approaches to solving the formulation. In Chapter 8 the FORTRAN finite element code written by Bonet (available via the world wide web) is described. In summary this book is written by experts, for future experts, and provides a very fast review of the field for people who already know the topic. The authors assume the reader is familiar with `elementary stress analysis' and has had some exposure to `the principle of the finite element method'. Their goals are summarized by the statement, `If the reader is prepared not to get too hung up on details, it is possible to use the book to obtain a reasonable overview of the subject'. This is a very nice summary of what is going on in the field but as a stand-alone text it is much too terse. The total bibliography is a page and a half. It would be an improvement if there were that much reference material for each chapter.

Parametric Studies of Square Solar Sails Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Sleight, David W.; Muheim, Danniella M.

2004-01-01

Parametric studies are performed on two generic square solar sail designs to identify parameters of interest. The studies are performed on systems-level models of full-scale solar sails, and include geometric nonlinearity and inertia relief, and use a Newton-Raphson scheme to apply sail pre-tensioning and solar pressure. Computational strategies and difficulties encountered during the analyses are also addressed. The purpose of this paper is not to compare the benefits of one sail design over the other. Instead, the results of the parametric studies may be used to identify general response trends, and areas of potential nonlinear structural interactions for future studies. The effects of sail size, sail membrane pre-stress, sail membrane thickness, and boom stiffness on the sail membrane and boom deformations, boom loads, and vibration frequencies are studied. Over the range of parameters studied, the maximum sail deflection and boom deformations are a nonlinear function of the sail properties. In general, the vibration frequencies and modes are closely spaced. For some vibration mode shapes, local deformation patterns that dominate the response are identified. These localized patterns are attributed to the presence of negative stresses in the sail membrane that are artifacts of the assumption of ignoring the effects of wrinkling in the modeling process, and are not believed to be physically meaningful. Over the range of parameters studied, several regions of potential nonlinear modal interaction are identified.

Poromechanics Parameters of Fluid-Saturated Chemically Active Fibrous Media Derived from a Micromechanical Approach.

PubMed

Misra, Anil; Parthasarathy, Ranganathan; Singh, Viraj; Spencer, Paulette

2013-01-01

The authors have derived macroscale poromechanics parameters for chemically active saturated fibrous media by combining microstructure-based homogenization with Hill's volume averaging. The stress-strain relationship of the dry fibrous media is first obtained by considering the fiber behavior. The constitutive relationships applicable to saturated media are then derived in the poromechanics framework using Hill's Lemmas. The advantage of this approach is that the resultant continuum model assumes a form suited to study porous materials, while retaining the effect of discrete fiber deformation. As a result, the model is able to predict the influence of microscale phenomena such as fiber buckling on the overall behavior, and in particular, on the poromechanics constants. The significance of the approach is demonstrated using the effect of drainage and fiber nonlinearity on monotonic compressive stress-strain behavior. The model predictions conform to the experimental observations for articular cartilage. The method can potentially be extended to other porous materials such as bone, clays, foams, and concrete.

Modeling the Nonlinear, Strain Rate Dependent Deformation of Woven Ceramic Matrix Composites With Hydrostatic Stress Effects Included

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Carney, Kelly S.

2004-01-01

An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites with a plain weave fiber architecture. In the developed model, the differences in the tension and compression response have also been considered. State variable based viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear stiffness is independent of the stiffness in the normal directions. The developed equations have been implemented into a commercially available transient dynamic finite element code, LS-DYNA, through the use of user defined subroutines (UMATs). The tensile, compressive, and shear deformation of a representative plain weave woven ceramic matrix composite are computed and compared to experimental results. The computed values correlate well to the experimental data, demonstrating the ability of the model to accurately compute the deformation response of woven ceramic matrix composites.

Hydrothermal deformation of granular quartz sand

NASA Astrophysics Data System (ADS)

Karner, Stephen L.; Kronenberg, Andreas K.; Chester, Frederick M.; Chester, Judith S.; Hajash, Andrew

2008-05-01

Isotropic and triaxial compression experiments were performed on porous aggregates of St Peter quartz sand to explore the influence of temperature (to 225°C). During isotropic stressing, samples loaded at elevated temperature exhibit the same sigmoidal stress-strain curves and non-linear acoustic emission rates as have previously been observed from room temperature studies on sands, sandstones, and soils. However, results from our hydrothermal experiments show that the critical effective pressure (P*) associated with the onset of significant pore collapse and pervasive cataclastic flow is lower at increased temperature. Samples subjected to triaxial loading at elevated temperature show yield behavior resembling that observed from room temperature studies on granular rocks and soils. When considered in terms of distortional and mean stresses, the yield strength data for a given temperature define an elliptical envelope consistent with critical state and CAP models from soil mechanics. For the conditions we tested, triaxial yield data at low effective pressure are essentially temperature-insensitive whereas yield levels at high effective pressure are lowered as a function of elevated temperature. We interpret our yield data in a manner consistent with Arrhenius behavior expected for thermally assisted subcritical crack growth. Taken together, our results indicate that increased stresses and temperatures associated with subsurface burial will significantly alter the yield strength of deforming granular media in systematic and predictable ways.

Fractional viscoelasticity of soft elastomers and auxetic foams

NASA Astrophysics Data System (ADS)

Solheim, Hannah; Stanisauskis, Eugenia; Miles, Paul; Oates, William

2018-03-01

Dielectric elastomers are commonly implemented in adaptive structures due to their unique capabilities for real time control of a structure's shape, stiffness, and damping. These active polymers are often used in applications where actuator control or dynamic tunability are important, making an accurate understanding of the viscoelastic behavior critical. This challenge is complicated as these elastomers often operate over a broad range of deformation rates. Whereas research has demonstrated success in applying a nonlinear viscoelastic constitutive model to characterize the behavior of Very High Bond (VHB) 4910, robust predictions of the viscoelastic response over the entire range of time scales is still a significant challenge. An alternative formulation for viscoelastic modeling using fractional order calculus has shown significant improvement in predictive capabilities. While fractional calculus has been explored theoretically in the field of linear viscoelasticity, limited experimental validation and statistical evaluation of the underlying phenomena have been considered. In the present study, predictions across several orders of magnitude in deformation rates are validated against data using a single set of model parameters. Moreover, we illustrate the fractional order is material dependent by running complementary experiments and parameter estimation on the elastomer VHB 4949 as well as an auxetic foam. All results are statistically validated using Bayesian uncertainty methods to obtain posterior densities for the fractional order as well as the hyperelastic parameters.

Nonlinear Analysis of the Space Shuttle Superlightweight LO2 Tank. Part 2; Behavior Under 3g End-of-Flight Loads

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H.,Jr.

1998-01-01

Results of linear bifurcation and nonlinear analyses of the Space Shuttle super lightweight (SLWT) external liquid-oxygen (LO2) tank are presented for an important end-of-flight loading condition. These results illustrate an important type of response mode for thin-walled shells, that are subjected to combined mechanical and thermal loads, that may be encountered in the design of other liquid-fuel launch vehicles. Linear bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the aft dome of the LO2 tank. In contrast, the nonlinear response phenomenon is shown to consist of a short-wavelength bending deformation in the aft elliptical dome of the LO2 tank that grows in amplitude in a stable manner with increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the aft dome. For the linear bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shell generally require a large-scale, high fidelity finite-element model. Results are also presented that show that the SLWT LO2 tank can support loads in excess of approximately 1.9 times the values of the operational loads considered.

Generalized Quantum Field Theory Based on a Nonlinear Deformed Heisenberg Algebra

NASA Astrophysics Data System (ADS)

Ribeiro-Silva, C. I.; Oliveira-Neto, N. M.

We consider a quantum field theory based on a nonlinear Heisenberg algebra which describes phenomenologically a composite particle. Perturbative computation, considering the λϕ4 interaction was done and we also performed some comparison with a quantum field theory based on the q-oscillator algebra.

Self-sustained peristaltic waves: Explicit asymptotic solutions

NASA Astrophysics Data System (ADS)

Dudchenko, O. A.; Guria, G. Th.

2012-02-01

A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

Laser-driven interactions and resultant instabilities in materials with high dielectric constant

NASA Astrophysics Data System (ADS)

Rajpoot, Moolchandra; Dixit, Sanjay

2015-07-01

An analytical investigation of nonlinear interactions resulting in parametric amplification of acoustic wave is made by obtaining the dispersion relation using hydrodynamic model of inhomogeneous plasma by applying large static field at an arbitrary angle with the pump wave. The investigation shows that many early studies have neglected dependence of dielectric constant on deformation of materials but deformation of materials does infect depends on the dielectric constant of medium. Thus we have assumed to high dielectric material like BaTiO3 which resulted in substantially high growth rate of threshold electric field which opens a new dimension to study nonlinear interactions and instabilities.

Triplex molecular layers with nonlinear nanomechanical response

NASA Astrophysics Data System (ADS)

Tsukruk, V. V.; Ahn, H.-S.; Kim, D.; Sidorenko, A.

2002-06-01

The molecular design of surface structures with built-in mechanisms for mechanical energy dissipation under nanomechanical deformation and compression resistance provided superior nanoscale wear stability. We designed robust, well-defined trilayer surface nanostructures chemically grafted to a silicon oxide surface with an effective composite modulus of about 1 GPa. The total thickness was within 20-30 nm and included an 8 nm rubber layer sandwiched between two hard layers. The rubber layer provides an effective mechanism for energy dissipation, facilitated by nonlinear, giant, reversible elastic deformations of the rubber matrix, restoring the initial status due to the presence of an effective nanodomain network and chemical grafting within the rubber matrix.

Nonlinear Equations of Equilibrium for Elastic Helicopter or Wind Turbine Blades Undergoing Moderate Deformation

NASA Technical Reports Server (NTRS)

Rosen, A.; Friedmann, P. P.

1978-01-01

A set of nonlinear equations of equilibrium for an elastic wind turbine or helicopter blades are presented. These equations are derived for the case of small strains and moderate rotations (slopes). The derivation includes several assumptions which are carefully stated. For the convenience of potential users the equations are developed with respect to two different systems of coordinates, the undeformed and the deformed coordinates of the blade. Furthermore, the loads acting on the blade are given in a general form so as to make them suitable for a variety of applications. The equations obtained in the study are compared with those obtained in previous studies.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1985-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1986-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

A discrete element model for the investigation of the geometrically nonlinear behaviour of solids

NASA Astrophysics Data System (ADS)

Ockelmann, Felix; Dinkler, Dieter

2018-07-01

A three-dimensional discrete element model for elastic solids with large deformations is presented. Therefore, an discontinuum approach is made for solids. The properties of elastic material are transferred analytically into the parameters of a discrete element model. A new and improved octahedron gap-filled face-centred cubic close packing of spheres is split into unit cells, to determine the parameters of the discrete element model. The symmetrical unit cells allow a model with equal shear components in each contact plane and fully isotropic behaviour for Poisson's ratio above 0. To validate and show the broad field of applications of the new model, the pin-pin Euler elastica is presented and investigated. The thin and sensitive structure tends to undergo large deformations and rotations with a highly geometrically nonlinear behaviour. This behaviour of the elastica can be modelled and is compared to reference solutions. Afterwards, an improved more realistic simulation of the elastica is presented which softens secondary buckling phenomena. The model is capable of simulating solids with small strains but large deformations and a strongly geometrically nonlinear behaviour, taking the shear stiffness of the material into account correctly.

Implementation of Improved Transverse Shear Calculations and Higher Order Laminate Theory Into Strain Rate Dependent Analyses of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Zhu, Lin-Fa; Kim, Soo; Chattopadhyay, Aditi; Goldberg, Robert K.

2004-01-01

A numerical procedure has been developed to investigate the nonlinear and strain rate dependent deformation response of polymer matrix composite laminated plates under high strain rate impact loadings. A recently developed strength of materials based micromechanics model, incorporating a set of nonlinear, strain rate dependent constitutive equations for the polymer matrix, is extended to account for the transverse shear effects during impact. Four different assumptions of transverse shear deformation are investigated in order to improve the developed strain rate dependent micromechanics model. The validities of these assumptions are investigated using numerical and theoretical approaches. A method to determine through the thickness strain and transverse Poisson's ratio of the composite is developed. The revised micromechanics model is then implemented into a higher order laminated plate theory which is modified to include the effects of inelastic strains. Parametric studies are conducted to investigate the mechanical response of composite plates under high strain rate loadings. Results show the transverse shear stresses cannot be neglected in the impact problem. A significant level of strain rate dependency and material nonlinearity is found in the deformation response of representative composite specimens.

A computational procedure for multibody systems including flexible beam dynamics

NASA Technical Reports Server (NTRS)

Downer, J. D.; Park, K. C.; Chiou, J. C.

1990-01-01

A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. A fully nonlinear continuum approach capable of accounting for both finite rotations and large deformations has been used to model a flexible beam component. The beam kinematics are referred directly to an inertial reference frame such that the degrees of freedom embody both the rigid and flexible deformation motions. As such, the beam inertia expression is identical to that of rigid body dynamics. The nonlinear coupling between gross body motion and elastic deformation is contained in the internal force expression. Numerical solution procedures for the integration of spatial kinematic systems can be directily applied to the generalized coordinates of both the rigid and flexible components. An accurate computation of the internal force term which is invariant to rigid motions is incorporated into the general solution procedure.

Deformation-Aware Log-Linear Models

NASA Astrophysics Data System (ADS)

Gass, Tobias; Deselaers, Thomas; Ney, Hermann

In this paper, we present a novel deformation-aware discriminative model for handwritten digit recognition. Unlike previous approaches our model directly considers image deformations and allows discriminative training of all parameters, including those accounting for non-linear transformations of the image. This is achieved by extending a log-linear framework to incorporate a latent deformation variable. The resulting model has an order of magnitude less parameters than competing approaches to handling image deformations. We tune and evaluate our approach on the USPS task and show its generalization capabilities by applying the tuned model to the MNIST task. We gain interesting insights and achieve highly competitive results on both tasks.

Mesoscale Modeling of Nonlinear Elasticity and Fracture in Ceramic Polycrystals Under Dynamic Shear and Compression

DTIC Science & Technology

2012-08-01

investigation of heterogeneous microplasticity in ceramics deformed under high confining stresses. Mech. Mater. 37, 95–112. Zhang, K., Wu, M., Feng, R., 2005b...Simulation of microplasticity -induced deformation in uniaxially strained ceramics by 3-D Voronoi polycrystal modeling. Int. J. Plasticity 21, 801–834

Solitons in a nonlinear model of spin transport in helical molecules

NASA Astrophysics Data System (ADS)

Albares, P.; Díaz, E.; Cerveró, Jose M.; Domínguez-Adame, F.; Diez, E.; Estévez, P. G.

2018-02-01

We study an effective integrable nonlinear model describing an electron moving along the axis of a deformable helical molecule. The helical conformation of dipoles in the molecular backbone induces an unconventional Rashba-like interaction that couples the electron spin with its linear momentum. In addition, a focusing nonlinearity arises from the electron-lattice interaction, enabling the formation of a variety of stable solitons such as bright solitons, breathers, and rogue waves. A thorough study of the soliton solutions for both focusing and defocusing nonlinear interaction is presented and discussed.

High-contrast imaging with an arbitrary aperture: active correction of aperture discontinuities

NASA Astrophysics Data System (ADS)

Pueyo, Laurent; Norman, Colin; Soummer, Rémi; Perrin, Marshall; N'Diaye, Mamadou; Choquet, Elodie

2013-09-01

We present a new method to achieve high-contrast images using segmented and/or on-axis telescopes. Our approach relies on using two sequential Deformable Mirrors to compensate for the large amplitude excursions in the telescope aperture due to secondary support structures and/or segment gaps. In this configuration the parameter landscape of Deformable Mirror Surfaces that yield high contrast Point Spread Functions is not linear, and non-linear methods are needed to find the true minimum in the optimization topology. We solve the highly non-linear Monge-Ampere equation that is the fundamental equation describing the physics of phase induced amplitude modulation. We determine the optimum configuration for our two sequential Deformable Mirror system and show that high-throughput and high contrast solutions can be achieved using realistic surface deformations that are accessible using existing technologies. We name this process Active Compensation of Aperture Discontinuities (ACAD). We show that for geometries similar to JWST, ACAD can attain at least 10-7 in contrast and an order of magnitude higher for future Extremely Large Telescopes, even when the pupil features a missing segment" . We show that the converging non-linear mappings resulting from our Deformable Mirror shapes actually damp near-field diffraction artifacts in the vicinity of the discontinuities. Thus ACAD actually lowers the chromatic ringing due to diffraction by segment gaps and strut's while not amplifying the diffraction at the aperture edges beyond the Fresnel regime and illustrate the broadband properties of ACAD in the case of the pupil configuration corresponding to the Astrophysics Focused Telescope Assets. Since details about these telescopes are not yet available to the broader astronomical community, our test case is based on a geometry mimicking the actual one, to the best of our knowledge.

The viscoelastic standard nonlinear solid model: predicting the response of the lumbar intervertebral disk to low-frequency vibrations.

PubMed

Groth, Kevin M; Granata, Kevin P

2008-06-01

Due to the mathematical complexity of current musculoskeletal spine models, there is a need for computationally efficient models of the intervertebral disk (IVD). The aim of this study is to develop a mathematical model that will adequately describe the motion of the IVD under axial cyclic loading as well as maintain computational efficiency for use in future musculoskeletal spine models. Several studies have successfully modeled the creep characteristics of the IVD using the three-parameter viscoelastic standard linear solid (SLS) model. However, when the SLS model is subjected to cyclic loading, it underestimates the load relaxation, the cyclic modulus, and the hysteresis of the human lumbar IVD. A viscoelastic standard nonlinear solid (SNS) model was used to predict the response of the human lumbar IVD subjected to low-frequency vibration. Nonlinear behavior of the SNS model was simulated by a strain-dependent elastic modulus on the SLS model. Parameters of the SNS model were estimated from experimental load deformation and stress-relaxation curves obtained from the literature. The SNS model was able to predict the cyclic modulus of the IVD at frequencies of 0.01 Hz, 0.1 Hz, and 1 Hz. Furthermore, the SNS model was able to quantitatively predict the load relaxation at a frequency of 0.01 Hz. However, model performance was unsatisfactory when predicting load relaxation and hysteresis at higher frequencies (0.1 Hz and 1 Hz). The SLS model of the lumbar IVD may require strain-dependent elastic and viscous behavior to represent the dynamic response to compressive strain.

Seismic Performance Evaluation of Reinforced Concrete Frames Subjected to Seismic Loads

NASA Astrophysics Data System (ADS)

Zameeruddin, Mohd.; Sangle, Keshav K.

2017-06-01

Ten storied-3 bays reinforced concrete bare frame designed for gravity loads following the guidelines of IS 456 and IS 13920 for ductility is subjected to seismic loads. The seismic demands on this building were calculated by following IS 1893 for response spectra of 5% damping (for hard soil type). Plastic hinges were assigned to the beam and column at both ends to represent the failure mode, when member yields. Non-linear static (pushover) analysis was performed to evaluate the performance of the building in reference to first (ATC 40), second (FEMA 356) and next-generation (FEMA 440) performance based seismic design procedures. Base shear against top displacement curve of structure, known as pushover curve was obtained for two actions of plastic hinge behavior, force-controlled (brittle) and deformation-controlled (ductile) actions. Lateral deformation corresponding to performance point proves the building capability to sustain a certain level of seismic loads. The failure is represented by a sequence of formation of plastic hinges. Deformation-controlled action of hinges showed that building behaves like strong-column-weak-beam mechanism, whereas force-controlled action showed formation of hinges in the column. The study aims to understand the first, second and next generation performance based design procedure in prediction of actual building responses and their conservatism into the acceptance criteria.

Hybrid High-Order methods for finite deformations of hyperelastic materials

NASA Astrophysics Data System (ADS)

Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas

2018-01-01

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.

A generalized electro-elastic theory of polymer networks

NASA Astrophysics Data System (ADS)

Cohen, Noy

2018-01-01

A rigorous multi-scale analysis of the electromechanical coupling in dielectric polymers is conducted. The body couples stemming from a misalignment between the electric field and the electric-dipole density vector are studied and the conservation laws for polymer networks are derived. Using variational principles, expressions for the polarization and the stress are determined. Interestingly, it is found that the stress tensor resulting from coupled loadings in which the electric field is misaligned with the principal stretch directions is not symmetric and the asymmetry arises from the body couples. Next, the electro-mechanical response of a chain is analyzed. The deformations of the individual polymer chains are related to the macroscopic deformation via two highly non-linear constraints - the first pertaining to the compatibility of the local deformations with the imposed macroscopic one and the second stems from the symmetric part of the stress at equilibrium. In accord with the proposed framework, an amended three-chains model is introduced. The predictions of this model are found to be in excellent agreement with experimental findings. Lastly, the behavior of a polymer subjected to a simple shear and an electric field is studied. The offset between the electric field and the principal directions gives rise to body couples, a polarization that is not aligned with the electric field, and an asymmetric stress tensor.

Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient.

PubMed

Weickenmeier, J; Jabareen, M

2014-11-01

The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery. Copyright © 2014 John Wiley & Sons, Ltd.

Nonlinear modeling, strength-based design, and testing of flexible piezoelectric energy harvesters under large dynamic loads for rotorcraft applications

NASA Astrophysics Data System (ADS)

Leadenham, Stephen; Erturk, Alper

2014-04-01

There has been growing interest in enabling wireless health and usage monitoring for rotorcraft applications, such as helicopter rotor systems. Large dynamic loads and acceleration fluctuations available in these environments make the implementation of vibration-based piezoelectric energy harvesters a very promising choice. However, such extreme loads transmitted to the harvester can also be detrimental to piezoelectric laminates and overall system reliability. Particularly flexible resonant cantilever configurations tuned to match the dominant excitation frequency can be subject to very large deformations and failure of brittle piezoelectric laminates due to excessive bending stresses at the root of the harvester. Design of resonant piezoelectric energy harvesters for use in these environments require nonlinear electroelastic dynamic modeling and strength-based analysis to maximize the power output while ensuring that the harvester is still functional. This paper presents a mathematical framework to design and analyze the dynamics of nonlinear flexible piezoelectric energy harvesters under large base acceleration levels. A strength-based limit is imposed to design the piezoelectric energy harvester with a proof mass while accounting for material, geometric, and dissipative nonlinearities, with a focus on two demonstrative case studies having the same linear fundamental resonance frequency but different overhang length and proof mass values. Experiments are conducted at different excitation levels for validation of the nonlinear design approach proposed in this work. The case studies in this work reveal that harvesters exhibiting similar behavior and power generation performance at low excitation levels (e.g. less than 0.1g) can have totally different strength-imposed performance limitations under high excitations (e.g. above 1g). Nonlinear modeling and strength-based design is necessary for such excitation levels especially when using resonant cantilevers with no geometric constraint.

A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2013-01-01

A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

Nonlinear material behaviour of spider silk yields robust webs.

PubMed

Cranford, Steven W; Tarakanova, Anna; Pugno, Nicola M; Buehler, Markus J

2012-02-01

Natural materials are renowned for exquisite designs that optimize function, as illustrated by the elasticity of blood vessels, the toughness of bone and the protection offered by nacre. Particularly intriguing are spider silks, with studies having explored properties ranging from their protein sequence to the geometry of a web. This material system, highly adapted to meet a spider's many needs, has superior mechanical properties. In spite of much research into the molecular design underpinning the outstanding performance of silk fibres, and into the mechanical characteristics of web-like structures, it remains unknown how the mechanical characteristics of spider silk contribute to the integrity and performance of a spider web. Here we report web deformation experiments and simulations that identify the nonlinear response of silk threads to stress--involving softening at a yield point and substantial stiffening at large strain until failure--as being crucial to localize load-induced deformation and resulting in mechanically robust spider webs. Control simulations confirmed that a nonlinear stress response results in superior resistance to structural defects in the web compared to linear elastic or elastic-plastic (softening) material behaviour. We also show that under distributed loads, such as those exerted by wind, the stiff behaviour of silk under small deformation, before the yield point, is essential in maintaining the web's structural integrity. The superior performance of silk in webs is therefore not due merely to its exceptional ultimate strength and strain, but arises from the nonlinear response of silk threads to strain and their geometrical arrangement in a web.

Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels

PubMed Central

Nam, Sungmin; Hu, Kenneth H.; Chaudhuri, Ovijit

2016-01-01

The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction. PMID:27140623

Multidirectional In Vivo Characterization of Skin Using Wiener Nonlinear Stochastic System Identification Techniques.

PubMed

Parker, Matthew D; Jones, Lynette A; Hunter, Ian W; Taberner, A J; Nash, M P; Nielsen, P M F

2017-01-01

A triaxial force-sensitive microrobot was developed to dynamically perturb skin in multiple deformation modes, in vivo. Wiener static nonlinear identification was used to extract the linear dynamics and static nonlinearity of the force-displacement behavior of skin. Stochastic input forces were applied to the volar forearm and thenar eminence of the hand, producing probe tip perturbations in indentation and tangential extension. Wiener static nonlinear approaches reproduced the resulting displacements with variances accounted for (VAF) ranging 94-97%, indicating a good fit to the data. These approaches provided VAF improvements of 0.1-3.4% over linear models. Thenar eminence stiffness measures were approximately twice those measured on the forearm. Damping was shown to be significantly higher on the palm, whereas the perturbed mass typically was lower. Coefficients of variation (CVs) for nonlinear parameters were assessed within and across individuals. Individual CVs ranged from 2% to 11% for indentation and from 2% to 19% for extension. Stochastic perturbations with incrementally increasing mean amplitudes were applied to the same test areas. Differences between full-scale and incremental reduced-scale perturbations were investigated. Different incremental preloading schemes were investigated. However, no significant difference in parameters was found between different incremental preloading schemes. Incremental schemes provided depth-dependent estimates of stiffness and damping, ranging from 300 N/m and 2 Ns/m, respectively, at the surface to 5 kN/m and 50 Ns/m at greater depths. The device and techniques used in this research have potential applications in areas, such as evaluating skincare products, assessing skin hydration, or analyzing wound healing.

[Research progress on real-time deformable models of soft tissues for surgery simulation].

PubMed

Xu, Shaoping; Liu, Xiaoping; Zhang, Hua; Luo, Jie

2010-04-01

Biological tissues generally exhibit nonlinearity, anisotropy, quasi-incompressibility and viscoelasticity about material properties. Simulating the behaviour of elastic objects in real time is one of the current objectives of virtual surgery simulation which is still a challenge for researchers to accurately depict the behaviour of human tissues. In this paper, we present a classification of the different deformable models that have been developed. We present the advantages and disadvantages of each one. Finally, we make a comparison of deformable models and perform an evaluation of the state of the art and the future of deformable models.

