Electronic structure, elasticity, bonding features and mechanical behaviour of zinc intermetallics: A DFT study

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

Fatima, Bushra, E-mail: bushrafatima25@gmail.com; Acharya, Nikita; Sanyal, Sankar P.

2016-05-06

The structural stability, electronic structure, elastic and mechanical properties of TiZn and ZrZn intermetallics have been studied using ab-initio full potential linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation for exchange and correlation potentials. The various structural parameters, such as lattice constant (a{sub 0}), bulk modulus (B), and its pressure derivative (B’) are analysed and compared. The investigation of elastic constants affirm that both TiZn and ZrZn are elastically stable in CsCl (B{sub 2} phase) structure. The electronic structures have been analysed quantitatively from the band structure which reveals the metallic nature of these compounds. To better illustratemore » the nature of bonding and charge transfer, we have also studied the Fermi surfaces. The three well known criterion of ductility namely Pugh’s rule, Cauchy’s pressure and Frantsevich rule elucidate the ductile nature of these compounds.« less

Microstructural dependence on relevant physical-mechanical properties on SiO2-Na2O-CaO-P2O5 biological glasses.

PubMed

Rajendran, V; Begum, A Nishara; Azooz, M A; el Batal, F H

2002-11-01

Bioactive glasses of the system SiO2-Na2O-CaO-P2O5 have been prepared by the normal melting and annealing technique. The elastic moduli, attenuation, Vickers hardness, fracture toughness and fracture surface energy have been obtained using the known method at room temperature. The temperature dependence of elastic moduli and attenuation measurements have been extended over a wide range of temperature from 150 to 500 K. The SiO2 content dependence of velocities, attenuation, elastic moduli, and other parameters show an interesting observation at 45 wt% of SiO2 by exhibiting an anomalous behaviour. A linear relation is developed for Tg, which explores the influence of Na2O on SiO2-Na2O-CaO-P2O5 bioactive glasses. The measured hardness, fracture toughness and fracture surface energy show a linear relation with Young's modulus. It is also interesting to note that the observed results are functions of polymerisation and the number of non-bridging oxygens (NBO) prevailing in the network with change in SiO2 content. The temperature dependence of velocities, attenuation and elastic moduli show the existence of softening in the glass network structure as temperature increases.

Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry.

PubMed

Malm, A V; Waigh, T A

2017-04-26

The flow instabilities of solutions of high molecular weight DNA in the entangled semi-dilute concentration regime were investigated using optical coherence tomography velocimetry, a technique that provides high spatial (probe volumes of 3.4 pL) and temporal resolution (sub μs) information on the flow behaviour of complex fluids in a rheometer. The velocity profiles of the opaque DNA solutions (high and low salt) were measured as a function of the distance across the gap of a parallel plate rheometer, and their evolution over time was measured. At lower DNA concentrations and low shear rates, the velocity fluctuations were well described by Gaussian functions and the velocity gradient was uniform across the rheometer gap, which is expected for Newtonian flows. As the DNA concentration and shear rate were increased there was a stable wall slip regime followed by an evolving wall slip regime, which is finally followed by the onset of elastic turbulence. Strain localization (shear banding) is observed on the boundaries of the flows at intermediate shear rates, but decreases in the high shear elastic turbulence regime, where bulk strain localization occurs. A dynamic phase diagram for non-linear flow was created to describe the different behaviours.

A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests

NASA Astrophysics Data System (ADS)

Collins, Ian F.; Hilder, Tamsyn

2002-11-01

Modern ideas of thermomechanics are used to develop families of models describing the elastic/plastic behaviour of cohesionless soils deforming under triaxial conditions. Once the form of the free energy and dissipation potential functions have been specified, the corresponding yield loci, flow rules, isotropic and kinematic hardening rules as well as the elasticity law are deduced in a systematic manner. The families contain the classical linear frictional (Coulomb type) models and the classical critical state models as special cases. The generalized models discussed here include non-associated flow rules, shear as well as volumetric hardening, anisotropic responses and rotational yield loci. The various parameters needed to describe the models can be interpreted in terms of ratio of the plastic work, which is dissipated, to that which is stored. Non-associated behaviour is found to occur whenever this division between dissipated and stored work is not equal. Micro-level interpretations of stored plastic work are discussed. The models automatically satisfy the laws of thermodynamics, and there is no need to invoke any stability postulates. Some classical forms of the peak-strength/dilatancy relationship are established theoretically. Some representative drained and undrained paths are computed.

Damage, crack growth and fracture characteristics of nuclear grade graphite using the Double Torsion technique

NASA Astrophysics Data System (ADS)

Becker, T. H.; Marrow, T. J.; Tait, R. B.

2011-07-01

The crack initiation and propagation characteristics of two medium grained polygranular graphites, nuclear block graphite (NBG10) and Gilsocarbon (GCMB grade) graphite, have been studied using the Double Torsion (DT) technique. The DT technique allows stable crack propagation and easy crack tip observation of such brittle materials. The linear elastic fracture mechanics (LEFM) methodology of the DT technique was adapted for elastic-plastic fracture mechanics (EPFM) in conjunction with a methodology for directly calculating the J-integral from in-plane displacement fields (JMAN) to account for the non-linearity of graphite deformation. The full field surface displacement measurement techniques of electronic speckle pattern interferometry (ESPI) and digital image correlation (DIC) were used to observe and measure crack initiation and propagation. Significant micro-cracking in the fracture process zone (FPZ) was observed as well as crack bridging in the wake of the crack tip. The R-curve behaviour was measured to determine the critical J-integral for crack propagation in both materials. Micro-cracks tended to nucleate at pores, causing deflection of the crack path. Rising R-curve behaviour was observed, which is attributed to the formation of the FPZ, while crack bridging and distributed micro-cracks are responsible for the increase in fracture resistance. Each contributes around 50% of the irreversible energy dissipation in both graphites.

Numerical study of suspensions of deformable particles.