Nonlinear integral equations for the sausage model

NASA Astrophysics Data System (ADS)

Ahn, Changrim; Balog, Janos; Ravanini, Francesco

2017-08-01

The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to ‘sausage’ shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λ integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonlinear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For a consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between ν and λ. Dedicated to the memory of Petr Petrovich Kulish.

Surface Spectroscopic Signatures of Mechanical Deformation in HDPE.

PubMed

Averett, Shawn C; Stanley, Steven K; Hanson, Joshua J; Smith, Stacey J; Patterson, James E

2018-01-01

High-density polyethylene (HDPE) has been extensively studied, both as a model for semi-crystalline polymers and because of its own industrial utility. During cold drawing, crystalline regions of HDPE are known to break up and align with the direction of tensile load. Structural changes due to deformation should also manifest at the surface of the polymer, but until now, a detailed molecular understanding of how the surface responds to mechanical deformation has been lacking. This work establishes a precedent for using vibrational sum-frequency generation (VSFG) spectroscopy to investigate changes in the molecular-level structure of the surface of HDPE after cold drawing. X-ray diffraction (XRD) was used to confirm that the observed surface behavior corresponds to the expected bulk response. Before tensile loading, the VSFG spectra indicate that there is significant variability in the surface structure and tilt of the methylene groups away from the surface normal. After deformation, the VSFG spectroscopic signatures are notably different. These changes suggest that hydrocarbon chains at the surface of visibly necked HDPE are aligned with the direction of loading, while the associated methylene groups are oriented with the local C 2 v symmetry axis roughly parallel to the surface normal. Small amounts of unaltered material are also found at the surface of necked HDPE, with the relative amount of unaltered material decreasing as the amount of deformation increases. Aspects of the nonresonant SFG response in the transition zone between necked and undeformed polymer provide additional insight into the deformation process and may provide the first indication of mechanical deformation. Nonlinear surface spectroscopy can thus be used as a noninvasive and nondestructive tool to probe the stress history of a HPDE sample in situations where X-ray techniques are not available or not applicable. Vibrational sum-frequency generation thus has great potential as a platform for material state awareness (MSA) and should be considered as part of a broader suite of tools for such applications.

Nonlinear optimization simplified by hypersurface deformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stillinger, F.H.; Weber, T.A.

1988-09-01

A general strategy is advanced for simplifying nonlinear optimization problems, the ant-lion method. This approach exploits shape modifications of the cost-function hypersurface which distend basins surrounding low-lying minima (including global minima). By intertwining hypersurface deformations with steepest-descent displacements, the search is concentrated on a small relevant subset of all minima. Specific calculations demonstrating the value of this method are reported for the partitioning of two classes of irregular but nonrandom graphs, the prime-factor graphs and the pi graphs. We also indicate how this approach can be applied to the traveling salesman problem and to design layout optimization, and that itmore » may be useful in combination with simulated annealing strategies.« less

Droplet Deformation in an Extensional Flow: The Role of Surfactant Physical Chemistry

NASA Technical Reports Server (NTRS)

Stebe, Kathleen J.

1996-01-01

Surfactant-induced Marangoni effects strongly alter the stresses exerted along fluid particle interfaces. In low gravity processes, these stresses can dictate the system behavior. The dependence of Marangoni effects on surfactant physical chemistry is not understood, severely impacting our ability to predict and control fluid particle flows. A droplet in an extensional flow allows the controlled study of stretching and deforming interfaces. The deformations of the drop allow both Marangoni stresses, which resist tangential shear, and Marangoni elasticities, which resist surface dilatation, to develop. This flow presents an ideal model system for studying these effects. Prior surfactant-related work in this flow considered a linear dependence of the surface tension on the surface concentration, valid only at dilute surface concentrations, or a non-linear framework at concentrations sufficiently dilute that the linear approximation was valid. The linear framework becomes inadequate for several reasons. The finite dimensions of surfactant molecules must be taken into account with a model that includes surfaces saturation. Nonideal interactions between adsorbed surfactant molecules alter the partitioning of surfactant between the bulk and the interface, the dynamics of surfactant adsorptive/desorptive exchange, and the sensitivity of the surface tension to adsorbed surfactant. For example, cohesion between hydrocarbon chains favors strong adsorption. Cohesion also slows the rate of desorption from interfaces, and decreases the sensitivity of the surface tension to adsorbed surfactant. Strong cohesive interactions result in first order surface phase changes with a plateau in the surface tension vs surface concentration. Within this surface concentration range, the surface tension is decoupled from surface concentration gradients. We are engaged in the study of the role of surfactant physical chemistry in determining the Marangoni stresses on a drop in an extensional flow in a numerical and experimental program. Using surfactants whose dynamics and equilibrium behavior have been characterized in our laboratory, drop deformation will be studied in ground-based experiment. In an accompanying numerical study, predictive drop deformations will be determined based on the isotherm and equation of state determined in our laboratory. This work will improve our abilities to predict and control all fluid particle flows.

Deformation Monitoring and Analysis of Lsp Landslide Based on Gbinsar

NASA Astrophysics Data System (ADS)

Zhou, L.; Guo, J.; Yang, F.

2018-05-01

Monitoring and analyzing the deformation of the river landslide in city to master the deformation law of landslide, which is an important means of landslide safety assessment. In this paper, aiming at the stability of the Liu Sha Peninsula Landslide during its strengthening process after the landslide disaster. Continuous and high precision deformation monitoring of the landslide was carried out by GBInSAR technique. Meanwhile, the two-dimensional deformation time series pictures of the landslide body were retrieved by the time series analysis method. The deformation monitoring and analysis results show that the reinforcement belt on the landslide body was basically stable and the deformation of most PS points on the reinforcement belt was within 1 mm. The deformation of most areas on the landslide body was basically within 4 mm, and the deformation presented obvious nonlinear changes. GBInSAR technique can quickly and effectively obtain the entire deformation information of the river landslide and the evolution process of deformation.

Towards classical spectrum generating algebras for f-deformations

NASA Astrophysics Data System (ADS)

Kullock, Ricardo; Latini, Danilo

2016-01-01

In this paper we revise the classical analog of f-oscillators, a generalization of q-oscillators given in Man'ko et al. (1997) [8], in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9]. We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f-deformations, shows an energy dependence both in the amplitude and the frequency of the motion.

Constitutive and Stability Behavior of Soils in Microgravity Environment

NASA Technical Reports Server (NTRS)

Alshibli, Khalid A.; Sture, Stein; Costes, Nicholas

2000-01-01

All aspects of soil stability, bearing capacity, slope stability, the supporting capacity of deep foundations, and penetration resistance depend on soil strength. The stress-deformation and stress-deformation-time behavior of soils are of importance in any problem where ground movements are of interest. In most engineering materials, the strength is derived from internal chemical and physico-chemical forces of interaction, which bond the atoms, molecules, and particles together. In soils, the constitutive relations are mainly derived from interparticle friction between particles and particle groups and dilatancy, and to a lesser extent from particle bonding by weak electrostatic, physico-chemical, and coulomb forces. For engineering purposes, soils are classified as cohesive (clays and silts; typical particle sizes range from 10 nm to 10 micrometers) and cohesionless (sand and gravel; typical particle sizes range from 10 micrometers to 75 mm). The mechanical or constitutive properties of cohesionless soils or granular materials are highly fabric-dependent, highly non-linear, and non-conservative with engineering properties primarily depending on the effects of gravity through self-weight and on the tractions or forces applied to the soil mass. Under moderate-to-high stress levels, the influence of gravity on the behavior of laboratory test specimens may not be pronounced and, therefore, the test results in terrestrial (1-g) environment may be sufficiently conclusive. However at low interparticle stresses, which can result either from low applied (confining) stresses or from excess pore fluid pressures developed within the soil mass without corresponding changes in the applied stresses, the presence of gravitational body forces acting on solid particles and interstitial fluids exerts a pronounced influence on movement of individual particles or particle groups. Such motions, in turn, cause changes in soil fabric which results in significant changes in the interparticle friction forces contributing to the soil's strength and deformation characteristics.

Flows in forward deformable roll coating gaps: Comparison between spring and plane-strain models of roll cover

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carvalho, M.S.; Scriven, L.E.

1997-12-01

In this report the flow between rigid and a deformable rotating rolls fully submerged in a liquid pool is studied. The deformation of compliant roll cover is described by two different models (1) independent, radially oriented springs that deform in response to the traction force applied at the extremity of each or one-dimensional model, and (2) a plane-strain deformation of an incompressible Mooney-Rivlin material or non-linear elastic model. Based on the flow rate predictions of both models, an empirical relation between the spring constant of the one dimensional model and the roll cover thickness and elastic modulus is proposed.

Shock Response and Dynamic Failure of Spatially Tailored Aero-Thermal Structures

DTIC Science & Technology

2012-09-15

Deformation Behavior of Nanolaminated Titanium Aluminum Carbide. 36th International Conference and Exposition on Advanced Ceramics and Composites ...Deformation Behavior of Nanolaminated Titanium Aluminum Carbide. Effect of Strain-rate and Temperature on Dynamic Deformation of Nanolaminated...conditions, we are unaware of any studies published in the open literature on the effect of high strain rate deformation behavior of Ti2AlC at room or

Loading Deformation Characteristic Simulation Study of Engineering Vehicle Refurbished Tire

NASA Astrophysics Data System (ADS)

Qiang, Wang; Xiaojie, Qi; Zhao, Yang; Yunlong, Wang; Guotian, Wang; Degang, Lv

2018-05-01

The paper constructed engineering vehicle refurbished tire computer geometry model, mechanics model, contact model, finite element analysis model, did simulation study on load-deformation property of engineering vehicle refurbished tire by comparing with that of the new and the same type tire, got load-deformation of engineering vehicle refurbished tire under the working condition of static state and ground contact. The analysis result shows that change rules of radial-direction deformation and side-direction deformation of engineering vehicle refurbished tire are close to that of the new tire, radial-direction and side-direction deformation value is a little less than that of the new tire. When air inflation pressure was certain, radial-direction deformation linear rule of engineer vehicle refurbished tire would increase with load adding, however, side-direction deformation showed linear change rule, when air inflation pressure was low; and it would show increase of non-linear change rule, when air inflation pressure was very high.

Aeroelasticity of morphing wings using neural networks

NASA Astrophysics Data System (ADS)

Natarajan, Anand

In this dissertation, neural networks are designed to effectively model static non-linear aeroelastic problems in adaptive structures and linear dynamic aeroelastic systems with time varying stiffness. The use of adaptive materials in aircraft wings allows for the change of the contour or the configuration of a wing (morphing) in flight. The use of smart materials, to accomplish these deformations, can imply that the stiffness of the wing with a morphing contour changes as the contour changes. For a rapidly oscillating body in a fluid field, continuously adapting structural parameters may render the wing to behave as a time variant system. Even the internal spars/ribs of the aircraft wing which define the wing stiffness can be made adaptive, that is, their stiffness can be made to vary with time. The immediate effect on the structural dynamics of the wing, is that, the wing motion is governed by a differential equation with time varying coefficients. The study of this concept of a time varying torsional stiffness, made possible by the use of active materials and adaptive spars, in the dynamic aeroelastic behavior of an adaptable airfoil is performed here. Another type of aeroelastic problem of an adaptive structure that is investigated here, is the shape control of an adaptive bump situated on the leading edge of an airfoil. Such a bump is useful in achieving flow separation control for lateral directional maneuverability of the aircraft. Since actuators are being used to create this bump on the wing surface, the energy required to do so needs to be minimized. The adverse pressure drag as a result of this bump needs to be controlled so that the loss in lift over the wing is made minimal. The design of such a "spoiler bump" on the surface of the airfoil is an optimization problem of maximizing pressure drag due to flow separation while minimizing the loss in lift and energy required to deform the bump. One neural network is trained using the CFD code FLUENT to represent the aerodynamic loading over the bump. A second neural network is trained for calculating the actuator loads, bump displacement and lift, drag forces over the airfoil using the finite element solver, ANSYS and the previously trained neural network. This non-linear aeroelastic model of the deforming bump on an airfoil surface using neural networks can serve as a fore-runner for other non-linear aeroelastic problems.

A multiscale red blood cell model with accurate mechanics, rheology, and dynamics.

PubMed

Fedosov, Dmitry A; Caswell, Bruce; Karniadakis, George Em

2010-05-19

Red blood cells (RBCs) have highly deformable viscoelastic membranes exhibiting complex rheological response and rich hydrodynamic behavior governed by special elastic and bending properties and by the external/internal fluid and membrane viscosities. We present a multiscale RBC model that is able to predict RBC mechanics, rheology, and dynamics in agreement with experiments. Based on an analytic theory, the modeled membrane properties can be uniquely related to the experimentally established RBC macroscopic properties without any adjustment of parameters. The RBC linear and nonlinear elastic deformations match those obtained in optical-tweezers experiments. The rheological properties of the membrane are compared with those obtained in optical magnetic twisting cytometry, membrane thermal fluctuations, and creep followed by cell recovery. The dynamics of RBCs in shear and Poiseuille flows is tested against experiments and theoretical predictions, and the applicability of the latter is discussed. Our findings clearly indicate that a purely elastic model for the membrane cannot accurately represent the RBC's rheological properties and its dynamics, and therefore accurate modeling of a viscoelastic membrane is necessary. Copyright 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Crashworthiness of light aircraft fuselage structures: A numerical and experimental investigation

NASA Technical Reports Server (NTRS)

Nanyaro, A. P.; Tennyson, R. C.; Hansen, J. S.

1984-01-01

The dynamic behavior of aircraft fuselage structures subject to various impact conditions was investigated. An analytical model was developed based on a self-consistent finite element (CFE) formulation utilizing shell, curved beam, and stringer type elements. Equations of motion were formulated and linearized (i.e., for small displacements), although material nonlinearity was retained to treat local plastic deformation. The equations were solved using the implicit Newmark-Beta method with a frontal solver routine. Stiffened aluminum fuselage models were also tested in free flight using the UTIAS pendulum crash test facility. Data were obtained on dynamic strains, g-loads, and transient deformations (using high speed photography in the latter case) during the impact process. Correlations between tests and predicted results are presented, together with computer graphics, based on the CFE model. These results include level and oblique angle impacts as well as the free-flight crash test. Comparisons with a hybrid, lumped mass finite element computer model demonstrate that the CFE formulation provides the test overall agreement with impact test data for comparable computing costs.

A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics

PubMed Central

Fedosov, Dmitry A.; Caswell, Bruce; Karniadakis, George Em

2010-01-01

Abstract Red blood cells (RBCs) have highly deformable viscoelastic membranes exhibiting complex rheological response and rich hydrodynamic behavior governed by special elastic and bending properties and by the external/internal fluid and membrane viscosities. We present a multiscale RBC model that is able to predict RBC mechanics, rheology, and dynamics in agreement with experiments. Based on an analytic theory, the modeled membrane properties can be uniquely related to the experimentally established RBC macroscopic properties without any adjustment of parameters. The RBC linear and nonlinear elastic deformations match those obtained in optical-tweezers experiments. The rheological properties of the membrane are compared with those obtained in optical magnetic twisting cytometry, membrane thermal fluctuations, and creep followed by cell recovery. The dynamics of RBCs in shear and Poiseuille flows is tested against experiments and theoretical predictions, and the applicability of the latter is discussed. Our findings clearly indicate that a purely elastic model for the membrane cannot accurately represent the RBC's rheological properties and its dynamics, and therefore accurate modeling of a viscoelastic membrane is necessary. PMID:20483330

Numerical and Experimental Studies on Impact Loaded Concrete Structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saarenheimo, Arja; Hakola, Ilkka; Karna, Tuomo

2006-07-01

An experimental set-up has been constructed for medium scale impact tests. The main objective of this effort is to provide data for the calibration and verification of numerical models of a loading scenario where an aircraft impacts against a nuclear power plant. One goal is to develop and take in use numerical methods for predicting response of reinforced concrete structures to impacts of deformable projectiles that may contain combustible liquid ('fuel'). Loading, structural behaviour, like collapsing mechanism and the damage grade, will be predicted by simple analytical methods and using non-linear FE-method. In the so-called Riera method the behavior ofmore » the missile material is assumed to be rigid plastic or rigid visco-plastic. Using elastic plastic and elastic visco-plastic material models calculations are carried out by ABAQUS/Explicit finite element code, assuming axisymmetric deformation mode for the missile. With both methods, typically, the impact force time history, the velocity of the missile rear end and the missile shortening during the impact were recorded for comparisons. (authors)« less

Methods for reducing energy dissipation in cosmetic gloves.

PubMed

Herder, J L; Cool, J C; Plettenburg, D H

1998-06-01

For cosmetic reasons, hand prostheses are provided with cosmetic gloves. Their pleasing appearance, however, is accompanied by poor mechanical behavior, resulting in a negative influence on prosthesis operation. Glove stiffness is high and nonlinear, and internal friction in the glove material causes energy dissipation (hysteresis). In this article, two methods for reducing hysteresis in cosmetic gloves are proposed, that may be applied independently or in combination. Glove modification. Altering the mechanical properties of the glove itself is the first method that is presented. It was found possible to reduce both stiffness and hysteresis about 50% by forming grooves into the inside of the glove. Together with the evaluation of this method, several properties of the cosmetic glove were determined. Motion optimization. Additionally, a second method for reducing hysteresis was developed. The amount of hysteresis is influenced by the way the glove is forced to deform. The prosthesis mechanism, determining this deformation, was designed for minimum hysteresis and maximum cosmesis. For the prosthesis-glove combination used in this study, thumb motion optimization reduced hysteresis by about 65%.

Surface plasticity: theory and computation

NASA Astrophysics Data System (ADS)

Esmaeili, A.; Steinmann, P.; Javili, A.

2017-11-01

Surfaces of solids behave differently from the bulk due to different atomic rearrangements and processes such as oxidation or aging. Such behavior can become markedly dominant at the nanoscale due to the large ratio of surface area to bulk volume. The surface elasticity theory (Gurtin and Murdoch in Arch Ration Mech Anal 57(4):291-323, 1975) has proven to be a powerful strategy to capture the size-dependent response of nano-materials. While the surface elasticity theory is well-established to date, surface plasticity still remains elusive and poorly understood. The objective of this contribution is to establish a thermodynamically consistent surface elastoplasticity theory for finite deformations. A phenomenological isotropic plasticity model for the surface is developed based on the postulated elastoplastic multiplicative decomposition of the surface superficial deformation gradient. The non-linear governing equations and the weak forms thereof are derived. The numerical implementation is carried out using the finite element method and the consistent elastoplastic tangent of the surface contribution is derived. Finally, a series of numerical examples provide further insight into the problem and elucidate the key features of the proposed theory.

The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models

NASA Technical Reports Server (NTRS)

Hesse, Michael; Birn, Joachim

2011-01-01

Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.

Mean template for tensor-based morphometry using deformation tensors.

PubMed

Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

2007-01-01

Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

Analytical Modeling of the High Strain Rate Deformation of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.; Gilat, Amos

2003-01-01

The results presented here are part of an ongoing research program to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric matrix materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical 5 plasticity theory definitions of effective stress and effective plastic strain are modified by applying variations of the Drucker-Prager yield criterion. To verify the revised formulation, the shear and tensile deformation of a representative toughened epoxy is analyzed across a wide range of strain rates (from quasi-static to high strain rates) and the results are compared to experimentally obtained values. For the analyzed polymers, both the tensile and shear stress-strain curves computed using the analytical model correlate well with values obtained through experimental tests. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. In the micromechanics, the unit cell is divided up into a number of independently analyzed slices, and laminate theory is then applied to obtain the effective deformation of the unit cell. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite (composed using the representative polymer analyzed for the correlation of the polymer constitutive equations) for several fiber orientation angles across a variety of strain rates. The computed values compare favorably to experimentally obtained results.

Nonlinear model and attitude dynamics of flexible spacecraft with large amplitude slosh

NASA Astrophysics Data System (ADS)

Deng, Mingle; Yue, Baozeng

2017-04-01

This paper is focused on the nonlinearly modelling and attitude dynamics of spacecraft coupled with large amplitude liquid sloshing dynamics and flexible appendage vibration. The large amplitude fuel slosh dynamics is included by using an improved moving pulsating ball model. The moving pulsating ball model is an equivalent mechanical model that is capable of imitating the whole liquid reorientation process. A modification is introduced in the capillary force computation in order to more precisely estimate the settling location of liquid in microgravity or zero-g environment. The flexible appendage is modelled as a three dimensional Bernoulli-Euler beam and the assumed modal method is employed to derive the nonlinear mechanical model for the overall coupled system of liquid filled spacecraft with appendage. The attitude maneuver is implemented by the momentum transfer technique, and a feedback controller is designed. The simulation results show that the liquid sloshing can always result in nutation behavior, but the effect of flexible deformation of appendage depends on the amplitude and direction of attitude maneuver performed by spacecraft. Moreover, it is found that the liquid sloshing and the vibration of flexible appendage are coupled with each other, and the coupling becomes more significant with more rapid motion of spacecraft. This study reveals that the appendage's flexibility has influence on the liquid's location and settling time in microgravity. The presented nonlinear system model can provide an important reference for the overall design of the modern spacecraft composed of rigid platform, liquid filled tank and flexible appendage.

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg; Zhou, Yu

2016-07-15

Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonantmore » frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.« less

Analysis of warping deformation modes using higher order ANCF beam element

NASA Astrophysics Data System (ADS)

Orzechowski, Grzegorz; Shabana, Ahmed A.

2016-02-01

Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.

Flicker Noise in GNSS Station Position Time Series: How much is due to Crustal Loading Deformations?

NASA Astrophysics Data System (ADS)

Rebischung, P.; Chanard, K.; Metivier, L.; Altamimi, Z.

2017-12-01

The presence of colored noise in GNSS station position time series was detected 20 years ago. It has been shown since then that the background spectrum of non-linear GNSS station position residuals closely follows a power-law process (known as flicker noise, 1/f noise or pink noise), with some white noise taking over at the highest frequencies. However, the origin of the flicker noise present in GNSS station position time series is still unclear. Flicker noise is often described as intrinsic to the GNSS system, i.e. due to errors in the GNSS observations or in their modeling, but no such error source has been identified so far that could explain the level of observed flicker noise, nor its spatial correlation.We investigate another possible contributor to the observed flicker noise, namely real crustal displacements driven by surface mass transports, i.e. non-tidal loading deformations. This study is motivated by the presence of power-law noise in the time series of low-degree (≤ 40) and low-order (≤ 12) Stokes coefficients observed by GRACE - power-law noise might also exist at higher degrees and orders, but obscured by GRACE observational noise. By comparing GNSS station position time series with loading deformation time series derived from GRACE gravity fields, both with their periodic components removed, we therefore assess whether GNSS and GRACE both plausibly observe the same flicker behavior of surface mass transports / loading deformations. Taking into account GRACE observability limitations, we also quantify the amount of flicker noise in GNSS station position time series that could be explained by such flicker loading deformations.

On the acoustic-radiation-induced strain and stress in elastic solids with quadratic nonlinearity (L).

PubMed

Qu, Jianmin; Jacobs, Laurence J; Nagy, Peter B

2011-06-01

This letter demonstrates that an eigenstrain is induced when a wave propagates through an elastic solid with quadratic nonlinearity. It is shown that this eigenstrain is intrinsic to the material, but the mean stress and the total mean strain are not. Instead, the mean stress and total means strain also depend on the boundary conditions, so care must be taken when using the static deformation to measure the acoustic nonlinearity parameter of a solid. © 2011 Acoustical Society of America

Deformation Invariant Attribute Vector for Deformable Registration of Longitudinal Brain MR Images

PubMed Central

Li, Gang; Guo, Lei; Liu, Tianming

2009-01-01

This paper presents a novel approach to define deformation invariant attribute vector (DIAV) for each voxel in 3D brain image for the purpose of anatomic correspondence detection. The DIAV method is validated by using synthesized deformation in 3D brain MRI images. Both theoretic analysis and experimental studies demonstrate that the proposed DIAV is invariant to general nonlinear deformation. Moreover, our experimental results show that the DIAV is able to capture rich anatomic information around the voxels and exhibit strong discriminative ability. The DIAV has been integrated into a deformable registration algorithm for longitudinal brain MR images, and the results on both simulated and real brain images are provided to demonstrate the good performance of the proposed registration algorithm based on matching of DIAVs. PMID:19369031

A Method for Calculating Strain Energy Release Rates in Preliminary Design of Composite Skin/Stringer Debonding Under Multi-Axial Loading

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Minguet, Pierre J.; OBrien, T. Kevin

1999-01-01

Three simple procedures were developed to determine strain energy release rates, G, in composite skin/stringer specimens for various combinations of unaxial and biaxial (in-plane/out-of-plane) loading conditions. These procedures may be used for parametric design studies in such a way that only a few finite element computations will be necessary for a study of many load combinations. The results were compared with mixed mode strain energy release rates calculated directly from nonlinear two-dimensional plane-strain finite element analyses using the virtual crack closure technique. The first procedure involved solving three unknown parameters needed to determine the energy release rates. Good agreement was obtained when the external loads were used in the expression derived. This superposition technique was only applicable if the structure exhibits a linear load/deflection behavior. Consequently, a second technique was derived which was applicable in the case of nonlinear load/deformation behavior. The technique involved calculating six unknown parameters from a set of six simultaneous linear equations with data from six nonlinear analyses to determine the energy release rates. This procedure was not time efficient, and hence, less appealing. A third procedure was developed to calculate mixed mode energy release rates as a function of delamination lengths. This procedure required only one nonlinear finite element analysis of the specimen with a single delamination length to obtain a reference solution for the energy release rates and the scale factors. The delamination was extended in three separate linear models of the local area in the vicinity of the delamination subjected to unit loads to obtain the distribution of G with delamination lengths. This set of sub-problems was Although additional modeling effort is required to create the sub- models, this local technique is efficient for parametric studies.

Elasticity and inelasticity of silicon nitride/boron nitride fibrous monoliths.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smirnov, B. I.; Burenkov, Yu. A.; Kardashev, B. K.