NASA Astrophysics Data System (ADS)

Brandt, Luca; Rosti, Marco Edoardo

2017-11-01

We consider a model non-Newtonian fluid consisting of a suspension of deformable particles in a Newtonian solvent. Einstein showed in his pioneering work that the relative increase in effective viscosity is a linear function of the particle volume fraction for dilute suspensions of rigid particles. Inertia has been shown to introduce deviations from the behaviour predicted by the different empirical fits, an effect that can be related to an increase of the effective volume fraction. We here focus on the effect of elasticity, i.e. visco-elastic deformable particles. To tackle the problem at hand, we perform three-dimensional Direct Numerical Simulation of a plane Couette flow with a suspension of neutrally buoyant deformable viscous hyper-elastic particles. We show that elasticity produces a shear-thinning effect in elastic suspensions (in comparison to rigid ones) and that it can be understood in terms of a reduction of the effective volume fraction of the suspension. The deformation modifies the particle motion reducing the level of mutual interaction. Normal stress differences will also be considered. European Research Council, Grant No. ERC-2013-CoG- 616186, TRITOS; SNIC (the Swedish National Infrastructure for Computing).

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.

A comparison of the two approaches of the theory of critical distances based on linear-elastic and elasto-plastic analyses

NASA Astrophysics Data System (ADS)

Terekhina, A. I.; Plekhov, O. A.; Kostina, A. A.; Susmel, L.

2017-06-01

The problem of determining the strength of engineering structures, considering the effects of the non-local fracture in the area of stress concentrators is a great scientific and industrial interest. This work is aimed on modification of the classical theory of critical distance that is known as a method of failure prediction based on linear-elastic analysis in case of elasto-plastic material behaviour to improve the accuracy of estimation of lifetime of notched components. Accounting plasticity has been implemented with the use of the Simplified Johnson-Cook model. Mechanical tests were carried out using a 300 kN electromechanical testing machine Shimadzu AG-X Plus. The cylindrical un-notched specimens and specimens with stress concentrators of titanium alloy Grade2 were tested under tensile loading with different grippers travel speed, which ensured several orders of strain rate. The results of elasto-plastic analyses of stress distributions near a wide variety of notches are presented. The results showed that the use of the modification of the TCD based on elasto-plastic analysis gives us estimates falling within an error interval of ±5-10%, that more accurate predictions than the linear elastic TCD solution. The use of an improved description of the stress-strain state at the notch tip allows introducing the critical distances as a material parameter.

Intervertebral disc response to cyclic loading--an animal model.

PubMed

Ekström, L; Kaigle, A; Hult, E; Holm, S; Rostedt, M; Hansson, T

1996-01-01

The viscoelastic response of a lumbar motion segment loaded in cyclic compression was studied in an in vivo porcine model (N = 7). Using surgical techniques, a miniaturized servohydraulic exciter was attached to the L2-L3 motion segment via pedicle fixation. A dynamic loading scheme was implemented, which consisted of one hour of sinusoidal vibration at 5 Hz, 50 N peak load, followed by one hour of restitution at zero load and one hour of sinusoidal vibration at 5 Hz, 100 N peak load. The force and displacement responses of the motion segment were sampled at 25 Hz. The experimental data were used for evaluating the parameters of two viscoelastic models: a standard linear solid model (three-parameter) and a linear Burger's fluid model (four-parameter). In this study, the creep behaviour under sinusoidal vibration at 5 Hz closely resembled the creep behaviour under static loading observed in previous studies. Expanding the three-parameter solid model into a four-parameter fluid model made it possible to separate out a progressive linear displacement term. This deformation was not fully recovered during restitution and is therefore an indication of a specific effect caused by the cyclic loading. High variability was observed in the parameters determined from the 50 N experimental data, particularly for the elastic modulus E1. However, at the 100 N load level, significant differences between the models were found. Both models accurately predicted the creep response under the first 800 s of 100 N loading, as displayed by mean absolute errors for the calculated deformation data from the experimental data of 1.26 and 0.97 percent for the solid and fluid models respectively. The linear Burger's fluid model, however, yielded superior predictions particularly for the initial elastic response.

Effects of biaxial strains on electronic and elastic properties of hexagonal XSi2 (X = Cr, Mo, W) from first-principles

NASA Astrophysics Data System (ADS)

Zhu, Haiyan; Shi, Liwei; Li, Shuaiqi; Zhang, Shaobo; Xia, Wangsuo

2018-02-01

Structural, electronic properties and elastic anisotropy of hexagonal C40 XSi2 (X = Cr, Mo, W) under equibiaxial in-plane strains are systematically studied using first-principle calculations. The energy gaps show significant changes with biaxial strains, whereas they are always indirect band-gap materials for -6% <ɛxx < 6%. All elastic constants, bulk modulus, shear modulus, Young's modulus increase (decrease) almost linearly with increasing compressive (tensile) strains. The evolutions of BH /GH ratio and Poisson's ratio indicate that these compounds have a better (worse) ductile behaviour under compressive (tensile) strains. A set of 3D plots show a larger directional variability in the Young's modulus E and shear modulus G at different strains for the three compounds, which is consist with the values of anisotropy factors. Moreover, the evolution of Debye temperature and anisotropy of sound velocities with biaxial strains are discussed.

Equilibrium stability of a cylindrical body subject to the internal structure of the material and inelastic behaviour of the completely compressed matrix

NASA Astrophysics Data System (ADS)

Gotsev, D. V.; Perunov, N. S.; Sviridova, E. N.

2018-03-01

The mathematical model describing the stress-strain state of a cylindrical body under the uniform radial compression effect is constructed. The model of the material is the porous medium model. The compressed skeleton of the porous medium possesses hardening elastic-plastic properties. Deforming of the porous medium under the specified compressive loads is divided into two stages: elastic deforming of the porous medium and further elastic-plastic deforming of the material with completely compressed matrix. The analytical relations that define the fields of stress and displacement at each stage of the deforming are obtained. The influence of the porosity and other physical, mechanical and geometric parameters of the construction on the size of the plastic zone is evaluated. The question of the ground state equilibrium instability is investigated within the framework of the three-dimensional linearized relationships of the stability theory of deformed bodies.