A study is reported on the effect of temperature and elastic vibration amplitude on Young's modulus E and internal friction in Si{sub 3}N{sub 4} and BN ceramic samples and Si{sub 3}N{sub 4}/BN monoliths obtained by hot pressing of BN-coated Si{sub 3}N{sub 4} fibers. The fibers were arranged along, across, or both along and across the specimen axis. The E measurements were carried out under thermal cycling within the 20-600 C range. It was found that high-modulus silicon-nitride specimens possess a high thermal stability; the E(T) dependences obtained under heating and cooling coincide well with one another. The low-modulus BN ceramicmore » exhibits a considerable hysteresis, thus indicating evolution of the defect structure under the action of thermoelastic (internal) stresses. Monoliths demonstrate a qualitatively similar behavior (with hysteresis). This behavior of the elastic modulus is possible under microplastic deformation initiated by internal stresses. The presence of microplastic shear in all the materials studied is supported by the character of the amplitude dependences of internal friction and the Young's modulus. The experimental data obtained are discussed in terms of a model in which the temperature dependences of the elastic modulus and their features are accounted for by both microplastic deformation and nonlinear lattice-atom vibrations, which depend on internal stresses.« less

Experimental validation of finite element model analysis of a steel frame in simulated post-earthquake fire environments

NASA Astrophysics Data System (ADS)

Huang, Ying; Bevans, W. J.; Xiao, Hai; Zhou, Zhi; Chen, Genda

2012-04-01

During or after an earthquake event, building system often experiences large strains due to shaking effects as observed during recent earthquakes, causing permanent inelastic deformation. In addition to the inelastic deformation induced by the earthquake effect, the post-earthquake fires associated with short fuse of electrical systems and leakage of gas devices can further strain the already damaged structures during the earthquakes, potentially leading to a progressive collapse of buildings. Under these harsh environments, measurements on the involved building by various sensors could only provide limited structural health information. Finite element model analysis, on the other hand, if validated by predesigned experiments, can provide detail structural behavior information of the entire structures. In this paper, a temperature dependent nonlinear 3-D finite element model (FEM) of a one-story steel frame is set up by ABAQUS based on the cited material property of steel from EN 1993-1.2 and AISC manuals. The FEM is validated by testing the modeled steel frame in simulated post-earthquake environments. Comparisons between the FEM analysis and the experimental results show that the FEM predicts the structural behavior of the steel frame in post-earthquake fire conditions reasonably. With experimental validations, the FEM analysis of critical structures could be continuously predicted for structures in these harsh environments for a better assistant to fire fighters in their rescue efforts and save fire victims.

Mechanical behavior, damage tolerance and durability of fiber metal laminates for aircraft structures

NASA Astrophysics Data System (ADS)

Wu, Guocai

This study systematically explores the mechanical behavior, damage tolerance and durability of fiber metal laminates, a promising candidate materials system for next generation aerospace structures. The experimental results indicated that GLARE laminates exhibited a bilinear deformation behavior under static in-plane loading. Both an analytical constitutive model based on a modified classical lamination theory which incorporates the elasto-plastic behavior of aluminum alloy and a numerical simulation based on finite element modeling are used to predict the nonlinear stress-strain response and deformation behavior of GLARE laminates. The blunt notched strength of GLARE laminates increased with decreasing specimen width and decreasing hole diameter. The notched strength of GLARE laminates was evaluated based on a modified point stress criterion. A computer simulation based on finite element method was performed to study stress concentration and distribution around the notch and verify the analytical and experimental results of notched strength. Good agreement is obtained between the model predictions and experimental results. Experimental results also indicate that GLARE laminates exhibited superior impact properties to those of monolithic 2024-T3 aluminum alloy at low velocity impact loading. The GLARE 5-2/1 laminate with 0°/90°/90°/0° fiber configuration exhibits a better impact resistance than the GLARE 4-3/2 laminate with 0°/90°/0° fiber orientation. The characteristic impact energies, the damage area, and the permanent deflection of laminates are used to evaluate the impact damage resistance. The post-impact residual tensile strength under various damage states ranging from the plastic dent, barely visible impact damage (BVID), clearly visible impact damage (CVID) up to the complete perforation was also measured and compared. The post-impact fatigue behavior under various stress levels and impact damage states was extensively explored. The damage initiation and progression, failure modes and crack propagation under different loading conditions were investigated and identified with microscopy, SEM, X-ray radiography, and by chemically removing outer aluminum layers.

Effect of Interface Structure on Mechanical Properties of Advanced Composite Materials

PubMed Central

Gan, Yong X.

2009-01-01

This paper deals with the effect of interface structures on the mechanical properties of fiber reinforced composite materials. First, the background of research, development and applications on hybrid composite materials is introduced. Second, metal/polymer composite bonded structures are discussed. Then, the rationale is given for nanostructuring the interface in composite materials and structures by introducing nanoscale features such as nanopores and nanofibers. The effects of modifying matrices and nano-architecturing interfaces on the mechanical properties of nanocomposite materials are examined. A nonlinear damage model for characterizing the deformation behavior of polymeric nanocomposites is presented and the application of this model to carbon nanotube-reinforced and reactive graphite nanotube-reinforced epoxy composite materials is shown. PMID:20054466

DYNA3D: A computer code for crashworthiness engineering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hallquist, J.O.; Benson, D.J.

1986-09-01

A finite element program with crashworthiness applications has been developed at LLNL. DYNA3D, an explicit, fully vectorized, finite deformation structural dynamics program, has four capabilities that are critical for the efficient and realistic modeling crash phenomena: (1) fully optimized nonlinear solid, shell, and beam elements for representing a structure; (2) a broad range of constitutive models for simulating material behavior; (3) sophisticated contact algorithms for impact interactions; (4) a rigid body capability to represent the bodies away from the impact region at a greatly reduced cost without sacrificing accuracy in the momentum calculations. Basic methodologies of the program are brieflymore » presented along with several crashworthiness calculations. Efficiencies of the Hughes-Liu and Belytschko-Tsay shell formulations are considered.« less

The effect of storage temperature on blue cheese mechanical properties.

PubMed

Joyner Melito, Helen S; Francis, Dorothy; Luzzi, Brooke; Johnson, John R

2018-06-01

Blue cheese is commonly aged for 60 days at 10°C after curing. However, some manufacturers store blue cheese at 4°C and the effect of lower storage temperature on blue cheese final properties is unknown. Thus, the objective of this study was to determine the effect of storage temperature and time on blue cheese mechanical behaviors. Blue cheeses were stored at 4 or 10°C for 77 days after production. Composition and small- and large-strain rheological behaviors were evaluated every 2 weeks of storage. Storage time had significant impact on blue cheese rheological behaviors; storage temperature did not. Large-strain compressive force and viscoelastic moduli decreased with storage time, and the extent of nonlinear viscoelastic behavior increased. These results indicated that sample microstructure likely weakened and was more easily deformed as storage time increased. Overall, blue cheese can be stored at 4-10°C without significant changes to its composition or mechanical behavior. The results of this work can be used by blue cheese manufacturers to better understand the impact of storage time and temperature on blue cheese end quality. Manufacturers can take advantage of the effects of storage time on blue cheese mechanical behaviors to determine how long to age blue cheese to achieve the desired texture. © 2017 Wiley Periodicals, Inc.

Interaction between mantle and crustal detachments: A nonlinear system controlling lithospheric extension

NASA Astrophysics Data System (ADS)

Rosenbaum, Gideon; Regenauer-Lieb, Klaus; Weinberg, Roberto F.

2010-11-01

We use numerical modeling to investigate the development of crustal and mantle detachments during lithospheric extension. Our models simulate a wide range of extensional systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles as a response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation. Crustal detachments, here referred as low-angle normal decoupling horizons, are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW m-2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30-40 km) and an intermediate heat flow (60-70 mW m-2). Results show a nonlinear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometimes unexpected switches in extension modes (e.g., from diffuse extensional deformation to effective lithospheric-scale rupturing) or from mantle- to crust-dominated strain localization. We interpret this nonlinearity to result from the interference of doming wavelengths in the presence of multiple necking instabilities. Disharmonic crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonic crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged history of extension prior to continental breakup.

Transversely Isotropic Hyperelastic Constitutive Model of Short Fiber Reinforced EPDM Based on Tensor Function

NASA Astrophysics Data System (ADS)

Feng, Q. L.; Li, C.; Liao, Y. F.

2017-12-01

Short fiber reinforced EPDM is a new kind of composite material used in solid rocket motor winding and coating. It has relatively large deformation under the small stress condition, and the physical non-linear characteristic is obvious. Due to the addition of fiber in the specific direction of the rubber, the macroscopic mechanical properties are expressed as transversely isotropic properties. In order to describe the mechanical behavior under the impact and vibration, the transversely isotropic hyperelastic constitutive model based on tensor function is proposed. The symmetry of the transversely isotropic incompressible material limits the stress tensor ‘ K ’ to be characterized as a function of 5 tensor invariants and 4 scalar invariants. The third power constitutive equations of the model give 12 independent elastic constants of the transversely isotropic nonlinear elastic material. The experimental results show that the non-zero elastic constants are different in the fiber direction and at the different strain rate. Number and value of adiabatic layer and related products R & D has a reference value.

Transport coefficients and mechanical response in hard-disk colloidal suspensions

NASA Astrophysics Data System (ADS)

Zhang, Bo-Kai; Li, Jian; Chen, Kang; Tian, Wen-De; Ma, Yu-Qiang

2016-11-01

We investigate the transport properties and mechanical response of glassy hard disks using nonlinear Langevin equation theory. We derive expressions for the elastic shear modulus and viscosity in two dimensions on the basis of thermal-activated barrier-hopping dynamics and mechanically accelerated motion. Dense hard disks exhibit phenomena such as softening elasticity, shear-thinning of viscosity, and yielding upon deformation, which are qualitatively similar to dense hard-sphere colloidal suspensions in three dimensions. These phenomena can be ascribed to stress-induced “landscape tilting”. Quantitative comparisons of these phenomena between hard disks and hard spheres are presented. Interestingly, we find that the density dependence of yield stress in hard disks is much more significant than in hard spheres. Our work provides a foundation for further generalizing the nonlinear Langevin equation theory to address slow dynamics and rheological behavior in binary or polydisperse mixtures of hard or soft disks. Project supported by the National Basic Research Program of China (Grant No. 2012CB821500) and the National Natural Science Foundation of China (Grant Nos. 21374073 and, 21574096).

Microstructural Characterization of Vocal Folds toward a Strain-Energy Model of Collagen Remodeling

PubMed Central

Miri, Amir K.; Heris, Hossein K.; Tripathy, Umakanta; Wiseman, Paul W.; Mongeau, Luc

2013-01-01

Collagen fibrils are believed to control the immediate deformation of soft tissues under biomechanical load. Most extracellular matrix proteins remain intact during frozen sectioning, which allows them to be scanned using atomic force microscopy (AFM). Collagen fibrils are distinguishable because of their helical shape. In the present study, the shape and organization of collagen fibrils in dissected porcine vocal folds were quantified using nonlinear laser scanning microscopy data at the micrometer scale and AFM data at the nanometer scale. Rope-shape collagen fibrils were observed. Geometric characteristics for the fibrils were fed to a hyperelastic model to predict the biomechanical response of the tissue. The model simulates the micrometer-scale unlocking behavior of collagen bundles when extended from their unloaded configuration. Force spectroscopy using AFM was used to estimate the stiffness of collagen fibrils (1 ± 0.5 MPa). The presence of rope-shape fibrils is postulated to change the slope of the force-deflection response near the onset of nonlinearity. The proposed model could ultimately be used to evaluate changes in elasticity of soft tissues that result from the collagen remodeling. PMID:23643604

Vibration isolation using extreme geometric nonlinearity

NASA Astrophysics Data System (ADS)

Virgin, L. N.; Santillan, S. T.; Plaut, R. H.

2008-08-01

A highly deformed, slender beam (or strip), attached to a vertically oscillating base, is used in a vibration isolation application to reduce the motion of a supported mass. The isolator is a thin strip that is bent so that the two ends are clamped together, forming a loop. The clamped ends are attached to an excitation source and the supported system is attached at the loop midpoint directly above the base. The strip is modeled as an elastica, and the resulting nonlinear boundary value problem is solved numerically using a shooting method. First the equilibrium shapes of the loop with varying static loads and lengths are studied. The analysis reveals a large degree of stiffness tunability; the stiffness is dependent on the geometric configuration, which itself is determined by the supported mass, loop length, and loop self-weight. Free vibration frequencies and mode shapes are also found. Finally, the case of forced vibration is studied, and the displacement transmissibility over a large range of forcing frequencies is determined for varying parameter values. Experiments using polycarbonate strips are conducted to verify equilibrium and dynamic behavior.

Strongly nonlinear theory of rapid solidification near absolute stability

NASA Astrophysics Data System (ADS)

Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the morphological number, as well as the amplitude. The critical amplitude, at which solutions loose periodicity, depends on a single combination of parameters independent of the morphological number that indicate that non-periodic growth is most commonly present for moderate disequilibrium parameters. The spatial distribution of the interface develops deepening roots at late times. Similar spatial distributions are also seen in the limit in which both the cellular and oscillatory modes are close to absolute stability, and the roots deepen with larger departures from the two absolute stability boundaries.

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

PubMed Central

Kang, Chang-kwon; Shyy, Wei

2013-01-01

We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier–Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid–structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing–wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots. PMID:23760300

Fluid-structure interaction simulations of deformable structures with non-linear thin shell elements

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Hedayat, Mohammadali; Borazjani, Iman; Scientific Computing; Biofluids Laboratory Team

2017-11-01

Large deformation of structures in a fluid is simulated using a strongly coupled partitioned fluid-structure interaction (FSI) approach which is stabilized with under-relaxation and the Aitken acceleration technique. The fluid is simulated using a recently developed implicit Newton-Krylov method with a novel analytical Jacobian. Structures are simulated using a triangular thin-shell finite element formulation, which considers only translational degrees of freedom. The thin-shell method is developed on the top of a previously implemented membrane finite element formulation. A sharp interface immersed boundary method is used to handle structures in the fluid domain. The developed FSI framework is validated against two three-dimensional experiments: (1) a flexible aquatic vegetation in the fluid and (2) a heaving flexible panel in fluid. Furthermore, the developed FSI framework is used to simulate tissue heart valves, which involve large deformations and non-linear material properties. This work was supported by American Heart Association (AHA) Grant 13SDG17220022 and the Center of Computational Research (CCR) of University at Buffalo.

Towards the map of quantum gravity

NASA Astrophysics Data System (ADS)

Mielczarek, Jakub; Trześniewski, Tomasz

2018-06-01

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Hořava-Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.

Compaction behavior and deformation mechanism of directly compressible textured mannitol in a rotary tablet press simulator.

PubMed

Tarlier, Nicolas; Soulairol, Ian; Bataille, Bernard; Baylac, Gilles; Ravel, Patrice; Nofrerias, Isaac; Lefèvre, Philippe; Sharkawi, Tahmer

2015-11-10

Textured mannitol powder is widely used as a pharmaceutical excipient for tablet compaction. In order to choose the right tableting parameters, it is necessary to understand its mechanical behavior during deformation under industrial tableting conditions. The aim of this study was to evaluate the mechanical behavior during deformation of a textured mannitol using a rotary tablet press simulator. Mean yield pressure (Py) obtained by Heckel modeling, Walker coefficients (W) and Stress Rate Sensitivity (SRS) were compared to reference excipients, known for either their plastic (microcrystalline cellulose) or fragmentary (lactose and dibasic calcium phosphate) deformation behavior. Py, W and SRS values showed that the studied textured mannitol has a fragmentary deformation mechanism. Furthermore, this mechanical behavior was not sensitive to lubrication, which is characteristic of fragmentary excipients. Copyright © 2015 Elsevier B.V. All rights reserved.

Nonlinear behavior of the tarka flute's distinctive sounds.

PubMed

Gérard, Arnaud; Yapu-Quispe, Luis; Sakuma, Sachiko; Ghezzi, Flavio; Ramírez-Ávila, Gonzalo Marcelo

2016-09-01

The Andean tarka flute generates multiphonic sounds. Using spectral techniques, we verify two distinctive musical behaviors and the nonlinear nature of the tarka. Through nonlinear time series analysis, we determine chaotic and hyperchaotic behavior. Experimentally, we observe that by increasing the blow pressure on different fingerings, peculiar changes from linear to nonlinear patterns are produced, leading ultimately to quenching.

Nonlinear behavior of the tarka flute's distinctive sounds

NASA Astrophysics Data System (ADS)

Gérard, Arnaud; Yapu-Quispe, Luis; Sakuma, Sachiko; Ghezzi, Flavio; Ramírez-Ávila, Gonzalo Marcelo

2016-09-01

The Andean tarka flute generates multiphonic sounds. Using spectral techniques, we verify two distinctive musical behaviors and the nonlinear nature of the tarka. Through nonlinear time series analysis, we determine chaotic and hyperchaotic behavior. Experimentally, we observe that by increasing the blow pressure on different fingerings, peculiar changes from linear to nonlinear patterns are produced, leading ultimately to quenching.

Flexible twist for pitch control in a high altitude long endurance aircraft with nonlinear response

NASA Astrophysics Data System (ADS)

Bond, Vanessa L.

Information dominance is the key motivator for employing high-altitude long-endurance (HALE) aircraft to provide continuous coverage in the theaters of operation. A joined-wing configuration of such a craft gives the advantage of a platform for higher resolution sensors. Design challenges emerge with structural flexibility that arise from a long-endurance aircraft design. The goal of this research was to demonstrate that scaling the nonlinear response of a full-scale finite element model was possible if the model was aeroelastically and "nonlinearly" scaled. The research within this dissertation showed that using the first three modes and the first bucking modes was not sufficient for proper scaling. In addition to analytical scaling several experiments were accomplished to understand and overcome design challenges of HALE aircraft. One such challenge is combated by eliminating pitch control surfaces and replacing them with an aft-wing twist concept. This design option was physically realized through wind tunnel measurement of forces, moments and pressures on a subscale experimental model. This design and experiment demonstrated that pitch control with aft-wing twist is feasible. Another challenge is predicting the nonlinear response of long-endurance aircraft. This was addressed by experimental validation of modeling nonlinear response on a subscale experimental model. It is important to be able to scale nonlinear behavior in this type of craft due to its highly flexible nature. The validation accomplished during this experiment on a subscale model will reduce technical risk for full-scale development of such pioneering craft. It is also important to experimentally reproduce the air loads following the wing as it deforms. Nonlinearities can be attributed to these follower forces that might otherwise be overlooked. This was found to be a significant influence in HALE aircraft to include the case study of the FEM and experimental models herein.

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

Re-centering variable friction device for vibration control of structures subjected to near-field earthquakes

NASA Astrophysics Data System (ADS)

Ozbulut, Osman E.; Hurlebaus, Stefan

2011-11-01

This paper proposes a re-centering variable friction device (RVFD) for control of civil structures subjected to near-field earthquakes. The proposed hybrid device has two sub-components. The first sub-component of this hybrid device consists of shape memory alloy (SMA) wires that exhibit a unique hysteretic behavior and full recovery following post-transformation deformations. The second sub-component of the hybrid device consists of variable friction damper (VFD) that can be intelligently controlled for adaptive semi-active behavior via modulation of its voltage level. In general, installed SMA devices have the ability to re-center structures at the end of the motion and VFDs can increase the energy dissipation capacity of structures. The full realization of these devices into a singular, hybrid form which complements the performance of each device is investigated in this study. A neuro-fuzzy model is used to capture rate- and temperature-dependent nonlinear behavior of the SMA components of the hybrid device. An optimal fuzzy logic controller (FLC) is developed to modulate voltage level of VFDs for favorable performance in a RVFD hybrid application. To obtain optimal controllers for concurrent mitigation of displacement and acceleration responses, tuning of governing fuzzy rules is conducted by a multi-objective heuristic optimization. Then, numerical simulation of a multi-story building is conducted to evaluate the performance of the hybrid device. Results show that a re-centering variable friction device modulated with a fuzzy logic control strategy can effectively reduce structural deformations without increasing acceleration response during near-field earthquakes.

Stiffness optimization of non-linear elastic structures

DOE PAGES

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

2017-11-13

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Energy-momentum conserving higher-order time integration of nonlinear dynamics of finite elastic fiber-reinforced continua

NASA Astrophysics Data System (ADS)

Erler, Norbert; Groß, Michael

2015-05-01

Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.

Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.

Stiffness optimization of non-linear elastic structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Mechanical characterization of soft materials using transparent indenter testing system and finite element simulation

NASA Astrophysics Data System (ADS)

Xuan, Yue

Background. Soft materials such as polymers and soft tissues have diverse applications in bioengineering, medical care, and industry. Quantitative mechanical characterization of soft materials at multiscales is required to assure that appropriate mechanical properties are presented to support the normal material function. Indentation test has been widely used to characterize soft material. However, the measurement of in situ contact area is always difficult. Method of Approach. A transparent indenter method was introduced to characterize the nonlinear behaviors of soft materials under large deformation. This approach made the direct measurement of contact area and local deformation possible. A microscope was used to capture the contact area evolution as well as the surface deformation. Based on this transparent indenter method, a novel transparent indentation measurement systems has been built and multiple soft materials including polymers and pericardial tissue have been characterized. Seven different indenters have been used to study the strain distribution on the contact surface, inner layer and vertical layer. Finite element models have been built to simulate the hyperelastic and anisotropic material behaviors. Proper material constants were obtained by fitting the experimental results. Results.Homogeneous and anisotropic silicone rubber and porcine pericardial tissue have been examined. Contact area and local deformation were measured by real time imaging the contact interface. The experimental results were compared with the predictions from the Hertzian equations. The accurate measurement of contact area results in more reliable Young's modulus, which is critical for soft materials. For the fiber reinforced anisotropic silicone rubber, the projected contact area under a hemispherical indenter exhibited elliptical shape. The local surface deformation under indenter was mapped using digital image correlation program. Punch test has been applied to thin films of silicone rubber and porcine pericardial tissue and results were analyzed using the same method. Conclusions. The transparent indenter testing system can effectively reduce the material properties measurement error by directly measuring the contact radii. The contact shape can provide valuable information for the anisotropic property of the material. Local surface deformation including contact surface, inner layer and vertical plane can be accurately tracked and mapped to study the strain distribution. The potential usage of the transparent indenter measurement system to investigate biological and biomaterials was verified. The experimental data including the real-time contact area combined with the finite element simulation would be powerful tool to study mechanical properties of soft materials and their relation to microstructure, which has potential in pathologies study such as tissue repair and surgery plan. Key words: transparent indenter, large deformation, soft material, anisotropic.

Spatial nonlinearities: Cascading effects in the earth system

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

2006-01-01

Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

Benchmark solution of the dynamic response of a spherical shell at finite strain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Versino, Daniele; Brock, Jerry S.

2016-09-28

Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method bymore » means of numerical examples with finite deformations and material non-linearities and inelasticity.« less

Nonlinear Dynamics and Control of Flexible Structures

DTIC Science & Technology

1991-03-01

of which might be used for space applications. This project was a collaborative one involving structural, electrical and mechanical engineers and...methods for vibration analysis and new models to analyze chaotic dynamics in nonlinear structures with large deformations and friction forces. Finally... electrical and mechanical engineers and resulted in nine doctoral dissertations and two masters theses wholly or partially supported by this grant

Vibration of mechanically-assembled 3D microstructures formed by compressive buckling

NASA Astrophysics Data System (ADS)

Wang, Heling; Ning, Xin; Li, Haibo; Luan, Haiwen; Xue, Yeguang; Yu, Xinge; Fan, Zhichao; Li, Luming; Rogers, John A.; Zhang, Yihui; Huang, Yonggang

2018-03-01

Micro-electromechanical systems (MEMS) that rely on structural vibrations have many important applications, ranging from oscillators and actuators, to energy harvesters and vehicles for measurement of mechanical properties. Conventional MEMS, however, mostly utilize two-dimensional (2D) vibrational modes, thereby imposing certain limitations that are not present in 3D designs (e.g., multi-directional energy harvesting). 3D vibrational micro-platforms assembled through the techniques of controlled compressive buckling are promising because of their complex 3D architectures and the ability to tune their vibrational behavior (e.g., natural frequencies and modes) by reversibly changing their dimensions by deforming their soft, elastomeric substrates. A clear understanding of such strain-dependent vibration behavior is essential for their practical applications. Here, we present a study on the linear and nonlinear vibration of such 3D mesostructures through analytical modeling, finite element analysis (FEA) and experiment. An analytical solution is obtained for the vibration mode and linear natural frequency of a buckled ribbon, indicating a mode change as the static deflection amplitude increases. The model also yields a scaling law for linear natural frequency that can be extended to general, complex 3D geometries, as validated by FEA and experiment. In the regime of nonlinear vibration, FEA suggests that an increase of amplitude of external loading represents an effective means to enhance the bandwidth. The results also uncover a reduced nonlinearity of vibration as the static deflection amplitude of the 3D structures increases. The developed analytical model can be used in the development of new 3D vibrational micro-platforms, for example, to enable simultaneous measurement of diverse mechanical properties (density, modulus, viscosity etc.) of thin films and biomaterials.

Numerical Study of Nonlinear Structures of Locally Excited Marangoni Convection in the Long-Wave Approximation

NASA Astrophysics Data System (ADS)

Wertgeim, Igor I.

2018-02-01

We investigate stationary and non-stationary solutions of nonlinear equations of the long-wave approximation for the Marangoni convection caused by a localized source of heat or a surface active impurity (surfactant) in a thin horizontal layer of a viscous incompressible fluid with a free surface. The distribution of heat or concentration flux is determined by the uniform vertical gradient of temperature or impurity concentration, distorted by the imposition of a slightly inhomogeneous heating or of surfactant, localized in the horizontal plane. The lower boundary of the layer is considered thermally insulated or impermeable, whereas the upper boundary is free and deformable. The equations obtained in the long-wave approximation are formulated in terms of the amplitudes of the temperature distribution or impurity concentration, deformation of the surface, and vorticity. For a simplification of the problem, a sequence of nonlinear equations is obtained, which in the simplest form leads to a nonlinear Schrödinger equation with a localized potential. The basic state of the system, its dependence on the parameters and stability are investigated. For stationary solutions localized in the region of the surface tension inhomogeneity, domains of parameters corresponding to different spatial patterns are delineated.

Multimaterial 4D Printing with Tailorable Shape Memory Polymers

PubMed Central

Ge, Qi; Sakhaei, Amir Hosein; Lee, Howon; Dunn, Conner K.; Fang, Nicholas X.; Dunn, Martin L.

2016-01-01

We present a new 4D printing approach that can create high resolution (up to a few microns), multimaterial shape memory polymer (SMP) architectures. The approach is based on high resolution projection microstereolithography (PμSL) and uses a family of photo-curable methacrylate based copolymer networks. We designed the constituents and compositions to exhibit desired thermomechanical behavior (including rubbery modulus, glass transition temperature and failure strain which is more than 300% and larger than any existing printable materials) to enable controlled shape memory behavior. We used a high resolution, high contrast digital micro display to ensure high resolution of photo-curing methacrylate based SMPs that requires higher exposure energy than more common acrylate based polymers. An automated material exchange process enables the manufacture of 3D composite architectures from multiple photo-curable SMPs. In order to understand the behavior of the 3D composite microarchitectures, we carry out high fidelity computational simulations of their complex nonlinear, time-dependent behavior and study important design considerations including local deformation, shape fixity and free recovery rate. Simulations are in good agreement with experiments for a series of single and multimaterial components and can be used to facilitate the design of SMP 3D structures. PMID:27499417

Mathematical nonlinear optics

NASA Astrophysics Data System (ADS)

McLaughlin, David W.