Fracture toughness of Kevlar 29/poly(methyl methacrylate) composite materials for surgical implantations.

PubMed

Pourdeyhimi, B; Robinson, H H; Schwartz, P; Wagner, H D

1986-01-01

A study of the fracture behaviour of Kevlar 29 reinforced dental cement is undertaken using both linear elastic and nonlinear elastic fracture mechanics techniques. Results from both approaches--of which the nonlinear elastic is believed to be more appropriate--indicate that a reinforcing effect is obtained for the fracture toughness even at very low fibre content. The flexural strength and modulus are apparently not improved, however, by the incorporation of Kevlar 29 fibres in the PMMA cement, probably because of the presence of voids, the poor fibre/matrix interfacial bonding and unsatisfying cement mixing practice. When compared to other PMMA composite cements, the present system appears to be probably more effective than carbon/PMMA, for example, in terms of fracture toughness. More experimental and analytical work is needed so as to optimize the mechanical properties with respect to structural parameters and cement preparation technique.

Polysoaps: Configurations and Elasticity

NASA Astrophysics Data System (ADS)

Halperin, A.

1997-03-01

Simple polymers are very long, flexible, linear molecules. Amphiphiles, soaps, are small molecules comprising of a part that prefers water over oil and a part that prefers oil over water. By combining the two we arrive at an interesting, little explored, class of materials: Polysoaps. These comprise of a water soluble backbone incorporating, at intervals, covalently bound amphiphilic monomers. In water, the polymerised amphiphiles aggregate into self assembled units known as micelles. This induces a dramatic modification of the spatial configurations of the polymers. What were featureless random coils now exhibit intramolecular, hierachial self organisation. Due to this self organisation it is necessary to modify the paradigms describing the large scale behaviour of these polymers: Their configurations, dimensions and elasticity. Understanding the behaviour of these polymers is of practical interest because of their wide range of industrial applications, ranging from cosmetics to paper coating. It is of fundamental interest because polysoaps are characterised by a rugged free energy landscape that is reminiscent of complex systems such as proteins and glasses. The talk concerns theoretical arguments regarding the following issues: (i) The design parameters that govern the spatial configurations of the polysoaps, (ii) The interaction between polysoaps and free amphiphiles, (iii) The effect of the intramolecular self organisation on the elasticity of the chains.

Forecasting volcanic eruptions: the control of elastic-brittle deformation

NASA Astrophysics Data System (ADS)

Kilburn, Christopher; Robertson, Robert; Wall, Richard; Steele, Alexander

2016-04-01

At volcanoes reawakening after long repose, patterns of unrest normally reflect the elastic-brittle deformation of crust above a magma reservoir. Local fault movements, detected as volcano-tectonic (VT) earthquakes, increase in number with surface deformation, at first approximately exponentially and then linearly. The trends describe how crustal behaviour evolves from quasi-elastic deformation under an increasing stress to inelastic deformation under a constant stress. They have been quantified and verified against experiments for deformation in compression [1]. We have extended the analysis to extensional deformation. The results agree well with field data for crust being stretched by a pressurizing magmatic system [2]. They also provide new criteria for enhancing the definitions of alert levels and preferred times to eruption. The VT-deformation sequence is a field proxy for changes in deformation with applied stress. The transition from quasi-elastic to inelastic behaviour is characterised in extension by the ratio of differential failure stress SF to tensile strength σT. Unrest data from at least basaltic to andesitic stratovolcanoes, as well as large calderas, yield preferred values for SF/σT ≤ 4, coinciding with the range for tensile failure expected from established theoretical constraints (from Mohr-Coulomb-Griffiths failure). We thus associate the transition with the approach to tensile rupture at the wall of a pressurized magma reservoir. In particular, values of about 2 are consistent with the rupture of a cylindrical reservoir, such as a closed conduit within a volcanic edifice, whereas values of about 3 suggest an approximately spherical reservoir, such as may exist at deeper levels. The onset of inelastic behaviour reflects the emergence of self-accelerating crack growth under a constant stress. Applied to forecasting eruptions, it provides a new and objective criterion for raising alert levels during an emergency; it yields the classic linear decrease in inverse-rate with time for VT seismicity, which can be extrapolated to an expected eruption time shortly after the inverse rate becomes zero [3]; and, for extension, it identifies preferred inverse-rate gradients of 0.001-0.01, which can be used to distinguish between physically-meaningful and spurious inverse-rate trends. [1] Kilburn CRJ (2012) J Geophys Res, doi: 10.1029/2011JB008703; [2] Robertson R, Kilburn CRJ (2016) Earth Planet Sci Lett, doi: 10.1016/j.epsl.2016.01.003; [3] Voight B (1988) Nature. 332: 125-130.

Gurtin-Murdoch surface elasticity theory revisit: An orbital-free density functional theory perspective

NASA Astrophysics Data System (ADS)

Zhu, Yichao; Wei, Yihai; Guo, Xu

2017-12-01

In the present paper, the well-established Gurtin-Murdoch theory of surface elasticity (Gurtin and Murdoch, 1975, 1978) is revisited from an orbital-free density functional theory (OFDFT) perspective by taking the boundary layer into consideration. Our analysis indicates that firstly, the quantities introduced in the Gurtin-Murdoch theory of surface elasticity can all find their explicit expressions in the derived OFDFT-based theoretical model. Secondly, the derived expression for surface energy density captures a competition between the surface normal derivatives of the electron density and the electrostatic potential, which well rationalises the onset of signed elastic constants that are observed both experimentally and computationally. Thirdly, the established model naturally yields an inversely linear relationship between the materials surface stiffness and its size, which conforms to relevant findings in literature. Since the proposed OFDFT-based model is established under arbitrarily imposed boundary condition of electron density, electrostatic potential and external load, it also has the potential of being used to investigate the electro-mechanical behaviour of nanoscale materials manifesting surface effect.