1995-08-01

The principal investigator, together with a post-doctoral fellows Tetsuji Ueda and Xiao Wang, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics and to equations directly relevant to nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals and chaotic, homoclinic, small dispersive, and random behavior of solutions of the nonlinear Schroedinger equation. In project 1, the extremely strong nonlinear response of a continuous wave laser beam in a nematic liquid crystal medium has produced striking undulation and filamentation of the laser beam which has been observed experimentally and explained theoretically. In project 2, qualitative properties of the nonlinear Schroedinger equation (which is the fundamental equation for nonlinear optics) have been identified and studied. These properties include optical shocking behavior in the limit of very small dispersion, chaotic and homoclinic behavior in discretizations of the partial differential equation, and random behavior.

Nonlinear thermal dynamic analysis of graphit/aluminum composite plates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tenneti, R.; Chandrashekhara, K.

1994-09-01

Because of the increased application of composite materials in high-temperature environments, the thermoelastic analysis of laminated composite structures is important. Many researchers have applied the classical lamination theory to analyze laminated plates under thermomechanical loading, which neglects shear deformation effects. The transverse shear deformation effects are not negligible as the ratios of inplane elastic modulus to transverse shear modulus are relatively large for fiber-reinforced composite laminates. The application of first-order shear deformation theory for the thermoelastic analysis of laminated plates has been reported by only a few investigators. Reddy and Hsu have considered the thermal bending of laminated plates. Themore » analytical and finite element solutions for the thermal bucking of laminated plates have been reported by Tauchert and Chandrashekara, respectively. However, the first-order shear deformation theory, based on the assumption of constant distribution of transverse shear through the thickness, requires a shear correction factor to account for the parabolic shear strain distribution. Higher order theories have been proposed which eliminate the need for a shear correction factor. In the present work, nonlinear dynamic analysis of laminated plates subjected to rapid heating is investigated using a higher order shear deformation theory. A C(sup 0) finite element model with seven degrees of freedom per node is implmented and numerical results are presented for laminated graphite/aluminum plates.« less

Microstructural controls on the viscoplasticity of Carbopol, and possible applications to shale deformation studies

NASA Astrophysics Data System (ADS)

Hayman, N. W.; Shafiei, M.; Balhoff, M.; Daigle, H.

2017-12-01

To a first order, sedimentary materials behave in an elastic-plastic manner for most experimental and natural conditions at short time scales. However, long-term patterns of leakage from carbon-capture and storage efforts, and reduced efficiency during unconventional hydrocarbon production, point to a broader range of subsurface behaviors. Our analyses of microstructural and porosity responses to experimental deformation of shale suggest that sedimentary rock deformation is not strictly elastic-plastic. For example, organic matter (OM) in mudrocks can fracture during failure, but elsewhere may be more viscous in the same rock volume. The fracture of OM can be accompanied by some combination of frictional and poroelastic deformation in the surrounding clay aggregates, potentially described by critical-state-line soil mechanics. What is less clear is the possible role of viscoplasticity in sedimentary rock deformation. Though not a good analog material for all rock deformation, the cross-linked polymer Carbopol provides an excellent opportunity to explore controls on viscoplasticity. Above the yield stress, carbopol plastic deformation follows a Herschel-Bulkley model wherein shear stress varies as function of strain rate to a power that is generally <1; i.e. it is a shear-thinning material. The rheology can then be tuned by changing the pH of the gel. Using images obtained from scanning electron microscopy, including using a cryogenic system, we found that a structural transition from a dilute neutralized dispersion to an aggregate of closely packed particulates occurs as the pH of the polymer solution increases. This closely packed microstructure thus controls the yield strength which in turn follows approximately a non-linear relationship with porosity. This "analog material" thus has allowed us to quantify the microstructural length-scales that govern viscoplasticity in this material. Future experiments and numerical modeling can evaluate if a viscoplastic component to sedimentary rock deformation is important during engineering efforts. Such an exploration might focus on porosity-yield stress relationships and the monitoring fracture propagation for a wide range of stress conditions, including those which enhance ductility.

Nonlinearity in cytoplasm viscosity can generate an essential symmetry breaking in cellular behaviors.

PubMed

Tachikawa, Masashi; Mochizuki, Atsushi

2015-01-07

The cytoplasms of ameboid cells are nonlinearly viscous. The cell controls this viscosity by modulating the amount, localization and interactions of bio-polymers. Here we investigated how the nonlinearity infers the cellular behaviors and whether nonlinearity-specific behaviors exist. We modeled the developed plasmodium of the slime mold Physarum polycephalum as a network of branching tubes and examined the linear and nonlinear viscous cytoplasm flows in the tubes. We found that the nonlinearity in the cytoplasm׳s viscosity induces a novel type of symmetry breaking in the protoplasmic flow. We also show that symmetry breaking can play an important role in adaptive behaviors, namely, connection of behavioral modes implemented on different time scales and transportation of molecular signals from the front to the rear of the cell during cellular locomotion. Copyright © 2014 Elsevier Ltd. All rights reserved.

Quantitative evaluation method for nonlinear characteristics of piezoelectric transducers under high stress with complex nonlinear elastic constant

NASA Astrophysics Data System (ADS)

Miyake, Susumu; Kasashima, Takashi; Yamazaki, Masato; Okimura, Yasuyuki; Nagata, Hajime; Hosaka, Hiroshi; Morita, Takeshi

2018-07-01

The high power properties of piezoelectric transducers were evaluated considering a complex nonlinear elastic constant. The piezoelectric LCR equivalent circuit with nonlinear circuit parameters was utilized to measure them. The deformed admittance curve of piezoelectric transducers was measured under a high stress and the complex nonlinear elastic constant was calculated by curve fitting. Transducers with various piezoelectric materials, Pb(Zr,Ti)O3, (K,Na)NbO3, and Ba(Zr,Ti)O3–(Ba,Ca)TiO3, were investigated by the proposed method. The measured complex nonlinear elastic constant strongly depends on the linear elastic and piezoelectric constants. This relationship indicates that piezoelectric high power properties can be controlled by modifying the linear elastic and piezoelectric constants.

A kinematically driven anisotropic viscoelastic constitutive model applied to tires

NASA Technical Reports Server (NTRS)

Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

1995-01-01

Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

A kinematically driven anisotropic viscoelastic constitutive model applied to tires

NASA Astrophysics Data System (ADS)

Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

1995-08-01

Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

Large Deformation and Adhesive Contact Studies of Axisymmetric Membranes

PubMed Central

Laprade, Evan J.; Long, Rong; Pham, Jonathan; Lawrence, Jimmy; Emrick, Todd; Crosby, Alfred; Hui, Chung-Yuen; Shull, Kenneth R.

2013-01-01

A model membrane contact system consisting of an acrylic copolymer membrane and polydimethyl-siloxane substrate was utilized to evaluate a recently developed nonlinear large-deformation adhesive contact analysis. Direct measurements of the local membrane apex strain during non-contact inflation indicated that the neo-Hookean model provides an accurate measure of membrane strain and supports its use as the strain energy function for the analysis. A time dependent modulus emerges from the analysis, with principal tensions obtained from a comparison of predicted and experimental membrane profiles. A displacement controlled geometry was more easily modeled than the pressure controlled geometry, the applicability of the analysis was limited by wrinkling instabilities. The substantial viscoelastic behavior of these membranes made it difficult to describe the entire membrane with a single modulus, given the nonuniform deformation history of the membranes. Given the difficulty in determining membrane tension from the measured pressure and profile fits using the model, the peel energy was used as a simpler measure of adhesion. Using an analytical balance in the displacement controlled geometry, the membrane tension at the contact line was directly measured. Coupled with contact angle imaging, the peel energy was determined. For the model membranes studied, this peel energy described the membrane/substrate adhesive interactions quite well, giving well-defined peel energies that were independent of the detailed strain state of the membrane. PMID:23289644

Modelling the 3D post-seismic deformation signal of the Maule 2010 earthquake: Viscosity heterogeneity or non-linear creep?

NASA Astrophysics Data System (ADS)

Peña, C.; Heidbach, O.; Moreno, M.; Li, S.; Bedford, J. R.; Oncken, O.

2017-12-01

The surface deformation associated with the 2010 Mw 8.8 Maule earthquake, Chile was recorded in great detail before, during and after the event. The quality of the post-seismic continuous GPS time series has facilitated a number of studies that have modelled the horizontal signal with a combination of after-slip and viscoelastic relaxation using linear Newtonian rheology. Li et al. (2017, GRL), one of the first studies that also looked into the details of the vertical post-seismic signal, showed that a homogeneous viscosity structure cannot well explain the vertical signal, but that with a heterogeneous viscosity distribution producing a better fit. It is, however, difficult to argue why viscous rock properties should change significantly with distance to the trench. Thus, here we investigate if a non-linear, strain-rate dependent power-law can fit the post-seismic signal in all three components - in particular the vertical one. We use the first 6 years of post-seismic cGPS data and investigate with a 2D geomechanical-numerical model along a profile at 36°S if non-linear creep can explain the deformation signal as well using reasonable rock properties and a temperature field derived for this region from Springer (1999). The 2D model geometry considers the slab as well as the Moho geometry. Our results show that with our model the post-seismic surface deformation signal can be reproduced as well as in the study of Li et al. (2017). These findings suggest that the largest deformations are produced by dislocation creep. Such a process would take place below the Andes ( 40 km depth) at the interface between the deeper, colder crust and the olivine-rich upper mantle, where the lowest effective viscosity results from the relaxation of tensional stresses imposed by the co-seismic displacement. Additionally, we present preliminary results from a 3D geomechanical-numerical model with the same rheology that provides more details of the post-seismic deformation especially along strike the subduction zone.

Quasi-static earthquake cycle simulation based on nonlinear viscoelastic finite element analyses

NASA Astrophysics Data System (ADS)

Agata, R.; Ichimura, T.; Hyodo, M.; Barbot, S.; Hori, T.

2017-12-01

To explain earthquake generation processes, simulation methods of earthquake cycles have been studied. For such simulations, the combination of the rate- and state-dependent friction law at the fault plane and the boundary integral method based on Green's function in an elastic half space is widely used (e.g. Hori 2009; Barbot et al. 2012). In this approach, stress change around the fault plane due to crustal deformation can be computed analytically, while the effects of complex physics such as mantle rheology and gravity are generally not taken into account. To consider such effects, we seek to develop an earthquake cycle simulation combining crustal deformation computation based on the finite element (FE) method with the rate- and state-dependent friction law. Since the drawback of this approach is the computational cost associated with obtaining numerical solutions, we adopt a recently developed fast and scalable FE solver (Ichimura et al. 2016), which assumes use of supercomputers, to solve the problem in a realistic time. As in the previous approach, we solve the governing equations consisting of the rate- and state-dependent friction law. In solving the equations, we compute stress changes along the fault plane due to crustal deformation using FE simulation, instead of computing them by superimposing slip response function as in the previous approach. In stress change computation, we take into account nonlinear viscoelastic deformation in the asthenosphere. In the presentation, we will show simulation results in a normative three-dimensional problem, where a circular-shaped velocity-weakening area is set in a square-shaped fault plane. The results with and without nonlinear viscosity in the asthenosphere will be compared. We also plan to apply the developed code to simulate the post-earthquake deformation of a megathrust earthquake, such as the 2011 Tohoku earthquake. Acknowledgment: The results were obtained using the K computer at the RIKEN (Proposal number hp160221).

Deformation and Breakup of Two Fluid Jets

NASA Astrophysics Data System (ADS)

Doshi, Pankaj; Ramkrishna, Doraiswamy; Basaran, Osman

2001-11-01

Two fluid jets consists of an inner liquid core surrounded by an annulus of outer immiscible liquid. The perturbation in the inner and outer interphase could cause capillary instability resulting in large deformation and breakup of the jet into drops. The jet breakup and drop size distribution is largely influenced by the properties of inner and outer fluid phases. Out of the various jet breakup phenomena one with most technological importance is the one in which inner interphase ruptures followed by the outer interphase resulting in the formation of compound drops. The compound drop formation is very useful for the microencapsulation technology, which find use in diverse pharmaceutical and chemical industry applications. In this paper we present a computational analysis of non-linear deformation and breakup of two fluid jets of Newtonian fluids. The analysis involves study of capillary instability driven deformation of a free jet with periodic boundary conditions. Although small amplitude deformation of two fluid jets have previously been studied, large amplitude deformation exhibiting interesting nonlinear dynamics and eventual breakup of the two fluid jets have been beyond the reach of previously used analytical and computational techniques. The computational difficulties result from the facts that (1) the inner and outer interphase can overturn during the motion and (2) pressure and normal stress are discontinuous at the inner interphase. We overcome both of these difficulties by using a new Galerkin/finite element algorithm that relies on a powerful elliptic mesh generation technique. The results to be presented includes jet deformation and breakup time as a function of inner and outer fluid phase properties. The highlight of the results will be prediction of drop size distribution which is of critical importance for microencapsulation technology.

Modeling viscoelasticity through spring–dashpot models in intermittent-contact atomic force microscopy

PubMed Central

López-Guerra, Enrique A

2014-01-01

Summary We examine different approaches to model viscoelasticity within atomic force microscopy (AFM) simulation. Our study ranges from very simple linear spring–dashpot models to more sophisticated nonlinear systems that are able to reproduce fundamental properties of viscoelastic surfaces, including creep, stress relaxation and the presence of multiple relaxation times. Some of the models examined have been previously used in AFM simulation, but their applicability to different situations has not yet been examined in detail. The behavior of each model is analyzed here in terms of force–distance curves, dissipated energy and any inherent unphysical artifacts. We focus in this paper on single-eigenmode tip–sample impacts, but the models and results can also be useful in the context of multifrequency AFM, in which the tip trajectories are very complex and there is a wider range of sample deformation frequencies (descriptions of tip–sample model behaviors in the context of multifrequency AFM require detailed studies and are beyond the scope of this work). PMID:25551043

Measurement of dynamic patterns of an elastic membrane at bi-modal vibration using high speed electronic speckle pattern interferometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Preciado, Jorge Sanchez; Lopez, Carlos Perez; Santoyo, Fernando Mendoza

2014-05-27

Implementing a hybrid arrangement of Laser Doppler Vibrometry (LDV) and high speed Electronic Speckle Pattern Interferometry (ESPI) we were able to measure the dynamic patterns of a flat rectangular elastic membrane clamped at its edges stimulated with the sum of two resonance frequencies. ESPI is a versatile technique to analyze in real-time the deformation of a membrane since its low computational cost and easy implementation of the optical setup. Elastic membranes present nonlinear behaviors when stimulated with low amplitude signals. The elastic membrane under test, with several non rational related vibrating modals below the 200 Hz, was stimulated with twomore » consecutives resonant frequencies. The ESPI patterns, acquired at high speed rates, shown a similar behavior for the dual frequency stimulation as in the case of patterns formed with the entrainment frequency. We think this may be related to the effects observed in the application of dual frequency stimulation in ultrasound.« less

Effect of microstructure on the coupled electromagnetic-thermo-mechanical response of cyclotrimethylenetrinitramine-estane energetic aggregates to infrared laser radiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Judith A.; Zikry, M. A., E-mail: zikry@ncsu.edu

2015-09-28

The coupled electromagnetic (EM)-thermo-mechanical response of cyclotrimethylenetrinitramine-estane energetic aggregates under laser irradiation and high strain rate loads has been investigated for various aggregate sizes and binder volume fractions. The cyclotrimethylenetrinitramine (RDX) crystals are modeled with a dislocation density-based crystalline plasticity formulation and the estane binder is modeled with finite viscoelasticity through a nonlinear finite element approach that couples EM wave propagation with laser heat absorption, thermal conduction, and inelastic deformation. Material property and local behavior mismatch at the crystal-binder interfaces resulted in geometric scattering of the EM wave, electric field and laser heating localization, high stress gradients, dislocation density, andmore » crystalline shear slip accumulation. Viscous sliding in the binder was another energy dissipation mechanism that reduced stresses in aggregates with thicker binder ligaments and larger binder volume fractions. This investigation indicates the complex interactions between EM waves and mechanical behavior, for accurate predictions of laser irradiation of heterogeneous materials.« less

Deformation partitioning provides insight into elastic, plastic, and viscous contributions to bone material behavior.

PubMed

Ferguson, V L

2009-08-01

The relative contributions of elastic, plastic, and viscous material behavior are poorly described by the separate extraction and analysis of the plane strain modulus, E('), the contact hardness, H(c) (a hybrid parameter encompassing both elastic and plastic behavior), and various viscoelastic material constants. A multiple element mechanical model enables the partitioning of a single indentation response into its fundamental elastic, plastic, and viscous deformation components. The objective of this study was to apply deformation partitioning to explore the role of hydration, tissue type, and degree of mineralization in bone and calcified cartilage. Wet, ethanol-dehydrated, and PMMA-embedded equine cortical bone samples and PMMA-embedded human femoral head tissues were analyzed for contributions of elastic, plastic and viscous deformation to the overall nanoindentation response at each site. While the alteration of hydration state had little effect on any measure of deformation, unembedded tissues demonstrated significantly greater measures of resistance to plastic deformation than PMMA-embedded tissues. The PMMA appeared to mechanically stabilize the tissues and prevent extensive permanent deformation within the bone material. Increasing mineral volume fraction correlated with positive changes in E('), H(c), and resistance to plastic deformation, H; however, the partitioned deformation components were generally unaffected by mineralization. The contribution of viscous deformation was minimal and may only play a significant role in poorly mineralized tissues. Deformation partitioning enables a detailed interpretation of the elastic, plastic, and viscous contributions to the nanomechanical behavior of mineralized tissues that is not possible when examining modulus and contact hardness alone. Varying experimental or biological factors, such as hydration or mineralization level, enables the understanding of potential mechanisms for specific mechanical behavior patterns that would otherwise be hidden within a more complex set of material property parameters.

Supervised local error estimation for nonlinear image registration using convolutional neural networks

NASA Astrophysics Data System (ADS)

Eppenhof, Koen A. J.; Pluim, Josien P. W.

2017-02-01

Error estimation in medical image registration is valuable when validating, comparing, or combining registration methods. To validate a nonlinear image registration method, ideally the registration error should be known for the entire image domain. We propose a supervised method for the estimation of a registration error map for nonlinear image registration. The method is based on a convolutional neural network that estimates the norm of the residual deformation from patches around each pixel in two registered images. This norm is interpreted as the registration error, and is defined for every pixel in the image domain. The network is trained using a set of artificially deformed images. Each training example is a pair of images: the original image, and a random deformation of that image. No manually labeled ground truth error is required. At test time, only the two registered images are required as input. We train and validate the network on registrations in a set of 2D digital subtraction angiography sequences, such that errors up to eight pixels can be estimated. We show that for this range of errors the convolutional network is able to learn the registration error in pairs of 2D registered images at subpixel precision. Finally, we present a proof of principle for the extension to 3D registration problems in chest CTs, showing that the method has the potential to estimate errors in 3D registration problems.

A drop in uniaxial and biaxial nonlinear extensional flows

NASA Astrophysics Data System (ADS)

Favelukis, M.

2017-08-01

In this theoretical report, we explore small deformations of an initially spherical drop subjected to uniaxial or biaxial nonlinear extensional creeping flows. The problem is governed by the capillary number (Ca), the viscosity ratio (λ), and the nonlinear intensity of the flow (E). When the extensional flow is linear (E = 0), the familiar internal circulations are obtained and the same is true with E > 0, except that the external and internal flow rates increase with increasing E. If E < 0, the external flow consists of some unconnected regions leading to the same number of internal circulations (-3/7 < E < 0) or twice the number of internal circulations (E < -3/7), when compared to the linear case. The shape of the deformed drop is represented in terms of a modified Taylor deformation parameter, and the conditions for the breakup of the drop by a center pinching mechanism are also established. When the flow is linear (E = 0), the literature predicts prolate spheroidal drops for uniaxial flows (Ca > 0) and oblate spheroidal drops for biaxial flows (Ca < 0). For the same |Ca|, if E > 0, the drop is more elongated than the linear case, while E < 0 results in less elongated drops than the linear case. Compared to the linear case, for both uniaxial and biaxial extensional flows, E > 0 tends to facilitate drop breakup, while E < 0 makes drop breakup more difficult.

Nonlinear Deformation and Stability of a Noncircular Cylindrical Shell Under Combined Loading with Bending and Twisting Moments

NASA Astrophysics Data System (ADS)

Belov, V. K.; Zheleznov, L. P.; Ognyanova, T. S.

2018-03-01

A previously developed technique is used to solve problems of strength and stability of discretely reinforced noncircular cylindrical shells made of a composite material with allowance for the moments and nonlinearity of their subcritical stress-strain state. Stability of a reinforced bay of the aircraft fuselage made of a composite material under combined loading with bending and twisting moments is studied. The effects of straining nonlinearity, stiffness of longitudinal ribs, and shell thickness on the critical loads that induce shell buckling are analyzed.

Realization of non-linear coherent states by photonic lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn

2015-06-15

In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.

Modeling of high-strength concrete-filled FRP tube columns under cyclic load

NASA Astrophysics Data System (ADS)

Ong, Kee-Yen; Ma, Chau-Khun; Apandi, Nazirah Mohd; Awang, Abdullah Zawawi; Omar, Wahid

2018-05-01

The behavior of high-strength concrete (HSC) - filled fiber-reinforced-polymer (FRP) tubes (HSCFFTs) column subjected to cyclic lateral loading is presented in this paper. As the experimental study is costly and time consuming, a finite element analysis (FEA) is chosen for the study. Most of the previous studies have focused on examining the axial load behavior of HSCFFT column instead of seismic behavior. The seismic behavior of HSCFFT columns has been the main interest in the industry. The key objective of this research is to develop a reliable numerical non-linear FEA model to represent the seismic behavior of such column. A FEA model was developed using the Concrete Damaged Plasticity Model (CDPM) available in the finite element software package (ABAQUS). Comparisons between experimental results from previous research and the predicted results were made based on load versus displacement relationships and ultimate strength of the column. The results showed that the column increased in ductility and able to deform to a greater extent with the increase of the FRP confinement ratio. With the increase of confinement ratio, HSCFFT column achieved a higher moment resistance, thus indicated a higher failure strength in the column under cyclic lateral load. It was found that the proposed FEA model can regenerate the experimental results with adequate accuracy.

The anelastic Ericksen problem: universal eigenstrains and deformations in compressible isotropic elastic solids.

PubMed

Yavari, Arash; Goriely, Alain

2016-12-01

The elastic Ericksen problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions. In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is, we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains. In a nonlinear solid, these eigenstrains can be modelled by a Riemannian material manifold whose metric depends on their distribution. In this framework, we show that the natural generalization of the concept of homogeneous deformations is the notion of covariantly homogeneous deformations -deformations with covariantly constant deformation gradients. We prove that these deformations are the only universal deformations and that they put severe restrictions on possible universal eigenstrains . We show that, in a simply-connected body, for any distribution of universal eigenstrains the material manifold is a symmetric Riemannian manifold and that in dimensions 2 and 3 the universal eigenstrains are zero-stress.

Elastic interaction of hydrogen atoms on graphene: A multiscale approach from first principles to continuum elasticity

NASA Astrophysics Data System (ADS)

Branicio, Paulo S.; Vastola, Guglielmo; Jhon, Mark H.; Sullivan, Michael B.; Shenoy, Vivek B.; Srolovitz, David J.

2016-10-01

The deformation of graphene due to the chemisorption of hydrogen atoms on its surface and the long-range elastic interaction between hydrogen atoms induced by these deformations are investigated using a multiscale approach based on first principles, empirical interactions, and continuum modeling. Focus is given to the intrinsic low-temperature structure and interactions. Therefore, all calculations are performed at T =0 , neglecting possible temperature or thermal fluctuation effects. Results from different methods agree well and consistently describe the local deformation of graphene on multiple length scales reaching 500 Å . The results indicate that the elastic interaction mediated by this deformation is significant and depends on the deformation of the graphene sheet both in and out of plane. Surprisingly, despite the isotropic elasticity of graphene, within the linear elastic regime, atoms elastically attract or repel each other depending on (i) the specific site they are chemisorbed; (ii) the relative position of the sites; (iii) and if they are on the same or on opposite surface sides. The interaction energy sign and power-law decay calculated from molecular statics agree well with theoretical predictions from linear elasticity theory, considering in-plane or out-of-plane deformations as a superposition or in a coupled nonlinear approach. Deviations on the exact power law between molecular statics and the linear elastic analysis are evidence of the importance of nonlinear effects on the elasticity of monolayer graphene. These results have implications for the understanding of the generation of clusters and regular formations of hydrogen and other chemisorbed atoms on graphene.

Influence of thermally activated processes on the deformation behavior during low temperature ECAP

NASA Astrophysics Data System (ADS)

Fritsch, S.; Scholze, M.; F-X Wagner, M.

2016-03-01

High strength aluminum alloys are generally hard to deform. Therefore, the application of conventional severe plastic deformation methods to generate ultrafine-grained microstructures and to further increase strength is considerably limited. In this study, we consider low temperature deformation in a custom-built, cooled equal channel angular pressing (ECAP) tool (internal angle 90°) as an alternative approach to severely plastically deform a 7075 aluminum alloy. To document the maximum improvement of mechanical properties, these alloys are initially deformed from a solid solution heat-treated condition. We characterize the mechanical behavior and the microstructure of the coarse grained initial material at different low temperatures, and we analyze how a tendency for the PLC effect and the strain-hardening rate affect the formability during subsequent severe plastic deformation at low temperatures. We then discuss how the deformation temperature and velocity influence the occurrence of PLC effects and the homogeneity of the deformed ECAP billets. Besides the mechanical properties and these microstructural changes, we discuss technologically relevant processing parameters (such as pressing forces) and practical limitations, as well as changes in fracture behavior of the low temperature deformed materials as a function of deformation temperature.

Toward efficient biomechanical-based deformable image registration of lungs for image-guided radiotherapy

NASA Astrophysics Data System (ADS)

Al-Mayah, Adil; Moseley, Joanne; Velec, Mike; Brock, Kristy

2011-08-01

Both accuracy and efficiency are critical for the implementation of biomechanical model-based deformable registration in clinical practice. The focus of this investigation is to evaluate the potential of improving the efficiency of the deformable image registration of the human lungs without loss of accuracy. Three-dimensional finite element models have been developed using image data of 14 lung cancer patients. Each model consists of two lungs, tumor and external body. Sliding of the lungs inside the chest cavity is modeled using a frictionless surface-based contact model. The effect of the type of element, finite deformation and elasticity on the accuracy and computing time is investigated. Linear and quadrilateral tetrahedral elements are used with linear and nonlinear geometric analysis. Two types of material properties are applied namely: elastic and hyperelastic. The accuracy of each of the four models is examined using a number of anatomical landmarks representing the vessels bifurcation points distributed across the lungs. The registration error is not significantly affected by the element type or linearity of analysis, with an average vector error of around 2.8 mm. The displacement differences between linear and nonlinear analysis methods are calculated for all lungs nodes and a maximum value of 3.6 mm is found in one of the nodes near the entrance of the bronchial tree into the lungs. The 95 percentile of displacement difference ranges between 0.4 and 0.8 mm. However, the time required for the analysis is reduced from 95 min in the quadratic elements nonlinear geometry model to 3.4 min in the linear element linear geometry model. Therefore using linear tetrahedral elements with linear elastic materials and linear geometry is preferable for modeling the breathing motion of lungs for image-guided radiotherapy applications.

Entanglement analysis of a two-atom nonlinear Jaynes-Cummings model with nondegenerate two-photon transition, Kerr nonlinearity, and two-mode Stark shift

NASA Astrophysics Data System (ADS)

Baghshahi, H. R.; Tavassoly, M. K.; Faghihi, M. J.

2014-12-01

An entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of a detuning parameter and Stark effect. It is assumed that the atom-field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom-field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately.

Hot compression deformation behavior of AISI 321 austenitic stainless steel

NASA Astrophysics Data System (ADS)

Haj, Mehdi; Mansouri, Hojjatollah; Vafaei, Reza; Ebrahimi, Golam Reza; Kanani, Ali

2013-06-01

The hot compression behavior of AISI 321 austenitic stainless steel was studied at the temperatures of 950-1100°C and the strain rates of 0.01-1 s-1 using a Baehr DIL-805 deformation dilatometer. The hot deformation equations and the relationship between hot deformation parameters were obtained. It is found that strain rate and deformation temperature significantly influence the flow stress behavior of the steel. The work hardening rate and the peak value of flow stress increase with the decrease of deformation temperature and the increase of strain rate. In addition, the activation energy of deformation ( Q) is calculated as 433.343 kJ/mol. The microstructural evolution during deformation indicates that, at the temperature of 950°C and the strain rate of 0.01 s-1, small circle-like precipitates form along grain boundaries; but at the temperatures above 950°C, the dissolution of such precipitates occurs. Energy-dispersive X-ray analyses indicate that the precipitates are complex carbides of Cr, Fe, Mn, Ni, and Ti.

Mechanical Behavior and Microstructure Evolution of Bearing Steel 52100 During Warm Compression

NASA Astrophysics Data System (ADS)

Huo, Yuanming; He, Tao; Chen, Shoushuang; Wu, Riming

2018-05-01

High-performance bearing steel requires a fine and homogeneous structure of carbide particles. Direct deformation spheroidizing of bearing steel in a dual-phase zone can contribute to achieving this important structure. In this work, warm compression testing of 52100 bearing steel was performed at temperatures in the range of 650-850°C and at strain rates of 0.1-10.0 s-1. The effect of deformation temperatures on mechanical behavior and microstructure evolution was investigated to determine the warm deformation temperature window. The effect of deformation rates on microstructure evolution and metal flow softening behavior of the warm compression was analyzed and discussed. Experimental results showed that the temperature range from 750°C to 800°C should be regarded as the critical range separating warm and hot deformation. Warm deformation at temperatures in the range of 650-750°C promoted carbide spheroidization, and this was determined to be the warm deformation temperature window. Metal flow softening during the warm deformation was caused by carbide spheroidization.

Nonlinear deformation of skeletal muscles in a passive state and in isotonic contraction

NASA Astrophysics Data System (ADS)

Shil'ko, S. V.; Chernous, D. A.; Pleskachevskii, Yu. M.

2012-07-01

A procedure for a two-level modeling of deformation of skeletal muscles is offered. Based on a phenomenological model of an individual muscle fiber, consisting of a viscous, a contractive, and two nonlinearly elastic elements (the first level), various means for describing a skeletal muscle as a whole (the second, macroscopic level) are considered. A method for identification of a muscle model by utilizing experimental elongation diagrams in a passive state and in isotonic contraction is put forward. The results of a biomechanical analysis are compared with known experimental data for the isotonic and isometric activation regimes of tailor's muscle of a frog. It is established that preferable is the description of a muscle that takes into account the different lengths of muscle fibers and their twist.

Prediction of dislocation generation during Bridgman growth of GaAs crystals

NASA Technical Reports Server (NTRS)

Tsai, C. T.; Yao, M. W.; Chait, Arnon

1992-01-01

Dislocation densities are generated in GaAs single crystals due to the excessive thermal stresses induced by temperature variations during growth. A viscoplastic material model for GaAs, which takes into account the movement and multiplication of dislocations in the plastic deformation, is developed according to Haasen's theory. The dislocation density is expressed as an internal state variable in this dynamic viscoplastic model. The deformation process is a nonlinear function of stress, strain rate, dislocation density and temperature. The dislocation density in the GaAs crystal during vertical Bridgman growth is calculated using a nonlinear finite element model. The dislocation multiplication in GaAs crystals for several temperature fields obtained from thermal modeling of both the GTE GaAs experimental data and artificially designed data are investigated.

Prediction of dislocation generation during Bridgman growth of GaAs crystals

NASA Astrophysics Data System (ADS)

Tsai, C. T.; Yao, M. W.; Chait, Arnon

1992-11-01

Dislocation densities are generated in GaAs single crystals due to the excessive thermal stresses induced by temperature variations during growth. A viscoplastic material model for GaAs, which takes into account the movement and multiplication of dislocations in the plastic deformation, is developed according to Haasen's theory. The dislocation density is expressed as an internal state variable in this dynamic viscoplastic model. The deformation process is a nonlinear function of stress, strain rate, dislocation density and temperature. The dislocation density in the GaAs crystal during vertical Bridgman growth is calculated using a nonlinear finite element model. The dislocation multiplication in GaAs crystals for several temperature fields obtained from thermal modeling of both the GTE GaAs experimental data and artificially designed data are investigated.

Two-dimensional nonlinear finite element analysis of well damage due to reservoir compaction, well-to-well interactions, and localization on weak layers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hilbert, L.B. Jr.; Fredrich, J.T.; Bruno, M.S.

1996-05-01

In this paper the authors present the results of a coupled nonlinear finite element geomechanics model for reservoir compaction and well-to-well interactions for the high-porosity, low strength diatomite reservoirs of the Belridge field near Bakersfield, California. They show that well damage and failures can occur under the action of two distinct mechanisms: shear deformations induced by pore compaction, and subsidence, and shear deformations due to well-to-well interactions during production or water injection. They show such casting damage or failure can be localized to weak layers that slide or slip under shear due to subsidence. The magnitude of shear displacements andmore » surface subsidence agree with field observations.« less

Analytical investigations of seismic responses for reinforced concrete bridge columns subjected to strong near-fault ground motion

NASA Astrophysics Data System (ADS)

Su, Chin-Kuo; Sung, Yu-Chi; Chang, Shuenn-Yih; Huang, Chao-Hsun

2007-09-01

Strong near-fault ground motion, usually caused by the fault-rupture and characterized by a pulse-like velocity-wave form, often causes dramatic instantaneous seismic energy (Jadhav and Jangid 2006). Some reinforced concrete (RC) bridge columns, even those built according to ductile design principles, were damaged in the 1999 Chi-Chi earthquake. Thus, it is very important to evaluate the seismic response of a RC bridge column to improve its seismic design and prevent future damage. Nonlinear time history analysis using step-by-step integration is capable of tracing the dynamic response of a structure during the entire vibration period and is able to accommodate the pulsing wave form. However, the accuracy of the numerical results is very sensitive to the modeling of the nonlinear load-deformation relationship of the structural member. FEMA 273 and ATC-40 provide the modeling parameters for structural nonlinear analyses of RC beams and RC columns. They use three parameters to define the plastic rotation angles and a residual strength ratio to describe the nonlinear load-deformation relationship of an RC member. Structural nonlinear analyses are performed based on these parameters. This method provides a convenient way to obtain the nonlinear seismic responses of RC structures. However, the accuracy of the numerical solutions might be further improved. For this purpose, results from a previous study on modeling of the static pushover analyses for RC bridge columns (Sung et al. 2005) is adopted for the nonlinear time history analysis presented herein to evaluate the structural responses excited by a near-fault ground motion. To ensure the reliability of this approach, the numerical results were compared to experimental results. The results confirm that the proposed approach is valid.

Nonlinear aspects of the EEG during sleep in children

NASA Astrophysics Data System (ADS)

Berryman, Matthew J.; Coussens, Scott W.; Pamula, Yvonne; Kennedy, Declan; Lushington, Kurt; Shalizi, Cosma; Allison, Andrew; Martin, A. James; Saint, David; Abbott, Derek

2005-05-01

Electroencephalograph (EEG) analysis enables the dynamic behavior of the brain to be examined. If the behavior is nonlinear then nonlinear tools can be used to glean information on brain behavior, and aid in the diagnosis of sleep abnormalities such as obstructive sleep apnea syndrome (OSAS). In this paper the sleep EEGs of a set of normal children and children with mild OSAS are evaluated for nonlinear brain behaviour. We found that there were differences in the nonlinearity of the brain behaviour between different sleep stages, and between the two groups of children.

Nonlinear dynamics of shells conveying pulsatile flow with pulse-wave propagation. Theory and numerical results for a single harmonic pulsation

NASA Astrophysics Data System (ADS)

Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.

2017-05-01

In deformable shells conveying pulsatile flow, oscillatory pressure changes cause local movements of the fluid and deformation of the shell wall, which propagate downstream in the form of a wave. In biomechanics, it is the propagation of the pulse that determines the pressure gradient during the flow at every location of the arterial tree. In this study, a woven Dacron aortic prosthesis is modelled as an orthotropic circular cylindrical shell described by means of the Novozhilov nonlinear shell theory. Flexible boundary conditions are considered to simulate connection with the remaining tissue. Nonlinear vibrations of the shell conveying pulsatile flow and subjected to pulsatile pressure are investigated taking into account the effects of the pulse-wave propagation. For the first time in literature, coupled fluid-structure Lagrange equations of motion for a non-material volume with wave propagation in case of pulsatile flow are developed. The fluid is modeled as a Newtonian inviscid pulsatile flow and it is formulated using a hybrid model based on the linear potential flow theory and considering the unsteady viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Contributions of pressure and velocity propagation are also considered in the pressure drop along the shell and in the pulsatile frictional traction on the internal wall in the axial direction. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior of a pressurized Dacron aortic graft conveying blood flow. A pulsatile time-dependent blood flow model is considered by applying the first harmonic of the physiological waveforms of velocity and pressure during the heart beating period. Geometrically nonlinear vibration response to pulsatile flow and transmural pulsatile pressure, considering the propagation of pressure and velocity changes inside the shell, is here presented via frequency-response curves, time histories, bifurcation diagrams and Poincaré maps. It is shown that traveling waves of pressure and velocity cause a delay in the radial displacement of the shell at different values of the axial coordinate. The effect of different pulse wave velocities is also studied. Comparisons with the corresponding ideal case without wave propagation (i.e. with the same pulsatile velocity and pressure at any point of the shell) are here discussed. Bifurcation diagrams of Poincaré maps obtained from direct time integration have been used to study the system in the spectral neighborhood of the fundamental natural frequency. By increasing the forcing frequency, the response undergoes very complex nonlinear dynamics (chaos, amplitude modulation and period-doubling bifurcation), here deeply investigated.

True-3D Strain Mapping for Assessment of Material Deformation by Synchrotron X-Ray Microtomography

NASA Astrophysics Data System (ADS)

Ahn, J. J.; Toda, H.; Niinomi, M.; Kobayashi, T.; Akahori, T.; Uesugi, K.

2005-04-01

Downsizing of products with complex shapes has been accelerated thanks to the rapid development of electrodevice manufacturing technology. Micro electromechanical systems (MEMS) are one of such typical examples. 3D strain measurement of such miniature products is needed to ensure their reliability. In the present study, as preliminary trial for it 3D tensile deformation behavior of a pure aluminum wire is examined using the synchrotron X-ray microtomography technique at Spring-8, Japan. Multipurpose in-situ tester is used to investigate real-time tensile deformation behavior of the Al wire. Tensile tests are carried out under strokes of 0, 0.005, 0.01 and 0.015mm. It measures 3D local deformation of a region of interest by tracking a relative movement of a pair of particles at each point. Local deformation behavior of the Al wire is identified to be different from macroscopic deformation behavior. It may be closely associated with underlying microstructure.

True-3D Strain Mapping for Assessment of Material Deformation by Synchrotron X-Ray Microtomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahn, J.J.; Toda, H.; Niinomi, M.

2005-04-09

Downsizing of products with complex shapes has been accelerated thanks to the rapid development of electrodevice manufacturing technology. Micro electromechanical systems (MEMS) are one of such typical examples. 3D strain measurement of such miniature products is needed to ensure their reliability. In the present study, as preliminary trial for it 3D tensile deformation behavior of a pure aluminum wire is examined using the synchrotron X-ray microtomography technique at Spring-8, Japan. Multipurpose in-situ tester is used to investigate real-time tensile deformation behavior of the Al wire. Tensile tests are carried out under strokes of 0, 0.005, 0.01 and 0.015mm. It measuresmore » 3D local deformation of a region of interest by tracking a relative movement of a pair of particles at each point. Local deformation behavior of the Al wire is identified to be different from macroscopic deformation behavior. It may be closely associated with underlying microstructure.« less

Dynamics of a gravity-gradient stabilized flexible spacecraft

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Juang, J. N.

1974-01-01

The dynamics of gravity-gradient stabilized flexible satellite in the neighborhood of a deformed equilibrium configuration are discussed. First the equilibrium configuration was determined by solving a set of nonlinear differential equations. Then stability of motion about the deformed equilibrium was tested by means of the Liapunov direct method. The natural frequencies of oscillation of the complete structure were calculated. The analysis is applicable to the RAE/B satellite.

Investigation of Liquid Sloshing in Spin-Stabilized Satellites.

DTIC Science & Technology

1993-01-31

deformation of the spinning structure in addition to the rigid body motion . A Lagrangian approach was used to develop the equations of motion which include...nonlinear relationships for the unknown rigid body motions and linear terms for the relatively small elastic deformations of the members. Appendix F...the rigid body motion of the test assembly. A pendulum analogy was used to model the sloshing liquid in that early program. Several numerical

Adaptive multiphoton endomicroscopy through a dynamically deformed multicore optical fiber using proximal detection.

PubMed

Warren, Sean C; Kim, Youngchan; Stone, James M; Mitchell, Claire; Knight, Jonathan C; Neil, Mark A A; Paterson, Carl; French, Paul M W; Dunsby, Chris

2016-09-19

This paper demonstrates multiphoton excited fluorescence imaging through a polarisation maintaining multicore fiber (PM-MCF) while the fiber is dynamically deformed using all-proximal detection. Single-shot proximal measurement of the relative optical path lengths of all the cores of the PM-MCF in double pass is achieved using a Mach-Zehnder interferometer read out by a scientific CMOS camera operating at 416 Hz. A non-linear least squares fitting procedure is then employed to determine the deformation-induced lateral shift of the excitation spot at the distal tip of the PM-MCF. An experimental validation of this approach is presented that compares the proximally measured deformation-induced lateral shift in focal spot position to an independent distally measured ground truth. The proximal measurement of deformation-induced shift in focal spot position is applied to correct for deformation-induced shifts in focal spot position during raster-scanning multiphoton excited fluorescence imaging.

A predictive model for failure properties of thermoset resins

NASA Technical Reports Server (NTRS)

Caruthers, James M.; Bowles, Kenneth J.

1989-01-01

A predictive model for the three-dimensional failure behavior of engineering polymers has been developed in a recent NASA-sponsored research program. This model acknowledges the underlying molecular deformation mechanisms and thus accounts for the effects of different chemical compositions, crosslink density, functionality of the curing agent, etc., on the complete nonlinear stress-strain response including yield. The material parameters required by the model can be determined from test-tube quantities of a new resin in only a few days. Thus, we can obtain a first-order prediction of the applicability of a new resin for an advanced aerospace application without synthesizing the large quantities of material needed for failure testing. This technology will effect order-of-magnitude reductions in the time and expense required to develop new engineering polymers.

Use of first derivative of displacement vs. force profiles to determine deformation behavior of compressed powders.

PubMed

Gharaibeh, Shadi F; Aburub, Aktham

2013-03-01

Displacement (D) vs. force (F) profiles obtained during compaction of powders have been reported by several researchers. These profiles are usually used to obtain mechanical energies associated with the compaction of powders. In this work, we obtained displacement-force data associated with the compression of six powders; Avicel PH101, Avicel PH301, pregelatinized corn starch, anhydrous lactose, dicalcium phosphate, and mannitol. The first three powders are known to deform predominantly by plastic behavior while the later ones are known to deform predominantly by brittle fracture. Displacement-force data was utilized to perform in-die Heckel analysis and to calculate the first derivative (dD/dF) of displacement-force plots. First derivative results were then plotted against mean force (F') at each point and against 1/F' at compression forces between 1 and 20 kN. Results of the in-die Heckle analysis are in very good agreement with the known deformation behavior of the compressed materials. First derivative plots show that materials that deform predominantly by plastic behavior have first derivative values (0.0006-0.0016 mm/ N) larger than those of brittle materials (0.0004 mm/N). Moreover, when dD/dF is plotted against 1/F' for each powder, a linear correlation can be obtained (R2=>0.98). The slopes of the dD/dF vs. 1/F' plots for plastically deforming materials are relatively larger than those for materials that deform by brittle behavior. It is concluded that first derivative plots of displacement-force profiles can be used to determine deformation behavior of powders.

The anelastic Ericksen problem: universal eigenstrains and deformations in compressible isotropic elastic solids

PubMed Central

2016-01-01

The elastic Ericksen problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions. In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is, we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains. In a nonlinear solid, these eigenstrains can be modelled by a Riemannian material manifold whose metric depends on their distribution. In this framework, we show that the natural generalization of the concept of homogeneous deformations is the notion of covariantly homogeneous deformations—deformations with covariantly constant deformation gradients. We prove that these deformations are the only universal deformations and that they put severe restrictions on possible universal eigenstrains. We show that, in a simply-connected body, for any distribution of universal eigenstrains the material manifold is a symmetric Riemannian manifold and that in dimensions 2 and 3 the universal eigenstrains are zero-stress. PMID:28119554

Nonlinear mechanics of thermoreversibly associating dendrimer glasses

NASA Astrophysics Data System (ADS)

Srikanth, Arvind; Hoy, Robert S.; Rinderspacher, Berend C.; Andzelm, Jan W.

2013-10-01

We model the mechanics of associating trivalent dendrimer network glasses with a focus on their energy dissipation properties. Various combinations of sticky bond (SB) strength and kinetics are employed. The toughness (work to fracture) of these systems displays a surprising deformation-protocol dependence; different association parameters optimize different properties. In particular, “strong, slow” SBs optimize strength, while “weak, fast” SBs optimize ductility via self-healing during deformation. We relate these observations to breaking, reformation, and partner switching of SBs during deformation. These studies point the way to creating associating-polymer network glasses with tailorable mechanical properties.

Nonlinear quasi-static analysis of ultra-deep-water top-tension riser

NASA Astrophysics Data System (ADS)

Gao, Guanghai; Qiu, Xingqi; Wang, Ke; Liu, Jianjun

2017-09-01

In order to analyse the ultra-deep-water top-tension riser deformation in drilling conditions, a nonlinear quasi-static analysis model and equation are established. The riser in this model is regarded as a simply supported beam located in the vertical plane and is subjected to non-uniform axial and lateral forces. The model and the equation are solved by the finite element method. The effects of riser outside diameter, top tension ratio, sea surface current velocity, drag force coefficient, floating system drift distance and water depth on the riser lateral displacement are discussed. Results show that the riser lateral displacement increase with the increase in the sea surface current velocity, drag force coefficient and water depth, whereas decrease with the increase in the riser outside diameter, top tension ratio. The top tension ratio has an important influence on the riser deformation and it should be set reasonably under different circumstances. The drift of the floating system has a complicated influence on the riser deformation and it should avoid a large drift distance in the proceedings of drilling and production.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Wonjung; Kovacic, Gregor; Cai, David

Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distributionmore » is in excellent agreement with the simulation of the full wave system in equilibrium.« less

Nonlinear viscoelasticity and generalized failure criterion for biopolymer gels

NASA Astrophysics Data System (ADS)

Divoux, Thibaut; Keshavarz, Bavand; Manneville, Sébastien; McKinley, Gareth

2016-11-01

Biopolymer gels display a multiscale microstructure that is responsible for their solid-like properties. Upon external deformation, these soft viscoelastic solids exhibit a generic nonlinear mechanical response characterized by pronounced stress- or strain-stiffening prior to irreversible damage and failure, most often through macroscopic fractures. Here we show on a model acid-induced protein gel that the nonlinear viscoelastic properties of the gel can be described in terms of a 'damping function' which predicts the gel mechanical response quantitatively up to the onset of macroscopic failure. Using a nonlinear integral constitutive equation built upon the experimentally-measured damping function in conjunction with power-law linear viscoelastic response, we derive the form of the stress growth in the gel following the start up of steady shear. We also couple the shear stress response with Bailey's durability criteria for brittle solids in order to predict the critical values of the stress σc and strain γc for failure of the gel, and how they scale with the applied shear rate. This provides a generalized failure criterion for biopolymer gels in a range of different deformation histories. This work was funded by the MIT-France seed fund and by the CNRS PICS-USA scheme (#36939). BK acknowledges financial support from Axalta Coating Systems.

A numerical model for modeling microstructure and THM couplings in fault gouges

NASA Astrophysics Data System (ADS)

Veveakis, M.; Rattez, H.; Stefanou, I.; Sulem, J.; Poulet, T.

2017-12-01

When materials are subjected to large deformations, most of them experience inelastic deformations, accompanied by a localization of these deformations into a narrow zone leading to failure. Localization is seen as an instability from the homogeneous state of deformation. Therefore a first approach to study it consists at looking at the possible critical conditions for which the constitutive equations of the material allow a bifurcation point (Rudnicki & Rice 1975). But in some cases, we would like to know the evolution of the material after the onset of localization. For example, a fault in the crustal part of the lithosphere is a shear band and the study of this localized zone enables to extract information about seismic slip. For that, we need to approximate the solution of a nonlinear boundary value problem numerically. It is a challenging task due to the complications that arise while dealing with a softening behavior. Indeed, the classical continuum theory cannot be used because the governing system of equations is ill-posed (Vardoulakis 1985). This ill-posedness can be tracked back to the fact that constitutive models don't contain material parameters with the dimension of a length. It leads to what is called "mesh dependency" for numerical simulations, as the deformations localize in only one element of the mesh and the behavior of the system depends thus on the mesh size. A way to regularize the problem is to resort to continuum models with microstructure, such as Cosserat continua (Sulem et al. 2011). Cosserat theory is particularly interesting as it can explicitly take into account the size of the microstructure in a fault gouge. Basically, it introduces 3 degrees of freedom of rotation on top of the 3 translations (Godio et al. 2016). The original work of (Mühlhaus & Vardoulakis 1987) is extended in 3D and thermo-hydro mechanical couplings are added to the model to study fault system in the crustal part of the lithosphere. The system of equations is approximated by Finite Element using Redback, an application based on the Moose software (Gaston et al. 2009; Poulet et al. 2016). It enables us to study the weakening effect of the couplings on a fault modelled as an infinite sheared layer and follow the evolution of the shear band thickness in the post-bifurcation regime.

Micromechanical model of lung parenchyma hyperelasticity

NASA Astrophysics Data System (ADS)

Concha, Felipe; Sarabia-Vallejos, Mauricio; Hurtado, Daniel E.

2018-03-01

Mechanics plays a key role in respiratory physiology, as lung tissue cyclically deforms to bring air in and out the lung, a life-long process necessary for respiration. The study of regional mechanisms of deformation in lung parenchyma has received great attention to date due to its clinical relevance, as local overstretching and stress concentration in lung tissue is currently associated to pathological conditions such as lung injury during mechanical ventilation therapy. This mechanical approach to lung physiology has motivated the development of constitutive models to better understand the relation between stress and deformation in the lung. While material models proposed to date have been key in the development of whole-lung simulations, either they do not directly relate microstructural properties of alveolar tissue with coarse-scale behavior, or they require a high computational effort when based on real alveolar geometries. Furthermore, most models proposed to date have not been thoroughly validated for anisotropic deformation states, which are commonly found in normal lungs in-vivo. In this work, we develop a novel micromechanical model of lung parenchyma hyperelasticity using the framework of finite-deformation homogenization. To this end, we consider a tetrakaidecahedron unit cell with incompressible Neo-Hookean structural elements that account for the alveolar wall tissue responsible for the elastic response, and derive expressions for its effective coarse-scale behavior that directly depend on the alveolar wall elasticity, reference porosity, and two other geometrical coefficients. To validate the proposed model, we simulate the non-linear elastic response of twelve representative volume elements (RVEs) of lung parenchyma with micrometric dimensions, whose geometry is obtained from micrometric computed-tomography reconstructions of murine lungs. We show that the proposed micromechanical model accurately captures the RVEs response not only for isotropic volumetric expansion, but also for three other anisotropic loading conditions for different levels of tissue porosity, while displaying superior computational efficiency and stability in estimating coarse-scale response when compared to direct numerical simulations of RVEs. Further, we find that the most influential microstructural parameters on the response of the micromechanical model are the reference porosity and the alveolar wall elasticity. We also show that the model can reproduce uniaxial experimental tests on lung tissue samples, and estimate the Poisson ratio to be 0.22. We envision that our model will enable predictive and efficient whole-organ simulations useful to study the normal and diseased lung.