Damageable contact between an elastic body and a rigid foundation

NASA Astrophysics Data System (ADS)

Campo, M.; Fernández, J. R.; Silva, A.

2009-02-01

In this work, the contact problem between an elastic body and a rigid obstacle is studied, including the development of material damage which results from internal compression or tension. The variational problem is formulated as a first-kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field. The existence of a unique local weak solution is stated. Then, a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, three two-dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme.

Rheological and physical characteristics of crustal-scaled materials for centrifuge analogue modelling

NASA Astrophysics Data System (ADS)

Waffle, Lindsay; Godin, Laurent; Harris, Lyal B.; Kontopoulou, M.

2016-05-01

We characterize a set of analogue materials used for centrifuge analogue modelling simulating deformation at different levels in the crust simultaneously. Specifically, we improve the rheological characterization in the linear viscoelastic region of materials for the lower and middle crust, and cohesive synthetic sands without petroleum-binding agents for the upper crust. Viscoelastic materials used in centrifuge analogue modelling demonstrate complex dynamic behaviour, so viscosity alone is insufficient to determine if a material will be an effective analogue. Two series of experiments were conducted using an oscillating bi-conical plate rheometer to measure the storage and loss moduli and complex viscosities of several modelling clays and silicone putties. Tested materials exhibited viscoelastic and shear-thinning behaviour. The silicone putties and some modelling clays demonstrated viscous-dominant behaviour and reached Newtonian plateaus at strain rates < 0.5 × 10-2 s-1, while other modelling clays demonstrated elastic-dominant power-law relationships. Based on these results, the elastic-dominant modelling clay is recommended as an analogue for basement cratons. Inherently cohesive synthetic sands produce fine-detailed fault and fracture patterns, and developed thrust, strike-slip, and extensional faults in simple centrifuge test models. These synthetic sands are recommended as analogues for the brittle upper crust. These new results increase the accuracy of scaling analogue models to prototype. Additionally, with the characterization of three new materials, we propose a complete lithospheric profile of analogue materials for centrifuge modelling, allowing future studies to replicate a broader range of crustal deformation behaviours.

Revisiting the blocking force test on ferroelectric ceramics using high energy x-ray diffraction

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

Daniel, L., E-mail: laurent.daniel@u-psud.fr; GeePs; Hall, D. A.

2015-05-07

The blocking force test is a standard test to characterise the properties of piezoelectric actuators. The aim of this study is to understand the various contributions to the macroscopic behaviour observed during this experiment that involves the intrinsic piezoelectric effect, ferroelectric domain switching, and internal stress development. For this purpose, a high energy diffraction experiment is performed in-situ during a blocking force test on a tetragonal lead zirconate titanate (PZT) ceramic (Pb{sub 0.98}Ba{sub 0.01}(Zr{sub 0.51}Ti{sub 0.49}){sub 0.98}Nb{sub 0.02}O{sub 3}). It is shown that the usual macroscopic linear interpretation of the test can also be performed at the single crystal scale,more » allowing the identification of local apparent piezoelectric and elastic properties. It is also shown that despite this apparent linearity, the blocking force test involves significant non-linear behaviour mostly due to domain switching under electric field and stress. Although affecting a limited volume fraction of the material, domain switching is responsible for a large part of the macroscopic strain and explains the high level of inter- and intra-granular stresses observed during the course of the experiment. The study shows that if apparent piezoelectric and elastic properties can be identified for PZT single crystals from blocking stress curves, they may be very different from the actual properties of polycrystalline materials due to the multiplicity of the physical mechanisms involved. These apparent properties can be used for macroscopic modelling purposes but should be considered with caution if a local analysis is aimed at.« less

The effect of acetabular cup size on the short-term stability of revision hip arthroplasty: a finite element investigation.

PubMed

Phillips, A T M; Pankaj; Usmani, A S; Howie, C R

2004-01-01

The study uses idealized two-dimensional finite element models to examine the behaviour of the acetabular construct following revision hip arthroplasty, carried out using the Slooff-Ling impaction grafting technique. The behaviour of bone graft was considered in detail, with non-linear elasticity and non-associated plasticity being adopted. Load was applied to the acetabular construct through a femoral head using smooth sliding surfaces. In particular, four models were subjected to two idealized cyclic load cases to investigate the effect of acetabular cup size on the short-term stability of the acetabular construct. The study suggests that benefits may be gained by using the largest practical size of acetabular cup.

Real time control and numerical simulation of pipeline subjected to landslide

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

Cuscuna, S.; Giusti, G.; Gramola, C.

1984-06-01

This paper describes SNAM research activity in the study of behaviour and real-time control of pipelines in landslide areas. The subject can be delt considering three different aspects: 1. Geotechnical characterization of unstable soils. The mechanical parameters of soil and the landslide types are defined; 2. Structural analysis of pipe-soil system. By means of a finite element program it's possible to study the pipe-soil interaction; in this numerical code the soil parameters attend by the non-linear elastic behaviour of pipe restraints. The results of this analysis are the location of the expected most stressed sections of pipe and the globalmore » behaviour of pipe inside the soil. 3. Instrumental control. The adoption of a suitable appliance of vibrating wire strain gauges allows the strain control of pipe in time. The aim is to make possible timely interventions in order to guarantee the installation safety.« less

Phenomenological study of a cellular material behaviour under dynamic loadings

NASA Astrophysics Data System (ADS)

Bouix, R.; Viot, Ph.; Lataillade, J.-L.

2006-08-01

Polypropylene foams are cellular materials, which are often use to fill structures subjected to crash or violent impacts. Therefore, it is necessary to know and to characterise in experiments their mechanical behaviour in compression at high strain rates. So, several apparatus have been used in order to highlight the influence of strain rate, material density and also temperature. A split Hopkinson Pressure Bar has been used for impact tests, a fly wheel to test theses materials at medium strain rate and an electro-mechanical testing machine associated to a climatic chamber for temperature tests. Then, a rheological model has been used in order to describe the material behaviour. The mechanical response to compression of these foams presents three typical domains: a linear elastic step, a wide collapse plateau stress, which leads to a densification, which are related to a standard rheological model.