Twinning behaviors of a rolled AZ31 magnesium alloy under multidirectional loading

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hou, Dewen

The microstructure and texture evolution of an AZ31 magnesium rolled sheet during quasi-static compression at strain rates of 10{sup −3} s{sup −1} has been investigated by in situ electron backscattered diffraction. The influence of the initial and pre-deformed texture on the predominant deformation mechanisms during compression has been examined. It has been found that extensive grain reorientation due to (10 − 12) tensile twinning appeared when compressed along transverse direction. Tensile twin variants were observed under this loading condition, and different variants will cause an effect to the following deformation. Several twinning modes occurred with continuative loading along rolling direction.more » - Highlights: •Twinning behaviors were investigated through in situ multidirectional compressive tests. •Deformation behavior was affected by the twin variants. •Four types of twinning behaviors were observed during deformation process.« less

Simulation of Thermo-viscoplastic Behaviors for AISI 4140 Steel

NASA Astrophysics Data System (ADS)

Li, Hong-Bin; Feng, Yun-Li

2016-04-01

The thermo-viscoplastic behaviors of AISI 4140 steel are investigated over wide ranges of strain rate and deformation temperature by isothermal compression tests. Based on the experimental results, a unified viscoplastic constitutive model is proposed to describe the hot compressive deformation behaviors of the studied steel. In order to reasonably evaluate the work hardening behaviors, a strain hardening material constant (h0) is expressed as a function of deformation temperature and strain rate in the proposed constitutive model. Also, the sensitivity of initial value of internal variable s to the deformation temperature is discussed. Furthermore, it is found that the initial value of internal variable s can be expressed as a linear function of deformation temperature. Comparisons between the measured and predicted results confirm that the proposed constitutive model can give an accurate and precise estimate of the inelastic stress-strain relationships for the studied high-strength steel.

High-Temperature Deformation Behavior of HCP Alloys -- An Internal Variable Approach

DTIC Science & Technology

2006-05-31

successfully to characterize the high temperature deformation behavior of various metallic materials such as Al alloys, Pb-Sn hyper- eutectic alloy, and...implying dynamic recrystallization (DRX) and GBS as the major deformation mechanisms at 523 K and 10-4 /s. Large cavities are observed at the

Auxetic metamaterials from disordered networks

NASA Astrophysics Data System (ADS)

Reid, Daniel R.; Pashine, Nidhi; Wozniak, Justin M.; Jaeger, Heinrich M.; Liu, Andrea J.; Nagel, Sidney R.; de Pablo, Juan J.

2018-02-01

Recent theoretical work suggests that systematic pruning of disordered networks consisting of nodes connected by springs can lead to materials that exhibit a host of unusual mechanical properties. In particular, global properties such as Poisson’s ratio or local responses related to deformation can be precisely altered. Tunable mechanical responses would be useful in areas ranging from impact mitigation to robotics and, more generally, for creation of metamaterials with engineered properties. However, experimental attempts to create auxetic materials based on pruning-based theoretical ideas have not been successful. Here we introduce a more realistic model of the networks, which incorporates angle-bending forces and the appropriate experimental boundary conditions. A sequential pruning strategy of select bonds in this model is then devised and implemented that enables engineering of specific mechanical behaviors upon deformation, both in the linear and in the nonlinear regimes. In particular, it is shown that Poisson’s ratio can be tuned to arbitrary values. The model and concepts discussed here are validated by preparing physical realizations of the networks designed in this manner, which are produced by laser cutting 2D sheets and are found to behave as predicted. Furthermore, by relying on optimization algorithms, we exploit the networks’ susceptibility to tuning to design networks that possess a distribution of stiffer and more compliant bonds and whose auxetic behavior is even greater than that of homogeneous networks. Taken together, the findings reported here serve to establish that pruned networks represent a promising platform for the creation of unique mechanical metamaterials.

Modeling and Simulation of Viscous Electro-Active Polymers

PubMed Central

Vogel, Franziska; Göktepe, Serdar; Steinmann, Paul; Kuhl, Ellen

2014-01-01

Electro-active materials are capable of undergoing large deformation when stimulated by an electric field. They can be divided into electronic and ionic electro-active polymers (EAPs) depending on their actuation mechanism based on their composition. We consider electronic EAPs, for which attractive Coulomb forces or local re-orientation of polar groups cause a bulk deformation. Many of these materials exhibit pronounced visco-elastic behavior. Here we show the development and implementation of a constitutive model, which captures the influence of the electric field on the visco-elastic response within a geometrically non-linear finite element framework. The electric field affects not only the equilibrium part of the strain energy function, but also the viscous part. To adopt the familiar additive split of the strain from the small strain setting, we formulate the governing equations in the logarithmic strain space and additively decompose the logarithmic strain into elastic and viscous parts. We show that the incorporation of the electric field in the viscous response significantly alters the relaxation and hysteresis behavior of the model. Our parametric study demonstrates that the model is sensitive to the choice of the electro-viscous coupling parameters. We simulate several actuator structures to illustrate the performance of the method in typical relaxation and creep scenarios. Our model could serve as a design tool for micro-electro-mechanical systems, microfluidic devices, and stimuli-responsive gels such as artificial skin, tactile displays, or artificial muscle. PMID:25267881

Current interactions from the one-form sector of nonlinear higher-spin equations

NASA Astrophysics Data System (ADS)

Gelfond, O. A.; Vasiliev, M. A.

2018-06-01

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η = exp ⁡ iφ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant η η bar . Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η = 0) η bar = 0.

Piezoelectric monolayers as nonlinear energy harvesters.

PubMed

López-Suárez, Miquel; Pruneda, Miguel; Abadal, Gabriel; Rurali, Riccardo

2014-05-02

We study the dynamics of h-BN monolayers by first performing ab-initio calculations of the deformation potential energy and then solving numerically a Langevine-type equation to explore their use in nonlinear vibration energy harvesting devices. An applied compressive strain is used to drive the system into a nonlinear bistable regime, where quasi-harmonic vibrations are combined with low-frequency swings between the minima of a double-well potential. Due to its intrinsic piezoelectric response, the nonlinear mechanical harvester naturally provides an electrical power that is readily available or can be stored by simply contacting the monolayer at its ends. Engineering the induced nonlinearity, a 20 nm2 device is predicted to harvest an electrical power of up to 0.18 pW for a noisy vibration of 5 pN.

Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams

NASA Technical Reports Server (NTRS)

Noor, A. K.; Peters, J. M.

1981-01-01

Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.

MEMS-based wide-bandwidth electromagnetic energy harvester with electroplated nickel structure

NASA Astrophysics Data System (ADS)

Sun, Shi; Dai, Xuhan; Sun, Yunna; Xiang, Xiaojian; Ding, Guifu; Zhao, Xiaolin

2017-11-01

A novel nickel-based nonlinear electromagnetic energy harvester has been designed, fabricated, and characterized in this work. Electroplated nickel is very suitable for a stretching-based mechanism to broaden the bandwidth due to its good process and mechanical properties. A strong hardening nonlinearity is induced due to the large deformation of the thin nickel based guided-beam structure. Combining the merits of both the mechanical properties and guided-beam structure, the energy harvester shows good bandwidth performance. It is found that increasing the thickness of the central platform could guarantee nonlinearity. Static and dynamic models of the energy harvester are simulated and validated. Test results show that the energy harvester has good repeatability without any destruction under a large deformation condition. At the acceleration of 0.5 g, comparative large bandwidths of 129 and 59 Hz are obtained for displacement and RMS output voltage, respectively. Power output of 3.4 µW and normalized power density of 125.92 µW cm-3 g-2 are achieved with the load resistance of 38 Ω.

Multibody dynamic analysis using a rotation-free shell element with corotational frame

NASA Astrophysics Data System (ADS)

Shi, Jiabei; Liu, Zhuyong; Hong, Jiazhen

2018-03-01

Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore, the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.

A fluid-structure interaction model of soft robotics using an active strain approach

NASA Astrophysics Data System (ADS)

Hess, Andrew; Lin, Zhaowu; Gao, Tong

2017-11-01

Soft robotic swimmers exhibit rich dynamics that stem from the non-linear interplay of the fluid and immersed soft elastic body. Due to the difficulty of handling the nonlinear two-way coupling of hydrodynamic flow and deforming elastic body, studies of flexible swimmers often employ either one-way coupling strategies with imposed motions of the solid body or some simplified elasticity models. To explore the nonlinear dynamics of soft robots powered by smart soft materials, we develop a computational model to deal with the two-way fluid/elastic structure interactions using the fictitious domain method. To mimic the dynamic response of the functional soft material under external actuations, we assume the solid phase to be neo-Hookean, and employ an active strain approach to incorporate actuation, which is based on the multiplicative decomposition of the deformation gradient tensor. We demonstrate the capability of our algorithm by performing a series of numerical explorations that manipulate an elastic structure with finite thickness, starting from simple rectangular or circular plates to soft robot prototypes such as stingrays and jellyfish.

Toward a 3D dynamic model of a faulty duplex ball bearing

NASA Astrophysics Data System (ADS)

Kogan, Gideon; Klein, Renata; Kushnirsky, Alex; Bortman, Jacob

2015-03-01

Bearings are vital components for safe and proper operation of machinery. Increasing efficiency of bearing diagnostics usually requires training of health and usage monitoring systems via expensive and time-consuming ground calibration tests. The main goal of this research, therefore, is to improve bearing dynamics modeling tools in order to reduce the time and budget needed to implement the health and usage monitoring approach. The proposed three-dimensional ball bearing dynamic model is based on the classic dynamic and kinematic equations. Interactions between the bodies are simulated using non-linear springs combined with dampers described by Hertz-type contact relation. The force friction is simulated using the hyperbolic-tangent function. The model allows simulation of a wide range of mechanical faults. It is validated by comparison to known bearing behavior and to experimental results. The model results are verified by demonstrating numerical convergence. The model results for the two cases of single and duplex angular ball bearings with axial deformation in the outer ring are presented. The qualitative investigation provides insight into bearing dynamics, the sensitivity study generalizes the qualitative findings for similar cases, and the comparison to the test results validates model reliability. The article demonstrates the variety of the cases that the 3D bearing model can simulate and the findings to which it may lead. The research allowed the identification of new patterns generated by single and duplex bearings with axially deformed outer race. It also enlightened the difference between single and duplex bearing manifestation. In the current research the dynamic model enabled better understanding of the physical behavior of the faulted bearings. Therefore, it is expected that the modeling approach has the potential to simplify and improve the development process of diagnostic algorithms. • A deformed outer race of a single axially loaded bearing is simulated. • The model results are subjected to a sensitivity study. • Duplex bearing with deformed outer race is simulated as well as tested. • The simulation results are in a good agreement with the experimental results.

An Analysis of the Macroscopic Tensile Behavior of a Nonlinear Nylon Reinforced Elastomeric Composite System Using MAC/GMC

NASA Technical Reports Server (NTRS)

Assaad, Mahmoud; Arnold, Steven M.

1999-01-01

A special class of composite laminates composed of soft rubbery matrices and stiff reinforcements made of steel wires or synthetic fibers is examined, where each constituent behaves in a nonlinear fashion even in the small strain domain. Composite laminates made of piles stacked at alternating small orientation angles with respect to the applied axial strain are primarily dominated by the nonlinear behavior of the reinforcing fibers. However; composites with large ply orientations or those perpendicular to the loading axis, will approximate the behavior of the matrix phase and respond in even a more complex fashion for arbitrarily stacked piles. The geometric nonlinearity due to small cord rotations during loading was deemed here to have a second order effect and consequently dropped from any consideration. The user subroutine USRMAT within the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC), was utilized to introduce the constituent material nonlinear behavior. Stress-strain behavior at the macro level was experimentally generated for single and multi ply composites comprised of continuous Nylon-66 reinforcements embedded in a carbon black loaded rubbery matrix. Comparisons between the predicted macro composite behavior and experimental results are excellent when material nonlinearity is included in the analysis. In this paper, a brief review of GMC is provided, along with a description of the nonlinear behavior of the constituents and associated constituent constitutive relations, and the improved macro (or composite) behavior predictions are documented and illustrated.

Finite Deformation of Magnetoelastic Film

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barham, Matthew Ian

2011-05-31

A nonlinear two-dimensional theory is developed for thin magnetoelastic lms capable of large deformations. This is derived directly from three-dimensional theory. Signi cant simpli cations emerge in the descent from three dimensions to two, permitting the self eld generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers with two material models. First weak magnetization is investigated leading to a free energy where magnetization and deformation are un-coupled. The second closely couples the magnetization and deformation. Numerical solutions are obtained to equilibrium boundary-value problems in which the membrane is subjected to lateral pressure andmore » an applied magnetic eld. An instability is inferred and investigated for the weak magnetization material model.« less

Simplified and refined finite element approaches for determining stresses and internal forces in geometrically nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Robinson, J. C.

1979-01-01

Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.

Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators

NASA Technical Reports Server (NTRS)

Taleghani, Barmac K.; Campbell, Joel F.

1999-01-01

A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.

Phase transformation and deformation behavior of NiTi-Nb eutectic joined NiTi wires

PubMed Central

Wang, Liqiang; Wang, Cong; Zhang, Lai-Chang; Chen, Liangyu; Lu, Weijie; Zhang, Di

2016-01-01

NiTi wires were brazed together via eutectic reaction between NiTi and Nb powder deposited at the wire contact region. Phase transformation and deformation behavior of the NiTi-Nb eutectic microstructure were investigated using transmission electron microscopy (TEM) and cyclic loading-unloading tests. Results show that R phase and B19′ martensite transformation are induced by plastic deformation. R phase transformation, which significantly contributes to superelasticity, preferentially occurs at the interfaces between NiTi and eutectic region. Round-shaped Nb-rich phase with rod-like and lamellar-type eutectics are observed in eutectic regions. These phases appear to affect the deformation behavior of the brazed NiTi-Nb region via five distinct stages in stress-strain curves: (I) R phase reorientation, (II) R phase transformation from parent phase, (III) elastic deformation of reoriented martensite accompanied by the plastic deformation of Nb-rich phase and lamellar NiTi-Nb eutectic, (IV) B19′ martensitic transformation, and (V) plastic deformation of the specimen. PMID:27049025

An activated energy approach for accelerated testing of the deformation of UHMWPE in artificial joints.

PubMed

Galetz, Mathias Christian; Glatzel, Uwe

2010-05-01

The deformation behavior of ultrahigh molecular polyethylene (UHMWPE) is studied in the temperature range of 23-80 degrees C. Samples are examined in quasi-static compression, tensile and creep tests to determine the accelerated deformation of UHMWPE at elevated temperatures. The deformation mechanisms under compression load can be described by one strain rate and temperature dependent Eyring process. The activation energy and volume of that process do not change between 23 degrees C and 50 degrees C. This suggests that the deformation mechanism under compression remains stable within this temperature range. Tribological tests are conducted to transfer this activated energy approach to the deformation behavior under loading typical for artificial knee joints. While this approach does not cover the wear mechanisms close to the surface, testing at higher temperatures is shown to have a significant potential to reduce the testing time for lifetime predictions in terms of the macroscopic creep and deformation behavior of artificial joints. Copyright 2010. Published by Elsevier Ltd.

Nonlinear Curvature Expressions for Combined Flapwise Bending, Chordwise Bending, Torsion and Extension of Twisted Rotor Blades

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; Kaza, K. R. V.

1976-01-01

The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.

Physics-based deformable organisms for medical image analysis

NASA Astrophysics Data System (ADS)

Hamarneh, Ghassan; McIntosh, Chris

2005-04-01

Previously, "Deformable organisms" were introduced as a novel paradigm for medical image analysis that uses artificial life modelling concepts. Deformable organisms were designed to complement the classical bottom-up deformable models methodologies (geometrical and physical layers), with top-down intelligent deformation control mechanisms (behavioral and cognitive layers). However, a true physical layer was absent and in order to complete medical image segmentation tasks, deformable organisms relied on pure geometry-based shape deformations guided by sensory data, prior structural knowledge, and expert-generated schedules of behaviors. In this paper we introduce the use of physics-based shape deformations within the deformable organisms framework yielding additional robustness by allowing intuitive real-time user guidance and interaction when necessary. We present the results of applying our physics-based deformable organisms, with an underlying dynamic spring-mass mesh model, to segmenting and labelling the corpus callosum in 2D midsagittal magnetic resonance images.

Nonlinear dynamics and numerical uncertainties in CFD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.

Nonlinear analysis of a rotor-bearing system using describing functions

NASA Astrophysics Data System (ADS)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Dynamics of thin-film piezoelectric microactuators with large vertical stroke subject to multi-axis coupling and fabrication asymmetries

NASA Astrophysics Data System (ADS)

Choi, Jongsoo; Wang, Thomas; Oldham, Kenn

2018-01-01

The high performance and small size of MEMS based scanners has allowed various optical imaging techniques to be realized in a small form factor. Many such devices are resonant scanners, and thus their linear and nonlinear dynamic behaviors have been studied in the past. Thin-film piezoelectric materials, in contrast, provide sufficient energy density to achieve both large static displacements and high-frequency resonance, but large deformation can in turn influence dynamic scanner behavior. This paper reports on the influence of very large stroke translation of a piezoelectric vertical actuator on its resonant behavior, which may not be otherwise explained fully by common causes of resonance shift such as beam stiffening or nonlinear forcing. To examine the change of structural compliance over the course of scanner motion, a model has been developed that includes internal forces from residual stress and the resultant additional multi-axis coupling among actuator leg structures. Like some preceding vertical scanning micro-actuators, the scanner of this work has four legs, with each leg featuring four serially connected thin-film PZT unimorphs that allow the scanner to generate larger than 400 µm of vertical displacement at 14 V DC. Using an excitation near one or more resonances, the input voltage can be lowered, and complementary multi-axis rotations can be also generated, but change of the resonant frequencies with scanner height needs to be understood to maximize scanner performance. The presented model well predicts the experimental observation of the decrease of the resonant frequencies of the scanner with the increase of a dc bias voltage. Also, the effects of the magnitude and uniformity of residual stress across the scanner structure on the natural frequencies have been studied.

Simple model of cable-stayed bridge deck subjected to static wind loading

NASA Astrophysics Data System (ADS)

Kang, Yi-Lung; Wang, Yang Cheng

1997-05-01

Cable-stayed bridges have been known since 18th century with aesthetics design. The structural system and the structural behavior are significantly different from those of continuous bridges. Compared to continuous bridge, cable- stayed bridges have more flexure bridge deck than those of continuous bridges.On the other hand, cable-stayed bridges have less stiffness to resist wind loading especially for lateral loads. The first considering of bridge engineering is safety. In 1940's, Tacoma Narrows Suspension Bridge destroyed by wind loading is a good example even though it is not a cable-stayed bridge. After the bridge was destroyed, a lot of research articles have been published regarding cable supported bridge subjected to wind loading. In recent days, high strength materials have been served. The bridge engineers use the advantages to expand the span length of cable-stayed bridges. Due to the span length increased and the use of high strength materials, cable- stayed bridges have more significant nonlinear behavior subjected to wind loading. In this paper, a slice bridge deck of cable-stayed bridge connected to internal support cables is considered. The deck has been considered to be subjected to lateral static wind loading. Since cables can not take compressive force, the deck has strongly nonlinear behavior even though the materials are linear elastic. Several primary load combinations have ben considered in this paper such as the bridge deck supposed to be moved horizontally without rotation or the bridge deck supposed to be moved horizontally with rotational deformation. The mathematical formulas and the numerical solutions are found and represented in graphical forms. The results can be provided to bridge designers and researchers for further study of this type of structure subjected to wind loading.

Inducing in situ, nonlinear soil response applying an active source

USGS Publications Warehouse

Johnson, P.A.; Bodin, P.; Gomberg, J.; Pearce, F.; Lawrence, Z.; Menq, F.-Y.

2009-01-01

[1] It is well known that soil sites have a profound effect on ground motion during large earthquakes. The complex structure of soil deposits and the highly nonlinear constitutive behavior of soils largely control nonlinear site response at soil sites. Measurements of nonlinear soil response under natural conditions are critical to advancing our understanding of soil behavior during earthquakes. Many factors limit the use of earthquake observations to estimate nonlinear site response such that quantitative characterization of nonlinear behavior relies almost exclusively on laboratory experiments and modeling of wave propagation. Here we introduce a new method for in situ characterization of the nonlinear behavior of a natural soil formation using measurements obtained immediately adjacent to a large vibrator source. To our knowledge, we are the first group to propose and test such an approach. Employing a large, surface vibrator as a source, we measure the nonlinear behavior of the soil by incrementally increasing the source amplitude over a range of frequencies and monitoring changes in the output spectra. We apply a homodyne algorithm for measuring spectral amplitudes, which provides robust signal-to-noise ratios at the frequencies of interest. Spectral ratios are computed between the receivers and the source as well as receiver pairs located in an array adjacent to the source, providing the means to separate source and near-source nonlinearity from pervasive nonlinearity in the soil column. We find clear evidence of nonlinearity in significant decreases in the frequency of peak spectral ratios, corresponding to material softening with amplitude, observed across the array as the source amplitude is increased. The observed peak shifts are consistent with laboratory measurements of soil nonlinearity. Our results provide constraints for future numerical modeling studies of strong ground motion during earthquakes.

Optics and Nonlinear Buckling Mechanics in Large-Area, Highly Stretchable Arrays of Plasmonic Nanostructures.

PubMed

Gao, Li; Zhang, Yihui; Zhang, Hui; Doshay, Sage; Xie, Xu; Luo, Hongying; Shah, Deesha; Shi, Yan; Xu, Siyi; Fang, Hui; Fan, Jonathan A; Nordlander, Peter; Huang, Yonggang; Rogers, John A

2015-06-23

Large-scale, dense arrays of plasmonic nanodisks on low-modulus, high-elongation elastomeric substrates represent a class of tunable optical systems, with reversible ability to shift key optical resonances over a range of nearly 600 nm at near-infrared wavelengths. At the most extreme levels of mechanical deformation (strains >100%), nonlinear buckling processes transform initially planar arrays into three-dimensional configurations, in which the nanodisks rotate out of the plane to form linear arrays with "wavy" geometries. Analytical, finite-element, and finite-difference time-domain models capture not only the physics of these buckling processes, including all of the observed modes, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, particularly to soft optical sensors that integrate on or in the human body.

Nonlinear evolution of Benjamin-Feir wave group based on third order solution of Benjamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Zahnur; Halfiani, Vera; Salmawaty; Tulus; Ramli, Marwan

2018-01-01

This study concerns on the evolution of trichromatic wave group. It has been known that the trichromatic wave group undergoes an instability during its propagation, which results wave deformation and amplification on the waves amplitude. The previous results on the KdV wave group showed that the nonlinear effect will deform the wave and lead to large wave whose amplitude is higher than the initial input. In this study we consider the Benjamin-Bona-Mahony equation and the theory of third order side band approximation to investigate the peaking and splitting phenomena of the wave groups which is initially in trichromatic signal. The wave amplitude amplification and the maximum position will be observed through a quantity called Maximal Temporal Amplitude (MTA) which measures the maximum amplitude of the waves over time.

Yield stress in amorphous solids: A mode-coupling-theory analysis

NASA Astrophysics Data System (ADS)

Ikeda, Atsushi; Berthier, Ludovic

2013-11-01

The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly nonlinear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyze several classes of disordered solids, using simple models of hard-sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome of numerical measurements. The theory correctly describes the emergence of a yield stress of entropic nature in hard-sphere glasses, and its rapid growth as density approaches random close packing at qualitative level. By contrast, the emergence of solid behavior in soft and metallic glasses, which originates from direct particle interactions is not well described by the theory. We show that similar shortcomings arise in the description of the caging dynamics of the glass phase at rest. We discuss the range of applicability of mode-coupling theory to understand the yield stress and nonlinear rheology of amorphous materials.

Investigation on the fiber based approach to estimate the axial load carrying capacity of the circular concrete filled steel tube (CFST)

NASA Astrophysics Data System (ADS)

Piscesa, B.; Attard, M. M.; Suprobo, P.; Samani, A. K.

2017-11-01

External confining devices are often used to enhance the strength and ductility of reinforced concrete columns. Among the available external confining devices, steel tube is one of the most widely used in construction. However, steel tube has some drawbacks such as local buckling which needs to be considered when estimating the axial load carrying capacity of the concrete-filled-steel-tube (CFST) column. To tackle this problem in design, Eurocode 4 provided guidelines to estimate the effective yield strength of the steel tube material. To study the behavior of CFST column, in this paper, a non-linear analysis using a fiber-based approach was conducted. The use of the fiber-based approach allows the engineers to predict not only the axial load carrying capacity but also the complete load-deformation curve of the CFST columns for a known confining pressure. In the proposed fiber-based approach, an inverse analysis is used to estimate the constant confining pressure similar to design-oriented models. This paper also presents comparisons between the fiber-based approach model with the experimental results and the 3D non-linear finite element analysis.

Nonlinear transport of soft droplets in pore networks

NASA Astrophysics Data System (ADS)

Vernerey, Franck; Benet Cerda, Eduard; Koo, Kanghyeon

A large number of biological and technological processes depend on the transport of soft colloidal particles through porous media; this includes the transport and separation of cells, viruses or drugs through tissues, membranes and microfluidic devices. In these systems, the interactions between soft particles, background fluid and the surrounding pore space yield complex, nonlinear behaviors such as non-Darcy flows, localization and jamming. We devise a computational strategy to investigate the transport of non-wetting and deformable water droplets in a microfluidic device made of a random distribution of cylindrical obstacles. We first derive scaling laws for the entry of the droplet in a single pore and discuss the role of surface tension, contact angle and size in this process. This information is then used to study the transport of multiple droplets in an obstacle network. We find that when the droplet size is close to the pore size, fluid flow and droplet trafficking strongly interact, leading to local redistributions in pressure fields, intermittent clogging and jamming. Importantly, it is found that the overall droplet and fluid transport display three different scaling regimes depending on the forcing pressure, and that these regimes can be related to droplet properties.

Finite-Element Analysis of a Mach-8 Flight Test Article Using Nonlinear Contact Elements

NASA Technical Reports Server (NTRS)

Richards, W. Lance

1997-01-01

A flight test article, called a glove, is required for a Mach-8 boundary-layer experiment to be conducted on a flight mission of the air-launched Pegasus(reg) space booster. The glove is required to provide a smooth, three-dimensional, structurally stable, aerodynamic surface and includes instrumentation to determine when and where boundary-layer transition occurs during the hypersonic flight trajectory. A restraint mechanism has been invented to attach the glove to the wing of the space booster. The restraint mechanism securely attaches the glove to the wing in directions normal to the wing/glove interface surface, but allows the glove to thermally expand and contract to alleviate stresses in directions parallel to the interface surface. A finite-element analysis has been performed using nonlinear contact elements to model the complex behavior of the sliding restraint mechanism. This paper provides an overview of the glove design and presents details of the analysis that were essential to demonstrate the flight worthiness of the wing-glove test article. Results show that all glove components are well within the allowable stress and deformation requirements to satisfy the objectives of the flight research experiment.

Experimental Study of the Bending Properties and Deformation Analysis of Web-Reinforced Composite Sandwich Floor Slabs with Four Simply Supported Edges.