Propagation of short stress pulses in discrete strongly nonlinear tunable metamaterials.

PubMed

Xu, Yichao; Nesterenko, Vitali F

2014-08-28

The propagation of short pulses with wavelength comparable to the size of a unit cell has been studied in a one-dimensional discrete metamaterial composed of steel discs alternating with toroidal nitrile O-rings under different levels of precompression using experiments, numerical simulations and theoretical analysis. This strongly nonlinear metamaterial is more tunable than granular chains composed of linear elastic spherical particles and has better potential for attenuation of dynamic loads. A double power-law relationship for compressed O-rings was found to describe adequately their quasi-static and dynamic behaviour with significantly different elastic moduli. It is demonstrated that the double power-law metamaterial investigated allows a dramatic increase in sound speed and acoustic impedance of three to four times using a moderate force. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Thermo-mechanical Modelling of Pebble Beds in Fusion Blankets and its Implementation by a Return-Mapping Algorithm

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

Gan, Yixiang; Kamlah, Marc

In this investigation, a thermo-mechanical model of pebble beds is adopted and developed based on experiments by Dr. Reimann at Forschungszentrum Karlsruhe (FZK). The framework of the present material model is composed of a non-linear elastic law, the Drucker-Prager-Cap theory, and a modified creep law. Furthermore, the volumetric inelastic strain dependent thermal conductivity of beryllium pebble beds is taken into account and full thermo-mechanical coupling is considered. Investigation showed that the Drucker-Prager-Cap model implemented in ABAQUS can not fulfill the requirements of both the prediction of large creep strains and the hardening behaviour caused by creep, which are of importancemore » with respect to the application of pebble beds in fusion blankets. Therefore, UMAT (user defined material's mechanical behaviour) and UMATHT (user defined material's thermal behaviour) routines are used to re-implement the present thermo-mechanical model in ABAQUS. An elastic predictor radial return mapping algorithm is used to solve the non-associated plasticity iteratively, and a proper tangent stiffness matrix is obtained for cost-efficiency in the calculation. An explicit creep mechanism is adopted for the prediction of time-dependent behaviour in order to represent large creep strains in high temperature. Finally, the thermo-mechanical interactions are implemented in a UMATHT routine for the coupled analysis. The oedometric compression tests and creep tests of pebble beds at different temperatures are simulated with the help of the present UMAT and UMATHT routines, and the comparison between the simulation and the experiments is made. (authors)« less

A SPH elastic-viscoplastic model for granular flows and bed-load transport

NASA Astrophysics Data System (ADS)

Ghaïtanellis, Alex; Violeau, Damien; Ferrand, Martin; Abderrezzak, Kamal El Kadi; Leroy, Agnès; Joly, Antoine

2018-01-01

An elastic-viscoplastic model (Ulrich, 2013) is combined to a multi-phase SPH formulation (Hu and Adams, 2006; Ghaitanellis et al., 2015) to model granular flows and non-cohesive sediment transport. The soil is treated as a continuum exhibiting a viscoplastic behaviour. Thus, below a critical shear stress (i.e. the yield stress), the soil is assumed to behave as an isotropic linear-elastic solid. When the yield stress is exceeded, the soil flows and behaves as a shear-thinning fluid. A liquid-solid transition threshold based on the granular material properties is proposed, so as to make the model free of numerical parameter. The yield stress is obtained from Drucker-Prager criterion that requires an accurate computation of the effective stress in the soil. A novel method is proposed to compute the effective stress in SPH, solving a Laplace equation. The model is applied to a two-dimensional soil collapse (Bui et al., 2008) and a dam break over mobile beds (Spinewine and Zech, 2007). Results are compared with experimental data and a good agreement is obtained.

Evaluation of a Nonlinear Finite Element Program - ABAQUS.

DTIC Science & Technology

1983-03-15

anisotropic properties. * MATEXP - Linearly elastic thermal expansions with isotropic, orthotropic and anisotropic properties. * MATELG - Linearly...elastic materials for general sections (options available for beam and shell elements). • MATEXG - Linearly elastic thermal expansions for general...decomposition of a matrix. * Q-R algorithm • Vector normalization, etc. Obviously, by consolidating all the utility subroutines in a library, ABAQUS has

Charge-regularized swelling kinetics of polyelectrolyte gels: Elasticity and diffusion

NASA Astrophysics Data System (ADS)

Sen, Swati; Kundagrami, Arindam

2017-11-01

We apply a recently developed method [S. Sen and A. Kundagrami, J. Chem. Phys. 143, 224904 (2015)], using a phenomenological expression of osmotic stress, as a function of polymer and charge densities, hydrophobicity, and network elasticity for the swelling of spherical polyelectrolyte (PE) gels with fixed and variable charges in a salt-free solvent. This expression of stress is used in the equation of motion of swelling kinetics of spherical PE gels to numerically calculate the spatial profiles for the polymer and free ion densities at different time steps and the time evolution of the size of the gel. We compare the profiles of the same variables obtained from the classical linear theory of elasticity and quantitatively estimate the bulk modulus of the PE gel. Further, we obtain an analytical expression of the elastic modulus from the linearized expression of stress (in the small deformation limit). We find that the estimated bulk modulus of the PE gel decreases with the increase of its effective charge for a fixed degree of deformation during swelling. Finally, we match the gel-front locations with the experimental data, taken from the measurements of charged reversible addition-fragmentation chain transfer gels to show an increase in gel-size with charge and also match the same for PNIPAM (uncharged) and imidazolium-based (charged) minigels, which specifically confirms the decrease of the gel modulus value with the increase of the charge. The agreement between experimental and theoretical results confirms general diffusive behaviour for swelling of PE gels with a decreasing bulk modulus with increasing degree of ionization (charge). The new formalism captures large deformations as well with a significant variation of charge content of the gel. It is found that PE gels with large deformation but same initial size swell faster with a higher charge.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

The power transfer from the neuromuscular machinery to its load as a vegetative and somatic behaviour.

PubMed

Federici, A; Nocera, L

1990-01-01

Models have been proposed in literature describing the contraction of visceral and somatic muscles as an interaction between the time-varying elastances of them and the loads they are working against. The aim of this paper is: 1) to make clear similarities between the models of visceral and somatic muscular contraction; 2) to stress the concept that the power transfer from a time-varying elastance to its load is a behaviour, i.e. an interaction between the entire neuromuscular machinery and the surrounding environment; 3) to propose a theory describing the various physiological and pathological behaviours of both visceral and somatic muscles as different ways of coupling between the time-varying muscular elastances and their loads. In this theory it is assumed that the entire neuromuscular machinery acts as a whole to set the most appropriate power transfer to achieve behavioural goals.

Thermo-elastic behaviour of liquid crystal elastomer

NASA Astrophysics Data System (ADS)

J, Jessy P.; Mani, Santosh A.; Amare, Jyoti R.; Gharde, Rita A.

2015-06-01

The effect of temperature on Liquid Crystal Elastomer was studied to understand thermo-elastic behaviour of these fantastic soft materials. The investigations were performed using Polarizing Microscopy Studies (PMS) and Differential Thermal Analysis (DTA). The relative length shows hysteresis as function of temperature. As temperature increases, the length shrinks, while it returns to original shape on cooling.

The Shock and Vibration Digest. Volume 18, Number 12

DTIC Science & Technology

1986-12-01

practical msthods for fracture mechanics analysis. Linear elastic methods can yield useful results. Elas- dc-plasdc methods are becoming useful with...geometry factors. Fracture mechanics analysis based on linear elastic concepts developed in the 1960s has become established during the last decade as...2) is slightly conservative [2,3]. Materials that ran be treated with linear elastic fracture mechanics usually belong in this category. No

Elastic robot control - Nonlinear inversion and linear stabilization

NASA Technical Reports Server (NTRS)

Singh, S. N.; Schy, A. A.

1986-01-01

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

A comparison between different finite elements for elastic and aero-elastic analyses.

PubMed

Mahran, Mohamed; ELsabbagh, Adel; Negm, Hani

2017-11-01

In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element's strain-displacement matrix in bending. The elements were compared using carefully selected elastic and aero-elastic bench mark problems, regarding the number of elements needed to reach convergence, the resulting accuracy, and the needed computation time. The best suitable element for elastic free vibration analysis was found to be the Linear Quadrilateral Element with deformation-based shape functions, whereas the most suitable element for stress analysis was the 8-Node Quadrilateral Element, and the most suitable element for aero-elastic analysis was the 9-Node Quadrilateral Element. Although the linear triangular element was the last choice for modal and stress analyses, it establishes more accurate results in aero-elastic analyses, however, with much longer computation time. Additionally, the nine-node quadrilateral element was found to be the best choice for laminated composite plates analysis.

On the influence of frequency-dependent elastic properties in vibro-acoustic modelling of porous materials under structural excitation

NASA Astrophysics Data System (ADS)

Van der Kelen, C.; Göransson, P.; Pluymers, B.; Desmet, W.

2014-12-01

The aspects related to modelling the frequency dependence of the elastic properties of air-saturated porous materials have been largely neglected in the past for several reasons. For acoustic excitation of porous materials, the material behaviour can be quite well represented by models where the properties of the solid frame have little influence. Only recently has the importance of the dynamic moduli of the frame come into focus. This is related to a growing interest in the material behaviour due to structural excitation. Two aspects stand out in connection with the elastic-dynamic behaviour. The first is related to methods for the characterisation of the dynamic moduli of porous materials. The second is a perceived lack of numerical methods able to model the complex material behaviour under structural excitation, in particular at higher frequencies. In the current paper, experimental data from a panel under structural excitation, coated with a porous material, are presented. In an attempt to correlate the experimental data to numerical predictions, it is found that the measured quasi-static material parameters do not suffice for an accurate prediction of the measured results. The elastic material parameters are then estimated by correlating the numerical prediction to the experimental data, following the physical behaviour predicted by the augmented Hooke's law. The change in material behaviour due to the frequency-dependent properties is illustrated in terms of the propagation of the slow wave and the shear wave in the porous material.

Explicit 2-D Hydrodynamic FEM Program

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

Lin, Jerry

1996-08-07

DYNA2D* is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D* contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. The isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL highmore » explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.« less

Model updating in flexible-link multibody systems

NASA Astrophysics Data System (ADS)

Belotti, R.; Caneva, G.; Palomba, I.; Richiedei, D.; Trevisani, A.

2016-09-01

The dynamic response of flexible-link multibody systems (FLMSs) can be predicted through nonlinear models based on finite elements, to describe the coupling between rigid- body and elastic behaviour. Their accuracy should be as high as possible to synthesize controllers and observers. Model updating based on experimental measurements is hence necessary. By taking advantage of the experimental modal analysis, this work proposes a model updating procedure for FLMSs and applies it experimentally to a planar robot. Indeed, several peculiarities of the model of FLMS should be carefully tackled. On the one hand, nonlinear models of a FLMS should be linearized about static equilibrium configurations. On the other, the experimental mode shapes should be corrected to be consistent with the elastic displacements represented in the model, which are defined with respect to a fictitious moving reference (the equivalent rigid link system). Then, since rotational degrees of freedom are also represented in the model, interpolation of the experimental data should be performed to match the model displacement vector. Model updating has been finally cast as an optimization problem in the presence of bounds on the feasible values, by also adopting methods to improve the numerical conditioning and to compute meaningful updated inertial and elastic parameters.

Three-dimensional modeling of flexible pavements : research implementation plan.

DOT National Transportation Integrated Search

2006-02-14

Many of the asphalt pavement analysis programs are based on linear elastic models. A linear viscoelastic models : would be superior to linear elastic models for analyzing the response of asphalt concrete pavements to loads. There : is a need to devel...