PubMed

Qi, Yujun; Fang, Hai; Liu, Weiqing

2016-01-01

Web-reinforced composite sandwich panels exhibit good mechanical properties in one-way bending, but few studies have investigated their flexural behavior and deformation calculation methods under conditions of four simply supported edges. This paper studies the bending performance of and deformation calculation methods for two-way web-reinforced composite sandwich panels with different web spacing and heights. Polyurethane foam, two-way orthogonal glass-fiber woven cloth and unsaturated resin were used as raw materials in this study. Vacuum infusion molding was used to prepare an ordinary composite sandwich panel and 5 web-reinforced composite sandwich panels with different spacing and web heights. The panels were subjected to two-way panel bending tests with simple support for all four edges. The mechanical properties of these sandwich panels during the elastic stage were determined by applying uniformly distributed loads. The non-linear mechanical characteristics and failure modes were obtained under centrally concentrated loading. Finally, simulations of the sandwich panels, which used the mechanical model established herein, were used to deduce the formulae for the deflection deformation for this type of sandwich panel. The experimental results show that webs can significantly improve the limit bearing capacity and flexural rigidity of sandwich panels, with smaller web spacing producing a stronger effect. When the web spacing is 75 mm, the limit bearing capacity is 4.63 times that of an ordinary sandwich panel. The deduced deflection calculation formulae provide values that agree well with the measurements (maximum error <15%). The results that are obtained herein can provide a foundation for the structural design of this type of panel.

Experimental Study of the Bending Properties and Deformation Analysis of Web-Reinforced Composite Sandwich Floor Slabs with Four Simply Supported Edges

PubMed Central

Qi, Yujun; Fang, Hai; Liu, Weiqing

2016-01-01

Web-reinforced composite sandwich panels exhibit good mechanical properties in one-way bending, but few studies have investigated their flexural behavior and deformation calculation methods under conditions of four simply supported edges. This paper studies the bending performance of and deformation calculation methods for two-way web-reinforced composite sandwich panels with different web spacing and heights. Polyurethane foam, two-way orthogonal glass-fiber woven cloth and unsaturated resin were used as raw materials in this study. Vacuum infusion molding was used to prepare an ordinary composite sandwich panel and 5 web-reinforced composite sandwich panels with different spacing and web heights. The panels were subjected to two-way panel bending tests with simple support for all four edges. The mechanical properties of these sandwich panels during the elastic stage were determined by applying uniformly distributed loads. The non-linear mechanical characteristics and failure modes were obtained under centrally concentrated loading. Finally, simulations of the sandwich panels, which used the mechanical model established herein, were used to deduce the formulae for the deflection deformation for this type of sandwich panel. The experimental results show that webs can significantly improve the limit bearing capacity and flexural rigidity of sandwich panels, with smaller web spacing producing a stronger effect. When the web spacing is 75 mm, the limit bearing capacity is 4.63 times that of an ordinary sandwich panel. The deduced deflection calculation formulae provide values that agree well with the measurements (maximum error <15%). The results that are obtained herein can provide a foundation for the structural design of this type of panel. PMID:26871435

Intraplate deformation due to continental collisions: A numerical study of deformation in a thin viscous sheet

NASA Technical Reports Server (NTRS)

Cohen, S. C.; Morgan, R. C.

1985-01-01

A model of crustal deformation from continental collision that involves the penetration of a rigid punch into a deformable sheet is investigated. A linear viscous flow law is used to compute the magnitude and rate of change of crustal thickness, the velocity of mass points, strain rates and their principal axes, modes of deformation, areal changes, and stress. In general, a free lateral boundary reduces the magnitude of changes in crustal thickening by allowing material to more readily escape the advancing punch. The shearing that occurs diagonally in front of the punch terminates in compression or extension depending on whether the lateral boundary is fixed or free. When the ratio of the diameter of the punch to that of the sheet exceeds one-third, the deformation is insenstive to the choice of lateral boundary conditions. When the punch is rigid with sharply defined edges, deformation is concentrated near the punch corners. With non-rigid punches, shearing results in deformation being concentrated near the center of the punch. Variations with respect to linearity and nonlinearity of flow are discussed.

The Time-Dependency of Deformation in Porous Carbonate Rocks

NASA Astrophysics Data System (ADS)

Kibikas, W. M.; Lisabeth, H. P.; Zhu, W.

2016-12-01

Porous carbonate rocks are natural reservoirs for freshwater and hydrocarbons. More recently, due to their potential for geothermal energy generation as well as carbon sequestration, there are renewed interests in better understanding of the deformation behavior of carbonate rocks. We conducted a series of deformation experiments to investigate the effects of strain rate and pore fluid chemistry on rock strength and transport properties of porous limestones. Indiana limestone samples with initial porosity of 16% are deformed at 25 °C under effective pressures of 10, 30, and 50 MPa. Under nominally dry conditions, the limestone samples are deformed under 3 different strain rates, 1.5 x 10-4 s-1, 1.5 x 10-5 s-1 and 1.5 x 10-6 s-1 respectively. The experimental results indicate that the mechanical behavior is both rate- and pressure-dependent. At low confining pressures, post-yielding deformation changes from predominantly strain softening to strain hardening as strain rate decreases. At high confining pressures, while all samples exhibit shear-enhanced compaction, decreasing strain rate leads to an increase in compaction. Slower strain rates enhance compaction at all confining pressure conditions. The rate-dependence of deformation behaviors of porous carbonate rocks at dry conditions indicates there is a strong visco-elastic coupling for the degradation of elastic modulus with increasing plastic deformation. In fluid saturated samples, inelastic strain of limestone is partitioned among low temperature plasticity, cataclasis and solution transport. Comparison of inelastic behaviors of samples deformed with distilled water and CO2-saturated aqueous solution as pore fluids provide experimental constraints on the relative activities of the various mechanisms. Detailed microstructural analysis is conducted to take into account the links between stress, microstructure and the inelastic behavior and failure mechanisms.

Effect of surface oxidation on thermomechanical behavior of NiTi shape memory alloy wire

NASA Astrophysics Data System (ADS)

Ng, Ching Wei; Mahmud, Abdus Samad

2017-12-01

Nickel titanium (NiTi) alloy is a unique alloy that exhibits special behavior that recovers fully its shape after being deformed to beyond elastic region. However, this alloy is sensitive to any changes of its composition and introduction of inclusion in its matrix. Heat treatment of NiTi shape memory alloy to above 600 °C leads to the formation of the titanium oxide (TiO2) layer. Titanium oxide is a ceramic material that does not exhibit shape memory behaviors and possess different mechanical properties than that of NiTi alloy, thus disturbs the shape memory behavior of the alloy. In this work, the effect of formation of TiO2 surface oxide layer towards the thermal phase transformation and stress-induced deformation behaviors of the NiTi alloy were studied. The NiTi wire with composition of Ti-50.6 at% Ni was subjected to thermal oxidation at 600 °C to 900 °C for 30 and 60 minutes. The formation of the surface oxide layers was characterized by using the Scanning Electron Microscope (SEM). The effect of surface oxide layers with different thickness towards the thermal phase transformation behavior was studied by using the Differential Scanning Calorimeter (DSC). The effect of surface oxidation towards the stress-induced deformation behavior was studied through the tensile deformation test. The stress-induced deformation behavior and the shape memory recovery of the NiTi wire under tensile deformation were found to be affected marginally by the formation of thick TiO2 layer.

Multi-scale sensitivity analysis of pile installation using DEM

NASA Astrophysics Data System (ADS)

Esposito, Ricardo Gurevitz; Velloso, Raquel Quadros; , Eurípedes do Amaral Vargas, Jr.; Danziger, Bernadete Ragoni

2017-12-01

The disturbances experienced by the soil due to the pile installation and dynamic soil-structure interaction still present major challenges to foundation engineers. These phenomena exhibit complex behaviors, difficult to measure in physical tests and to reproduce in numerical models. Due to the simplified approach used by the discrete element method (DEM) to simulate large deformations and nonlinear stress-dilatancy behavior of granular soils, the DEM consists of an excellent tool to investigate these processes. This study presents a sensitivity analysis of the effects of introducing a single pile using the PFC2D software developed by Itasca Co. The different scales investigated in these simulations include point and shaft resistance, alterations in porosity and stress fields and particles displacement. Several simulations were conducted in order to investigate the effects of different numerical approaches showing indications that the method of installation and particle rotation could influence greatly in the conditions around the numerical pile. Minor effects were also noted due to change in penetration velocity and pile-soil friction. The difference in behavior of a moving and a stationary pile shows good qualitative agreement with previous experimental results indicating the necessity of realizing a force equilibrium process prior to any load-test to be simulated.

Multi-scale sensitivity analysis of pile installation using DEM

NASA Astrophysics Data System (ADS)

Esposito, Ricardo Gurevitz; Velloso, Raquel Quadros; , Eurípedes do Amaral Vargas, Jr.; Danziger, Bernadete Ragoni

2018-07-01

The disturbances experienced by the soil due to the pile installation and dynamic soil-structure interaction still present major challenges to foundation engineers. These phenomena exhibit complex behaviors, difficult to measure in physical tests and to reproduce in numerical models. Due to the simplified approach used by the discrete element method (DEM) to simulate large deformations and nonlinear stress-dilatancy behavior of granular soils, the DEM consists of an excellent tool to investigate these processes. This study presents a sensitivity analysis of the effects of introducing a single pile using the PFC2D software developed by Itasca Co. The different scales investigated in these simulations include point and shaft resistance, alterations in porosity and stress fields and particles displacement. Several simulations were conducted in order to investigate the effects of different numerical approaches showing indications that the method of installation and particle rotation could influence greatly in the conditions around the numerical pile. Minor effects were also noted due to change in penetration velocity and pile-soil friction. The difference in behavior of a moving and a stationary pile shows good qualitative agreement with previous experimental results indicating the necessity of realizing a force equilibrium process prior to any load-test to be simulated.

Continuous Dynamic Simulation of Nonlinear Aerodynamics/Nonlinear Structure Interaction (NANSI) for Morphing Vehicles

DTIC Science & Technology

2010-03-31

presented in the AFRL organized Aeroelastic Workshop in Sedona October 2008, and at the AVT-168 Symposium on Morphing Vehicles, Lisbon, Portugal April 2009...surface geometry. - Conventional deforming grid methods will fail at a point when the geometry change becomes large, no matter how good the method...Numb’ Martian Entry* Knudson number: Kn _ M.a GasKinetic parameter ASU . flttA TKHNOLOGY Overview • Ballute aeroelastic problem requires

Characterization of Metal Matrix Composites

NASA Technical Reports Server (NTRS)

Daniel, I. M.; Chun, H. J.; Karalekas, D.

1994-01-01

Experimental methods were developed, adapted, and applied to the characterization of a metal matrix composite system, namely, silicon carbide/aluminim (SCS-2/6061 Al), and its constituents. The silicon carbide fiber was characterized by determining its modulus, strength, and coefficient of thermal expansion. The aluminum matrix was characterized thermomechanically up to 399 C (750 F) at two strain rates. The unidirectional SiC/Al composite was characterized mechanically under longitudinal, transverse, and in-plane shear loading up to 399 C (750 F). Isothermal and non-isothermal creep behavior was also measured. The applicability of a proposed set of multifactor thermoviscoplastic nonlinear constitutive relations and a computer code was investigated. Agreement between predictions and experimental results was shown in a few cases. The elastoplastic thermomechanical behavior of the composite was also described by a number of new analytical models developed or adapted for the material system studied. These models include the rule of mixtures, composite cylinder model with various thermoelastoplastic analyses and a model based on average field theory. In most cases satisfactory agreement was demonstrated between analytical predictions and experimental results for the cases of stress-strain behavior and thermal deformation behavior at different temperatures. In addition, some models yielded detailed three-dimensional stress distributions in the constituents within the composite.

Fatigue Assessment of Nickel-Titanium Peripheral Stents: Comparison of Multi-Axial Fatigue Models

NASA Astrophysics Data System (ADS)

Allegretti, Dario; Berti, Francesca; Migliavacca, Francesco; Pennati, Giancarlo; Petrini, Lorenza

2018-03-01

Peripheral Nickel-Titanium (NiTi) stents exploit super-elasticity to treat femoropopliteal artery atherosclerosis. The stent is subject to cyclic loads, which may lead to fatigue fracture and treatment failure. The complexity of the loading conditions and device geometry, coupled with the nonlinear material behavior, may induce multi-axial and non-proportional deformation. Finite element analysis can assess the fatigue risk, by comparing the device state of stress with the material fatigue limit. The most suitable fatigue model is not fully understood for NiTi devices, due to its complex thermo-mechanical behavior. This paper assesses the fatigue behavior of NiTi stents through computational models and experimental validation. Four different strain-based models are considered: the von Mises criterion and three critical plane models (Fatemi-Socie, Brown-Miller, and Smith-Watson-Topper models). Two stents, made of the same material with different cell geometries are manufactured, and their fatigue behavior is experimentally characterized. The comparison between experimental and numerical results highlights an overestimation of the failure risk by the von Mises criterion. On the contrary, the selected critical plane models, even if based on different damage mechanisms, give a better fatigue life estimation. Further investigations on crack propagation mechanisms of NiTi stents are required to properly select the most reliable fatigue model.

Role of Hydrogen Bonding on Nonlinear Mechano-Optical Behavior of L-Phenylalanine-based Poly(ester urea)s.

NASA Astrophysics Data System (ADS)

Chen, Keke; Yu, Jiayi; Guzman, Gustavo; Es-Haghi, S. Shams; Becker, Matthew L.; Cakmak, Miko

The uniaxial mechano-optical behavior of a series of amorphous L-phenylalanine-based poly(ester urea) (PEU) films was studied in the rubbery state using a custom real-time measurement system. When the materials were subjected to deformation at temperatures near the glass transition temperature (Tg) , the photoelastic behavior was manifested by a small increase in birefringence with a significant increase in true stress. At temperatures above Tg, PEUs with a shorter diol chain length exhibited a liquid-liquid (Tll) transition at about 1.06 Tg (K), above which the material transforms from a heterogeneous ``liquid of fixed-structure'' to a ``true liquid'' state. The initial photoelastic behavior disappears with increasing temperature, as the initial slope of the stress optical curves becomes temperature independent. Fourier transform infrared spectra of PEUs revealed that the average strength of hydrogen bonding diminishes with increasing temperature. For PEUs with the longest diol chain length, the area associated with N-H stretching region exhibits a linear temperature dependence. The presence of hydrogen bonding enhances the ``stiff'' segmental correlations between adjacent chains in the PEU structure. As a result, the photoelastic constant decreases with increasing hydrogen bonding strength. This work was supported by the Ohio Department of Development's Innovation Platform Program and The National Science Foundation.

Fatigue Assessment of Nickel-Titanium Peripheral Stents: Comparison of Multi-Axial Fatigue Models

NASA Astrophysics Data System (ADS)

Allegretti, Dario; Berti, Francesca; Migliavacca, Francesco; Pennati, Giancarlo; Petrini, Lorenza

2018-02-01

Peripheral Nickel-Titanium (NiTi) stents exploit super-elasticity to treat femoropopliteal artery atherosclerosis. The stent is subject to cyclic loads, which may lead to fatigue fracture and treatment failure. The complexity of the loading conditions and device geometry, coupled with the nonlinear material behavior, may induce multi-axial and non-proportional deformation. Finite element analysis can assess the fatigue risk, by comparing the device state of stress with the material fatigue limit. The most suitable fatigue model is not fully understood for NiTi devices, due to its complex thermo-mechanical behavior. This paper assesses the fatigue behavior of NiTi stents through computational models and experimental validation. Four different strain-based models are considered: the von Mises criterion and three critical plane models (Fatemi-Socie, Brown-Miller, and Smith-Watson-Topper models). Two stents, made of the same material with different cell geometries are manufactured, and their fatigue behavior is experimentally characterized. The comparison between experimental and numerical results highlights an overestimation of the failure risk by the von Mises criterion. On the contrary, the selected critical plane models, even if based on different damage mechanisms, give a better fatigue life estimation. Further investigations on crack propagation mechanisms of NiTi stents are required to properly select the most reliable fatigue model.

Two Back Stress Hardening Models in Rate Independent Rigid Plastic Deformation

NASA Astrophysics Data System (ADS)

Yun, Su-Jin

In the present work, the constitutive relations based on the combination of two back stresses are developed using the Armstrong-Frederick, Phillips and Ziegler’s type hardening rules. Various evolutions of the kinematic hardening parameter can be obtained by means of a simple combination of back stress rate using the rule of mixtures. Thus, a wide range of plastic deformation behavior can be depicted depending on the dominant back stress evolution. The ultimate back stress is also determined for the present combined kinematic hardening models. Since a kinematic hardening rule is assumed in the finite deformation regime, the stress rate is co-rotated with respect to the spin of substructure obtained by incorporating the plastic spin concept. A comparison of the various co-rotational rates is also included. Assuming rigid plasticity, the continuum body consists of the elastic deformation zone and the plastic deformation zone to form a hybrid finite element formulation. Then, the plastic deformation behavior is investigated under various loading conditions with an assumption of the J2 deformation theory. The plastic deformation localization turns out to be strongly dependent on the description of back stress evolution and its associated hardening parameters. The analysis for the shear deformation with fixed boundaries is carried out to examine the deformation localization behavior and the evolution of state variables.

Phase correction and error estimation in InSAR time series analysis

NASA Astrophysics Data System (ADS)

Zhang, Y.; Fattahi, H.; Amelung, F.

2017-12-01

During the last decade several InSAR time series approaches have been developed in response to the non-idea acquisition strategy of SAR satellites, such as large spatial and temporal baseline with non-regular acquisitions. The small baseline tubes and regular acquisitions of new SAR satellites such as Sentinel-1 allows us to form fully connected networks of interferograms and simplifies the time series analysis into a weighted least square inversion of an over-determined system. Such robust inversion allows us to focus more on the understanding of different components in InSAR time-series and its uncertainties. We present an open-source python-based package for InSAR time series analysis, called PySAR (https://yunjunz.github.io/PySAR/), with unique functionalities for obtaining unbiased ground displacement time-series, geometrical and atmospheric correction of InSAR data and quantifying the InSAR uncertainty. Our implemented strategy contains several features including: 1) improved spatial coverage using coherence-based network of interferograms, 2) unwrapping error correction using phase closure or bridging, 3) tropospheric delay correction using weather models and empirical approaches, 4) DEM error correction, 5) optimal selection of reference date and automatic outlier detection, 6) InSAR uncertainty due to the residual tropospheric delay, decorrelation and residual DEM error, and 7) variance-covariance matrix of final products for geodetic inversion. We demonstrate the performance using SAR datasets acquired by Cosmo-Skymed and TerraSAR-X, Sentinel-1 and ALOS/ALOS-2, with application on the highly non-linear volcanic deformation in Japan and Ecuador (figure 1). Our result shows precursory deformation before the 2015 eruptions of Cotopaxi volcano, with a maximum uplift of 3.4 cm on the western flank (fig. 1b), with a standard deviation of 0.9 cm (fig. 1a), supporting the finding by Morales-Rivera et al. (2017, GRL); and a post-eruptive subsidence on the same area, with a maximum of -3 +/- 0.9 cm (fig. 1c). Time-series displacement map (fig. 2) shows a highly non-linear deformation behavior, indicating the complicated magma propagation process during this eruption cycle.

Law of damage accumulation and fracture criteria in highly filled polymer materials

NASA Astrophysics Data System (ADS)

Bykov, D. L.; Kazakov, A. V.; Konovalov, D. N.; Mel'nikov, V. P.; Milyokhin, Yu. M.; Peleshko, V. A.; Sadovnichii, D. N.

2014-09-01

We present the results of a large series of experiments aimed at the study of laws of damage accumulation and fracture in highly filled polymer materials under loading conditions of various types: monotone, repeated, low- and high-cycle, with varying type of stress state, dynamic (in general, more than 50 programs implemented on specimens from one lot of material). The data obtained in these test allow one to make conclusions about the constitutive role of the attained maximum of strain intensity when estimating the accumulated damage in the process of uniaxial tension by various programs (in particular, an additional cyclic deformation below the preliminary attained strain maximum does not affect the limit values of strain and stress in the subsequent active extension), about the strong influence of the stress state on the deformation and fracture, about the specific features of the nonlinear behavior of the material under the shock loading conditions and its influence on the repeated deformation. All tests are described (with an accuracy acceptable in practical calculations, both with respect to stresses and strains in the process of loading and at the moment of fracture) in the framework of the same model of nonlinear viscoelasticity with the same set of constants. The constants of the proposed model are calculated according to a relatively simple algorithm by using the results of standard uniaxial tension tests with constant values of the strain rate and hydrostatic pressure (each test for 2-3 levels of these parameters chosen from the ranges proposed in applications, each loading lasts until the fracture occurs, and one of the tests contains an intermediate interval of total loading and repeated loading) and one axial shock compression test if there are dynamic problems in the applications. The model is based on the use of the criterion fracture parameter which, in the class of proportional loading processes, is the sum of partial increments of the strain intensity on active segments of the process (where the strain intensity is at its historical maximum) with the form of the stress state and the intensity of strain rates taken into account.

Nanomechanics of biocompatible hollow thin-shell polymer microspheres.

PubMed

Glynos, Emmanouil; Koutsos, Vasileios; McDicken, W Norman; Moran, Carmel M; Pye, Stephen D; Ross, James A; Sboros, Vassilis

2009-07-07

The nanomechanical properties of biocompatible thin-shell hollow polymer microspheres with approximately constant ratio of shell thickness to microsphere diameter were measured by nanocompression tests in aqueous conditions. These microspheres encapsulate an inert gas and are used as ultrasound contrast agents by releasing free microbubbles in the presence of an ultrasound field as a result of free gas leakage from the shell. The tests were performed using an atomic force microscope (AFM) employing the force-distance curve technique. An optical microscope, on which the AFM was mounted, was used to guide the positioning of tipless cantilevers on top of individual microspheres. We performed a systematic study using several cantilevers with spring constants varying from 0.08 to 2.3 N/m on a population of microspheres with diameters from about 2 to 6 microm. The use of several cantilevers with various spring constants allowed a systematic study of the mechanical properties of the microsphere thin shell at different regimes of force and deformation. Using thin-shell mechanics theory for small deformations, the Young's modulus of the thin wall material was estimated and was shown to exhibit a strong size effect: it increased as the shell became thinner. The Young's modulus of thicker microsphere shells converged to the expected value for the macroscopic bulk material. For high applied forces, the force-deformation profiles showed a reversible and/or irreversible nonlinear behavior including "steps" and "jumps" which were attributed to mechanical instabilities such as buckling events.

Compressive Deformation Behavior of Closed-Cell Micro-Pore Magnesium Composite Foam.

PubMed

Wang, Jing; Wang, Nannan; Liu, Xin; Ding, Jian; Xia, Xingchuan; Chen, Xueguang; Zhao, Weimin

2018-05-04

The closed-cell micro-pore magnesium composite foam with hollow ceramic microspheres (CMs) was fabricated by a modified melt foaming method. The effect of CMs on the compressive deformation behavior of CM-containing magnesium composite foam was investigated. Optical microscopy and scanning electron microscopy were used for observation of the microstructure. Finite element modeling of the magnesium composite foam was established to predict localized stress, fracture of CMs, and the compressive deformation behavior of the foam. The results showed that CMs and pores directly affected the compressive deformation behavior of the magnesium composite foam by sharing a part of load applied on the foam. Meanwhile, the presence of Mg₂Si phase influenced the mechanical properties of the foam by acting as the crack source during the compression process.

Modeling of deformation behavior and texture evolution in magnesium alloy using the intermediate $$\\phi$$-model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Dongsheng; Ahzi, Said; M'Guil, S. M.

2014-01-06

The viscoplastic intermediate phi-model was applied in this work to predict the deformation behavior and texture evolution in a magnesium alloy, an HCP material. We simulated the deformation behavior with different intergranular interaction strengths and compared the predicted results with available experimental results. In this approach, elasticity is neglected and the plastic deformation mechanisms are assumed as a combination of crystallographic slip and twinning systems. Tests are performed for rolling (plane strain compression) of random textured Mg polycrystal as well as for tensile and compressive tests on rolled Mg sheets. Simulated texture evolutions agree well with experimental data. Activities of twinning and slip, predicted by the intermediatemore » $$\\phi$$-model, reveal the strong anisotropic behavior during tension and compression of rolled sheets.« less

Compressive Deformation Behavior of Closed-Cell Micro-Pore Magnesium Composite Foam

PubMed Central

Wang, Jing; Wang, Nannan; Liu, Xin; Ding, Jian; Xia, Xingchuan; Chen, Xueguang; Zhao, Weimin

2018-01-01

The closed-cell micro-pore magnesium composite foam with hollow ceramic microspheres (CMs) was fabricated by a modified melt foaming method. The effect of CMs on the compressive deformation behavior of CM-containing magnesium composite foam was investigated. Optical microscopy and scanning electron microscopy were used for observation of the microstructure. Finite element modeling of the magnesium composite foam was established to predict localized stress, fracture of CMs, and the compressive deformation behavior of the foam. The results showed that CMs and pores directly affected the compressive deformation behavior of the magnesium composite foam by sharing a part of load applied on the foam. Meanwhile, the presence of Mg2Si phase influenced the mechanical properties of the foam by acting as the crack source during the compression process. PMID:29734700

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

NASA Astrophysics Data System (ADS)

Fontanela, F.; Grolet, A.; Salles, L.; Chabchoub, A.; Hoffmann, N.

2018-01-01

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

Nonlinear Acoustic Propagation into the Seafloor

NASA Astrophysics Data System (ADS)

McDonald, B. Edward

2006-05-01

Explosions near the seafloor result in shock waves entering a much more complicated medium than water or air. Nonlinearities may be increased by two processes inherent to granular media: (1) a poroelastic nonlinearity comparable to the addition of bubbles to water, and (2) the Hertz force resulting from elastic deformation of grains, proportional to the Youngs modulus of the grains times the strain rate to the power 3/2. These two types of nonlinearity for shock propagation into the seafloor are investigated using a variant of the NPE model. The traditional Taylor series expansion of the equation of state (pressure as a function of density) is not appropriate to the Hertz force in the limit of small strain. We present a simple nonlinear wave equation model for compressional waves in marine sediments that retains the Hertz force explicitly with overdensity to the power 3/2. Numerical results for shock propagation are compared with similarity solutions for quadratic nonlinearity and for the fractional nonlinearity of the Hertz force.