The importance of being elastic: deflection of a badminton racket during a stroke.

PubMed

Kwan, Maxine; Rasmussen, John

2010-03-01

The deflection profiles of a badminton racket during strokes performed by elite and world-class badminton players were recorded by strain gauges and subsequently analysed to determine the role of shaft stiffness in racket performance. Deflection behaviour was consistent in all strokes across all players, suggesting a controlled use of racket elasticity. In addition, all impacts occurred within 100 ms of each other, a duration in which deflection velocity provides an increase in racket velocity, indicating that the players were able to use racket elasticity to their advantage. Since deflection behaviour is a product of the racket-player interaction, further work is required to determine the effects of different racket properties and player techniques on the elastic response of rackets during strokes.

The role of elastic stored energy in controlling the long term rheological behaviour of the lithosphere

NASA Astrophysics Data System (ADS)

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

2012-04-01

The traditional definition of lithospheric strength is derived from the differential stresses required to form brittle and ductile structures at a constant strain rate. This definition is based on dissipative brittle and ductile deformation and does not take into account the ability of the lithosphere to store elastic strain. Here we show the important role of elasticity in controlling the long-term behaviour of the lithosphere. This is particularly evident when describing deformation in a thermodynamic framework, which differentiates between stored (Helmholtz free energy) and dissipative (entropy) energy potentials. In our model calculations we stretch a continental lithosphere with a wide range of crustal thickness (30-60 km) and heat flow (50-80 mW/m2) at a constant velocity. We show that the Helmholtz free energy, which in our simple calculation describes the energy stored elastically, converges for all models within a 25% range, while the dissipated energy varies over an order of magnitude. This variation stems from complex patterns in the local strain distributions of the different models, which together operate to minimize the Helmholtz free energy. This energy minimization is a fundamental material behaviour of the lithosphere, which in our simple case is defined by its elastic properties. We conclude from this result that elasticity (more generally Helmholtz free energy) is an important regulator of the long-term geological strength of the lithosphere.

Two-dimensional membrane as elastic shell with proof on the folds revealed by three-dimensional atomic mapping

NASA Astrophysics Data System (ADS)

Zhao, Jiong; Deng, Qingming; Ly, Thuc Hue; Han, Gang Hee; Sandeep, Gorantla; Rümmeli, Mark H.

2015-11-01

The great application potential for two-dimensional (2D) membranes (MoS2, WSe2, graphene and so on) aroused much effort to understand their fundamental mechanical properties. The out-of-plane bending rigidity is the key factor that controls the membrane morphology under external fields. Herein we provide an easy method to reconstruct the 3D structures of the folded edges of these 2D membranes on the atomic scale, using high-resolution (S)TEM images. After quantitative comparison with continuum mechanics shell model, it is verified that the bending behaviour of the studied 2D materials can be well explained by the linear elastic shell model. And the bending rigidities can thus be derived by fitting with our experimental results. Recall almost only theoretical approaches can access the bending properties of these 2D membranes before, now a new experimental method to measure the bending rigidity of such flexible and atomic thick 2D membranes is proposed.

A computational study of crimping and expansion of bioresorbable polymeric stents

NASA Astrophysics Data System (ADS)

Qiu, T. Y.; Song, M.; Zhao, L. G.

2018-05-01

This paper studied the mechanical performance of four bioresorbable PLLA stents, i.e., Absorb, Elixir, Igaki-Tamai and RevaMedical, during crimping and expansion using the finite element method. Abaqus CAE was used to create the geometrical models for the four stents. A tri-folded balloon was created using NX software. For the stents, elastic-plastic behaviour was used, with hardening implemented by considering the increase of yield stress with the plastic strain. The tri-folded balloon was treated as linear elastic. To simulate the crimping of stents, a set of 12 rigid plates were generated around the stents with a radially enforced displacement. During crimping, the stents were compressed from a diameter of 3 mm to 1.2 mm, with the maximum stress developed at both inner and outer sides of the U-bends. During expansion, the stent inner diameter increased to 3 mm at the peak pressure and then recoiled to different final diameters after balloon deflation due to different stent designs. The maximum stress was found again at the U-bends of stents. Diameter change, recoiling effect and radial strength/stiffness were also compared for the four stents to assess the effect of design variation on stent performance. The effect of loading rate on stent deformation was also simulated by considering the time-dependent plastic behaviour of polymeric material.

A computational study of crimping and expansion of bioresorbable polymeric stents

NASA Astrophysics Data System (ADS)

Qiu, T. Y.; Song, M.; Zhao, L. G.

2017-10-01

This paper studied the mechanical performance of four bioresorbable PLLA stents, i.e., Absorb, Elixir, Igaki-Tamai and RevaMedical, during crimping and expansion using the finite element method. Abaqus CAE was used to create the geometrical models for the four stents. A tri-folded balloon was created using NX software. For the stents, elastic-plastic behaviour was used, with hardening implemented by considering the increase of yield stress with the plastic strain. The tri-folded balloon was treated as linear elastic. To simulate the crimping of stents, a set of 12 rigid plates were generated around the stents with a radially enforced displacement. During crimping, the stents were compressed from a diameter of 3 mm to 1.2 mm, with the maximum stress developed at both inner and outer sides of the U-bends. During expansion, the stent inner diameter increased to 3 mm at the peak pressure and then recoiled to different final diameters after balloon deflation due to different stent designs. The maximum stress was found again at the U-bends of stents. Diameter change, recoiling effect and radial strength/stiffness were also compared for the four stents to assess the effect of design variation on stent performance. The effect of loading rate on stent deformation was also simulated by considering the time-dependent plastic behaviour of polymeric material.