Emergent electromechanical coupling of electrets and some exact relations — The effective properties of soft materials with embedded external charges and dipoles

NASA Astrophysics Data System (ADS)

Liu, Liping; Sharma, Pradeep

2018-03-01

Soft robotics, energy harvesting, large-deformation sensing and actuation, are just some of the applications that can be enabled by soft dielectrics that demonstrate substantive electromechanical coupling. Most soft dielectrics including elastomers, however, are not piezoelectric and rely on the universally present electrostriction and the Maxwell stress effect to enable the aforementioned applications. Electrostriction is a one-way electromechanical coupling and the induced elastic strain scales as (∝E2) upon the application of an electric field, E. The quadratic dependence of electrostriction on the electric field and the one-way coupling imply that, (i) A rather high voltage is required to induce appreciable strain, (ii) reversal of an applied bias will not reverse the sign of the deformation, and (iii) since it is a one-way coupling i.e. electrical stimuli may cause mechanical deformation but electricity cannot be generated by mechanical deformation, prospects for energy harvesting are rather difficult. An interesting approach for realizing an apparent piezoelectric-like behavior is to dope soft dielectrics with immobile charges and dipoles. Such materials, called electrets, are rather unique composites where a secondary material (in principle) is not necessary. Both experiments and supporting theoretical work have shown that soft electrets can exhibit a very large electromechanical coupling including a piezoelectric-like response. In this work, we present a homogenization theory for electret materials and provide, in addition to several general results, variational bounds and closed-form expressions for specific microstructures such as laminates and ellipsoidal inclusions. While we consider the nonlinear coupled problem, to make analytical progress, we work within the small-deformation setting. The specific conditions necessary to obtain a piezoelectric-like response and enhanced electrostriction are highlighted. There are very few universal, microstructure-independent exact results in the theory of composites. We succeed in establishing several such relations in the context of electrets.

Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion

NASA Astrophysics Data System (ADS)

Sikora, Roman; Markiewicz, Przemysław; Pabjańczyk, Wiesława

2018-04-01

The power systems usually include a number of nonlinear receivers. Nonlinear receivers are the source of disturbances generated to the power system in the form of higher harmonics. The level of these disturbances describes the total harmonic distortion coefficient THD. Its value depends on many factors. One of them are the deformation and change in RMS value of supply voltage. A modern LED luminaire is a nonlinear receiver as well. The paper presents the results of the analysis of the influence of change in RMS value of supply voltage and the level of dimming of the tested luminaire on the value of the current THD. The analysis was made using a mathematical model based on multivariable polynomial fitting.

Nonlinear flap-lag axial equations of a rotating beam

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.; Kvaternik, R. G.

1977-01-01

It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.

Auxetics in smart systems and structures 2013

NASA Astrophysics Data System (ADS)

Scarpa, Fabrizio; Ruzzene, Massimo; Alderson, Andrew; Wojciechowski, Krzysztof W.

2013-08-01

Auxetics comes from the Greek (auxetikos), meaning 'that which tends to expand'. The term indicates specifically materials and structures with negative Poisson's ratio (NPR). Although the Poisson's ratio is a mechanical property, auxetic solids have shown evidence of multifunctional characteristics, ranging from increased stiffness and indentation resistance, to energy absorption under static and dynamic loading, soundproofing qualities and dielectric tangent loss. NPR solids and structures have also been used in the past as material platforms to build smart structural systems. Auxetics in general can be considered also a part of the 'negative materials' field, which includes solids and structures exhibiting negative thermal expansion, negative stiffness and compressibility. All these unusual deformation characteristics have the potential to provide a significant contribution to the area of smart materials systems and structures. In this focus issue, we are pleased to present some examples of novel multifunctional behaviors provided by auxetic, negative stiffness and negative compressibility in smart systems and structures. Particular emphasis has been placed upon the multidisciplinary and systems approach provided by auxetics and negative materials, also with examples applied to energy absorption, vibration damping, structural health monitoring and active deployment aspects. Three papers in this focus issue provide significant new clarifications on the role of auxeticity in the mechanical behavior of shear deformation in plates (Lim), stress wave characteristics (Lim again), and thermoelastic damping (Maruszewski et al ). Kochmann and Venturini describe the performance of auxetic composites in finite strain elasticity. New types of microstructures for auxetic systems are depicted for the first time in three works by Ge et al , Zhang et al , and Kim and co-workers. Tubular auxetic structures and their mechanical performance are also analyzed by Karnessis and Burriesci. Foams with negative Poisson's ratio constitute one of the main examples of auxetic materials available. The focus issue presents two papers on this topic, one on a novel microstructure numerical modeling technique (Pozniak et al ), the other on experimental and model identification results of linear and nonlinear vibration behavior (Bianchi and Scarpa). Nonlinearity (now in wave propagation for SHM applications) is also investigated by Klepka and co-workers, this time in auxetic chiral sandwich structures. Vibration damping and nonlinear behavior is also a key feature of the auxetic structural damper with metal rubber particles proposed by Ma et al . Papers on negative material properties are introduced by the negative stiffness and high-frequency damper concept proposed by Kalathur and Lakes. A cellular structure exhibiting a zero Poisson's ratio, together with zero and negative stiffness, is presented in the work of Virk and co-workers. Negative compressibility is examined by Grima et al in truss-type structures with constrained angle stretching. Finally, Grima and co-workers propose a concept of tunable auxetic metamaterial with magnetic inclusions for multifunctional applications. Acknowledgments We would like to thank all the authors for their high quality contributions. Special thanks go also to the Smart Materials and Structures Editorial Board and the IOP Publishing team, with particular mention to Natasha Leeper and Bethan Davies for their continued support in arranging this focus issue in Smart Materials and Structures .

Nonlinear viscoelastic characterization of polymer materials using a dynamic-mechanical methodology

NASA Technical Reports Server (NTRS)

Strganac, Thomas W.; Payne, Debbie Flowers; Biskup, Bruce A.; Letton, Alan

1995-01-01

Polymer materials retrieved from LDEF exhibit nonlinear constitutive behavior; thus the authors present a method to characterize nonlinear viscoelastic behavior using measurements from dynamic (oscillatory) mechanical tests. Frequency-derived measurements are transformed into time-domain properties providing the capability to predict long term material performance without a lengthy experimentation program. Results are presented for thin-film high-performance polymer materials used in the fabrication of high-altitude scientific balloons. Predictions based upon a linear test and analysis approach are shown to deteriorate for moderate to high stress levels expected for extended applications. Tests verify that nonlinear viscoelastic response is induced by large stresses. Hence, an approach is developed in which the stress-dependent behavior is examined in a manner analogous to modeling temperature-dependent behavior with time-temperature correspondence and superposition principles. The development leads to time-stress correspondence and superposition of measurements obtained through dynamic mechanical tests. Predictions of material behavior using measurements based upon linear and nonlinear approaches are compared with experimental results obtained from traditional creep tests. Excellent agreement is shown for the nonlinear model.

Large-Deformation Displacement Transfer Functions for Shape Predictions of Highly Flexible Slender Aerospace Structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2013-01-01

Large deformation displacement transfer functions were formulated for deformed shape predictions of highly flexible slender structures like aircraft wings. In the formulation, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (Eulerian), physical (Lagrangian), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.

Infiltration of MHD liquid into a deformable porous material

NASA Astrophysics Data System (ADS)

Naseem, Anum; Mahmood, Asif; Siddique, J. I.; Zhao, Lifeng

2018-03-01

We analyze the capillary rise dynamics for magnetohydrodynamics (MHD) fluid flow through deformable porous material in the presence of gravity effects. The modeling is performed using mixture theory approach and mathematical manipulation yields a nonlinear free boundary problem. Due to the capillary rise action, the pressure gradient in the liquid generates a stress gradient that results in the deformation of porous substrate. The capillary rise process for MHD fluid slows down as compared to Newtonian fluid case. Numerical solutions are obtained using a method of lines approach. The graphical results are presented for important physical parameters, and comparison is presented with Newtonian fluid case.

Incremental analysis of large elastic deformation of a rotating cylinder

NASA Technical Reports Server (NTRS)

Buchanan, G. R.

1976-01-01

The effect of finite deformation upon a rotating, orthotropic cylinder was investigated using a general incremental theory. The incremental equations of motion are developed using the variational principle. The governing equations are derived using the principle of virtual work for a body with initial stress. The governing equations are reduced to those for the title problem and a numerical solution is obtained using finite difference approximations. Since the problem is defined in terms of one independent space coordinate, the finite difference grid can be modified as the incremental deformation occurs without serious numerical difficulties. The nonlinear problem is solved incrementally by totaling a series of linear solutions.

Bulk rheology and simulated episodic tremor and slip within a numerically-modeled block-dominated subduction melange

NASA Astrophysics Data System (ADS)

Webber, S.; Ellis, S. M.; Fagereng, A.

2015-12-01

We investigate the influence of melange rheology in a subduction thrust interface on stress and slip cycling constrained by observations from an exhumed subduction complex at Chrystalls Beach, New Zealand. A two-phase mélange dominated by large, competent brittle-viscous blocks surrounded by a weak non-linear viscous matrix is numerically modeled, and the evolution of bulk stress are analysed as the domain deforms. The models produce stress cycling behaviour under constant shear strain rate boundary conditions for a wide range of physical conditions that roughly corresponds to depths and strain rates calculated for instrumentally observed episodic tremor and slip (ETS) in presently-deforming subduction thrust interfaces. Stress cycling is accompanied by mixed brittle plastic-viscous deformation, and occurs as a consequence of geometric reorganisation and the progressive development and breakdown of stress bridges as blocks mutually obstruct one another. We argue that periods of low differential stress correspond to periods of rapid mixed-mode deformation and ETS. Stress cycling episodicities are a function of shear strain rate and pressure/temperature conditions at depth. The time period of stress cycling is principally controlled by the geometry (block distribution and density through time) and stress cycling amplitudes are controlled by effective stress. The duration of stress cycling events in the models (months-years) and rapid strain rates are comparable to instrumentally observed ETS. Shear strain rates are 1 - 2 orders of magnitude slower between stress cycling events, suggesting episodic return times within a single model domain are long duration (> centennial timescales), assuming constant flow stress. Finally, we derive a bulk viscous flow law for block dominated subduction mélanges for conditions 300 - 500°C and elevated pore fluid pressures. Bulk flow laws calculated for block-dominated subduction mélanges are non-linear, owing to a combination of non-linear matrix viscosity and development of tensile fractures at rapid shear strain rates. Model behaviour, including the generation of mixed-mode deformation, is highly comparable to the exhumed block-dominated melange found within the Chrystalls Beach Complex.

Analytical modeling of structure-soil systems for lunar bases

NASA Technical Reports Server (NTRS)

Macari-Pasqualino, Jose Emir

1989-01-01

The study of the behavior of granular materials in a reduced gravity environment and under low effective stresses became a subject of great interest in the mid 1960's when NASA's Surveyor missions to the Moon began the first extraterrestrial investigation and it was found that Lunar soils exhibited properties quite unlike those on Earth. This subject gained interest during the years of the Apollo missions and more recently due to NASA's plans for future exploration and colonization of Moon and Mars. It has since been clear that a good understanding of the mechanical properties of granular materials under reduced gravity and at low effective stress levels is of paramount importance for the design and construction of surface and buried structures on these bodies. In order to achieve such an understanding it is desirable to develop a set of constitutive equations that describes the response of such materials as they are subjected to tractions and displacements. This presentation examines issues associated with conducting experiments on highly nonlinear granular materials under high and low effective stresses. The friction and dilatancy properties which affect the behavior of granular soils with low cohesion values are assessed. In order to simulate the highly nonlinear strength and stress-strain behavior of soils at low as well as high effective stresses, a versatile isotropic, pressure sensitive, third stress invariant dependent, cone-cap elasto-plastic constitutive model was proposed. The integration of the constitutive relations is performed via a fully implicit Backward Euler technique known as the Closest Point Projection Method. The model was implemented into a finite element code in order to study nonlinear boundary value problems associated with homogeneous as well as nonhomogeneous deformations at low as well as high effective stresses. The effect of gravity (self-weight) on the stress-strain-strength response of these materials is evaluated. The calibration of the model is performed via three techniques: (1) physical identification, (2) optimized calibration at the constitutive level, and (3) optimized calibration at the finite element level (Inverse Identification). Activities are summarized in graphic and outline form.

Deformable Bullnose Energy Absorbing System (BEAS). Report 2: Head-On Impact with a Deformable BEAS and Introducing a Collapsible Arch

DTIC Science & Technology

2011-07-01

gate operations at Belleville Locks and Dam. ........................... 105 Figure 5.20 The non-linear costs for full closure of the locks and dam...Super Cone Fender Front Arch Results ................................................. 96 Table 5.3 Costs Over Time for Full Closure at Particular Corps...Corps Navigation Economics PDT tabulation of costs over time for full closure at the Corps lock and dam structures. Bob Willis also supplied the

Large-deformation electrohydrodynamics of an elastic capsule in a DC electric field

NASA Astrophysics Data System (ADS)

Das, Sudip; Thaokar, Rochish M.

2018-04-01

The dynamics of a spherical elastic capsule, containing a Newtonian fluid bounded by an elastic membrane and immersed in another Newtonian fluid, in a uniform DC electric field is investigated. Discontinuity of electrical properties such as conductivities of the internal and external fluid media as well as capacitance and conductance of the membrane lead to a net interfacial Maxwell stress which can cause the deformation of such an elastic capsule. We investigate this problem considering well established membrane laws for a thin elastic membrane, with fully resolved hydrodynamics in the Stokes flow limit and describe the electrostatics using the capacitor model. In the limit of small deformation, the analytical theory predicts the dynamics fairly satisfactorily. Large deformations at high capillary number though necessitate a numerical approach (Boundary element method in the present case) to solve this highly non-linear problem. Akin to vesicles, at intermediate times, highly nonlinear biconcave shapes along with squaring and hexagon like shapes are observed when the outer medium is more conducting. The study identifies the essentiality of parameters such as high membrane capacitance, low membrane conductance, low hydrodynamic time scales and high capillary number for observation of these shape transitions. The transition is due to large compressive Maxwell stress at the poles at intermediate times. Thus such shape transition can be seen in spherical globules admitting electrical capacitance, possibly, irrespective of the nature of the interfacial restoring force.

Porosity and mechanical properties of zirconium ceramics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buyakova, S., E-mail: sbuyakova@ispms.tsc.ru; Kulkov, S.; Tomsk Polytechnic University

2015-11-17

Has been studied a porous ceramics obtained from ultra-fine powders. Porous ceramic ZrO{sub 2}(MgO), ZrO{sub 2}(Y{sub 2}O{sub 3}) powder was prepared by pressing and subsequent sintering of compacts homologous temperatures ranging from 0.63 to 0.56 during the isothermal holding duration of 1 to 5 hours. The porosity of ceramic samples was from 15 to 80%. The structure of the ceramic materials produced from plasma-sprayed ZrO{sub 2} powder was represented as a system of cell and rod structure elements. Cellular structure formed by stacking hollow powder particles can be easily seen at the images of fracture surfaces of obtained ceramics. Theremore » were three types of pores in ceramics: large cellular hollow spaces, small interparticle pores which are not filled with powder particles and the smallest pores in the shells of cells. The cells generally did not have regular shapes. The size of the interior of the cells many times exceeded the thickness of the walls which was a single-layer packing of ZrO{sub 2} grains. A distinctive feature of all deformation diagrams obtained in the experiment was their nonlinearity at low deformations which was described by the parabolic law. It was shown that the observed nonlinear elasticity for low deformation on deformation diagrams is due to mechanical instability of the cellular elements in the ceramic carcass.« less

Monitoring of urban subsidence with SAR interferometric point target analysis: A case study in Suzhou, China

NASA Astrophysics Data System (ADS)

Zhang, Yonghong; Zhang, Jixian; Wu, Hongan; Lu, Zhong; Guangtong, Sun

2011-10-01

Ground subsidence, mainly caused by over exploitation of groundwater and other underground resources, such as oil, gas and coal, occurs in many cities in China. The annual direct loss associated with subsidence across the country is estimated to exceed 100 million US dollar. Interferometric SAR (InSAR) is a powerful tool to map ground deformation at an unprecedented level of spatial detail. It has been widely used to investigate the deformation resulting from earthquakes, volcanoes and subsidence. Repeat-pass InSAR, however, may fail due to impacts of spatial decorrelation, temporal decorrelation and heterogeneous refractivity of atmosphere. In urban areas, a large amount of natural stable radar reflectors exists, such as buildings and engineering structures, at which radar signals can remain coherent during a long time interval. Interferometric point target analysis (IPTA) technique, also known as persistent scatterers (PS) InSAR is based on these reflectors. It overcomes the shortfalls in conventional InSAR. This paper presents a procedure for urban subsidence monitoring with IPTA. Calculation of linear deformation rate and height residual, and the non-linear deformation estimate, respectively, are discussed in detail. Especially, the former is highlighted by a novel and easily implemented 2-dimensional spatial search algorithm. Practically useful solutions that can significantly improve the robustness of IPTA, are recommended. Finally, the proposed procedure is applied to mapping the ground subsidence in Suzhou city, Jiangsu province, China. Thirty-four ERS-1/2 SAR scenes are analyzed, and the deformation information over 38,881 point targets between 1992 and 2000 are generated. The IPTA-derived deformation estimates correspond well with leveling measurements, demonstrating the potential of the proposed subsidence monitoring procedure based on IPTA technique. Two shortcomings of the IPTA-based procedure, e.g., the requirement of large number of SAR images and assumed linear plus non-linear deformation model, are discussed as the topics of further research.

Deformed twistors and higher spin conformal (super-)algebras in four dimensions

DOE PAGES

Govil, Karan; Gunaydin, Murat

2015-03-05

Massless conformal scalar field in d = 4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2, 2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The minrep and its deformations were obtained by quantization of the nonlinear realization of SU(2, 2) as a quasiconformal group in arXiv:0908.3624. We show that the generators of SU(2,2) for these unitary irreducible representations can be written as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group and apply them to define and study higher spin algebras and superalgebras in AdS 5.more » The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS 5 is simply the enveloping algebra of SU(2, 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS 5. Furthermore, the enveloping algebras of the deformations of the minrep define a one parameter family of HS algebras in AdS 5 for which certain 4d covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras SU(2, 2|N) and we find a one parameter family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a family of (supersymmetric) HS theories in AdS 5 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 4d. We also discuss the corresponding picture in HS algebras in AdS 4 where the corresponding 3d conformal group Sp(4,R) admits only two massless representations (minreps), namely the scalar and spinor singletons.« less

Influence of Deformation Mechanisms on the Mechanical Behavior of Metals and Alloys: Experiments, Constitutive Modeling, and Validation

NASA Astrophysics Data System (ADS)

Gray, G. T.; Cerreta, E.; Chen, Shuh Rong; Maudlin, P. J.

2004-06-01

Jim Williams has made seminal contributions to the field of structure / property relations and its controlling effects on the mechanical behavior of metals and alloys. This talk will discuss experimental results illustrating the role of interstitial content, grain size, texture, temperature, and strain rate on the operative deformation mechanisms, mechanical behavior, and substructure evolution in titanium, zirconium, hafnium, and rhenium. Increasing grain size is shown to significantly decrease the dynamic flow strength of Ti and Zr while increasing work-hardening rates due to an increased incidence of deformation twinning. Increasing oxygen interstitial content is shown to significantly alter both the constitutive response and α-ω shock-induced phase transition in Zr. The influence of crystallographic texture on the mechanical behavior in Ti, Zr, and Hf is discussed in terms of slip system and deformation twinning activity. An example of the utility of incorporation of operative deformation mechanisms into a polycrystalline plasticity constitutive model and validation using Taylor cylinder impact testing is presented.

Dielectric elastomer membranes undergoing inhomogeneous deformation

NASA Astrophysics Data System (ADS)

He, Tianhu; Zhao, Xuanhe; Suo, Zhigang

2009-10-01

Dielectric elastomers are capable of large deformation subject to an electric voltage and are promising for use as actuators, sensors, and generators. Because of large deformation, nonlinear equations of states, and diverse modes of failure, modeling the process of electromechanical transduction has been challenging. This paper studies a membrane of a dielectric elastomer deformed into an out-of-plane axisymmetric shape, a configuration used in a family of commercial devices known as the universal muscle actuators. The kinematics of deformation and charging, together with thermodynamics, leads to equations that govern the state of equilibrium. Numerical results indicate that the field in the membrane can be very inhomogeneous, and that the membrane is susceptible to several modes of failure, including electrical breakdown, loss of tension, and rupture by stretch. Care is needed in the design to balance the requirements of averting various modes of failure while using the material efficiently.

Nonlinear Acoustic Landmine Detection: Profiling Soil Surface Vibrations and Modeling Mesoscopic Elastic Behavior

DTIC Science & Technology

2007-05-04

TITLE AND SUBTITLE Nonlinear Acoustic Landmine Detection: Profiling Soil Surface Vibrations and Modeling Mesoscopic Elastic Behavior 6. AUTHOR(S...project report; no. 352 (2007) NONLINEAR ACOUSTIC LANDMINE DETECTION: PROFILING SOIL SURFACE VIBRATIONS AND MODELING MESOSCOPIC ELASTIC... model (Caughey 1966). Nonlinear acoustic landmine detection experiments are performed in the anechoic chamber facility using both a buried acrylic

Deformation behavior of Nb nanowires in TiNiCu shape memory alloy matrix

DOE PAGES

Jiang, Daqiang; Liu, Yinong; Yu, Cun; ...

2015-08-18

An in-situ nanowire Nb/TiNiCu composite is fabricated based on the concept of strain under-matching between a phase transforming matrix and high strength nanomaterials. The deformation behavior of the Nb nanowire was investigated by means of in-situ synchrotron X-ray diffraction when the TiNiCu matrix underwent different deformation modes. The maximum lattice strain of the Nb nanowires was about 5% when the matrix deformed via martensitic transformation or 1% when deforming plastically by dislocation slip. As a result, the Nb nanowires showed a lattice strain of 3.5% when the matrix deformed in the mixed mode of plastic deformation and martensitic transformation, whichmore » means that the occurrence of plastic deformation does not impede load transfer from the matrix to the nanowires.« less

Some Aspects of Nonlinear Dynamics and CFD

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Merriam, Marshal (Technical Monitor)

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

Needle-tissue interactive mechanism and steering control in image-guided robot-assisted minimally invasive surgery: a review.

PubMed

Li, Pan; Yang, Zhiyong; Jiang, Shan

2018-06-01

Image-guided robot-assisted minimally invasive surgery is an important medicine procedure used for biopsy or local target therapy. In order to reach the target region not accessible using traditional techniques, long and thin flexible needles are inserted into the soft tissue which has large deformation and nonlinear characteristics. However, the detection results and therapeutic effect are directly influenced by the targeting accuracy of needle steering. For this reason, the needle-tissue interactive mechanism, path planning, and steering control are investigated in this review by searching literatures in the last 10 years, which results in a comprehensive overview of the existing techniques with the main accomplishments, limitations, and recommendations. Through comprehensive analyses, surgical simulation for insertion into multi-layer inhomogeneous tissue is verified as a primary and propositional aspect to be explored, which accurately predicts the nonlinear needle deflection and tissue deformation. Investigation of the path planning of flexible needles is recommended to an anatomical or a deformable environment which has characteristics of the tissue deformation. Nonholonomic modeling combined with duty-cycled spinning for needle steering, which tracks the tip position in real time and compensates for the deviation error, is recommended as a future research focus in the steering control in anatomical and deformable environments. Graphical abstract a Insertion force when the needle is inserted into soft tissue. b Needle deflection model when the needle is inserted into soft tissue [68]. c Path planning in anatomical environments [92]. d Duty-cycled spinning incorporated in nonholonomic needle steering [64].

A viscoelastic strain energy principle expressed in fold thrust belts and other compressional regimes

NASA Astrophysics Data System (ADS)

Patton, Regan L.; Watkinson, A. John

2005-07-01

A mathematical folding theory for stratified viscoelastic media in layer parallel compression is presented. The second order fluid, in slow flow, is used to model rock rheological behavior because it is the simplest nonlinear constitutive equation exhibiting viscoelastic effects. Scaling and non-dimensionalization of the model system reveals the presence of Weissenberg number ( Wi), defined as a ratio of time scales τ*/( H*/ V*). V*/ H* is the strain rate (s -1) imposed by an assumed far field velocity V* acting on a layer of thickness H*, while τ* (s) is related to the relaxation of normal stresses. Our most significant finding is a transitional behavior as Wi→½, which is independent of the viscosity contrast. A change of variables shows that lengths associated with this transition are scaled by a parameter α=[(1-2 Wi)/(1+2 Wi)] 1/2, which is inversely proportional to local strain energy. On this basis a scaling law representing a distribution of non-dimensional wavelengths (wavelength/layer thickness) is derived. Geologically this is consistent with a transition from folding to faulting, as observed in fold-thrust belts. Folding, a distributed deformation scaling as Wi-1, is found to be energetically favored at non-dimensional wavelengths ranging from about three to seven. Furthermore, the transition from folding to faulting, a localized deformation scaling as ( αWi) -1, is predicted at a non-dimensional wavelength of about seven. These findings are consistent with measurements of thrust sheets in the Sawtooth Mountains of western Montana, USA and other fold-thrust belts. A review of the literature reveals a similar distribution of non-dimensional wavelengths spanning a wide range of observational scales in compressional deformation. Specific examples include lithospheric scale folding in the central Indian Basin and microscopic scale failure of ice columns between splay microcracks in laboratory studies.

Advances and trends in structural and solid mechanics; Proceedings of the Symposium, Washington, DC, October 4-7, 1982

NASA Technical Reports Server (NTRS)

Noor, A. K. (Editor); Housner, J. M.

1983-01-01

The mechanics of materials and material characterization are considered, taking into account micromechanics, the behavior of steel structures at elevated temperatures, and an anisotropic plasticity model for inelastic multiaxial cyclic deformation. Other topics explored are related to advances and trends in finite element technology, classical analytical techniques and their computer implementation, interactive computing and computational strategies for nonlinear problems, advances and trends in numerical analysis, database management systems and CAD/CAM, space structures and vehicle crashworthiness, beams, plates and fibrous composite structures, design-oriented analysis, artificial intelligence and optimization, contact problems, random waves, and lifetime prediction. Earthquake-resistant structures and other advanced structural applications are also discussed, giving attention to cumulative damage in steel structures subjected to earthquake ground motions, and a mixed domain analysis of nuclear containment structures using impulse functions.

Large Hysteresis effect in Synchronization of Nanocontact Vortex Oscillators by Microwave Fields

PubMed Central

Perna, S.; Lopez-Diaz, L.; d’Aquino, M.; Serpico, C.

2016-01-01

Current-induced vortex oscillations in an extended thin-film with point-contact geometry are considered. The synchronization of these oscillations with a microwave external magnetic field is investigated by a reduced order model that takes into account the dynamical effects associated with the significant deformation of the vortex structure produced by the current, which cannot be taken care of by using the standard rigid vortex theory. The complete phase diagram of the vortex oscillation dynamics is derived and it is shown that strong hysteretic behavior occurs in the synchronization with the external field. The complex nonlinear nature of the synchronization manifests itself also through the appearance of asymmetry in the locking frequency bands for moderate microwave field amplitudes. Predictions from the reduced order model are confirmed by full micromagnetic simulations. PMID:27538476