An elastic-plastic contact model for line contact structures

NASA Astrophysics Data System (ADS)

Zhu, Haibin; Zhao, Yingtao; He, Zhifeng; Zhang, Ruinan; Ma, Shaopeng

2018-06-01

Although numerical simulation tools are now very powerful, the development of analytical models is very important for the prediction of the mechanical behaviour of line contact structures for deeply understanding contact problems and engineering applications. For the line contact structures widely used in the engineering field, few analytical models are available for predicting the mechanical behaviour when the structures deform plastically, as the classic Hertz's theory would be invalid. Thus, the present study proposed an elastic-plastic model for line contact structures based on the understanding of the yield mechanism. A mathematical expression describing the global relationship between load history and contact width evolution of line contact structures was obtained. The proposed model was verified through an actual line contact test and a corresponding numerical simulation. The results confirmed that this model can be used to accurately predict the elastic-plastic mechanical behaviour of a line contact structure.

Analytic analysis of auxetic metamaterials through analogy with rigid link systems

NASA Astrophysics Data System (ADS)

Rayneau-Kirkhope, Daniel; Zhang, Chengzhao; Theran, Louis; Dias, Marcelo A.

2018-02-01

In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value. This paper develops a novel methodology in the analysis of auxetic metamaterials which exhibit elastic instability through analogy with rigid link lattice systems. The results of our analytic approach are confirmed by finite-element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson's ratio. The method gives insight into the relationships between mechanisms within lattices and their mechanical behaviour; as such, it has the potential to allow existing knowledge of rigid link lattices with auxetic paths to be used in the design of future buckling-induced auxetic metamaterials.

Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

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

Preston, Leiph

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti)more » by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.« less

On some problems in a theory of thermally and mechanically interacting continuous media. Ph.D. Thesis; [linearized theory of interacting mixture of elastic solid and viscous fluid

NASA Technical Reports Server (NTRS)

Lee, Y. M.

1971-01-01

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

Matrix elasticity of void-forming hydrogels controls transplanted-stem-cell-mediated bone formation

NASA Astrophysics Data System (ADS)

Huebsch, Nathaniel; Lippens, Evi; Lee, Kangwon; Mehta, Manav; Koshy, Sandeep T.; Darnell, Max C.; Desai, Rajiv M.; Madl, Christopher M.; Xu, Maria; Zhao, Xuanhe; Chaudhuri, Ovijit; Verbeke, Catia; Kim, Woo Seob; Alim, Karen; Mammoto, Akiko; Ingber, Donald E.; Duda, Georg N.; Mooney, David J.

2015-12-01

The effectiveness of stem cell therapies has been hampered by cell death and limited control over fate. These problems can be partially circumvented by using macroporous biomaterials that improve the survival of transplanted stem cells and provide molecular cues to direct cell phenotype. Stem cell behaviour can also be controlled in vitro by manipulating the elasticity of both porous and non-porous materials, yet translation to therapeutic processes in vivo remains elusive. Here, by developing injectable, void-forming hydrogels that decouple pore formation from elasticity, we show that mesenchymal stem cell (MSC) osteogenesis in vitro, and cell deployment in vitro and in vivo, can be controlled by modifying, respectively, the hydrogel’s elastic modulus or its chemistry. When the hydrogels were used to transplant MSCs, the hydrogel’s elasticity regulated bone regeneration, with optimal bone formation at 60 kPa. Our findings show that biophysical cues can be harnessed to direct therapeutic stem cell behaviours in situ.

A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, Gerald W.; Mahadevan, L.

1987-01-01

A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.

A General Framework for Thermodynamically Consistent Parameterization and Efficient Sampling of Enzymatic Reactions

PubMed Central

Saa, Pedro; Nielsen, Lars K.

2015-01-01

Kinetic models provide the means to understand and predict the dynamic behaviour of enzymes upon different perturbations. Despite their obvious advantages, classical parameterizations require large amounts of data to fit their parameters. Particularly, enzymes displaying complex reaction and regulatory (allosteric) mechanisms require a great number of parameters and are therefore often represented by approximate formulae, thereby facilitating the fitting but ignoring many real kinetic behaviours. Here, we show that full exploration of the plausible kinetic space for any enzyme can be achieved using sampling strategies provided a thermodynamically feasible parameterization is used. To this end, we developed a General Reaction Assembly and Sampling Platform (GRASP) capable of consistently parameterizing and sampling accurate kinetic models using minimal reference data. The former integrates the generalized MWC model and the elementary reaction formalism. By formulating the appropriate thermodynamic constraints, our framework enables parameterization of any oligomeric enzyme kinetics without sacrificing complexity or using simplifying assumptions. This thermodynamically safe parameterization relies on the definition of a reference state upon which feasible parameter sets can be efficiently sampled. Uniform sampling of the kinetics space enabled dissecting enzyme catalysis and revealing the impact of thermodynamics on reaction kinetics. Our analysis distinguished three reaction elasticity regions for common biochemical reactions: a steep linear region (0> ΔGr >-2 kJ/mol), a transition region (-2> ΔGr >-20 kJ/mol) and a constant elasticity region (ΔGr <-20 kJ/mol). We also applied this framework to model more complex kinetic behaviours such as the monomeric cooperativity of the mammalian glucokinase and the ultrasensitive response of the phosphoenolpyruvate carboxylase of Escherichia coli. In both cases, our approach described appropriately not only the kinetic behaviour of these enzymes, but it also provided insights about the particular features underpinning the observed kinetics. Overall, this framework will enable systematic parameterization and sampling of enzymatic reactions. PMID:25874556

Deformed soft matter under constraints

NASA Astrophysics Data System (ADS)

Bertrand, Martin

In the last few decades, an increasing number of physicists specialized in soft matter, including polymers, have turned their attention to biologically relevant materials. The properties of various molecules and fibres, such as DNA, RNA, proteins, and filaments of all sorts, are studied to better understand their behaviours and functions. Self-assembled biological membranes, or lipid bilayers, are also the focus of much attention as many life processes depend on these. Small lipid bilayers vesicles dubbed liposomes are also frequently used in the pharmaceutical and cosmetic industries. In this thesis, work is presented on both the elastic properties of polymers and the response of lipid bilayer vesicles to extrusion in narrow-channels. These two areas of research may seem disconnected but they both concern deformed soft materials. The thesis contains four articles: the first presenting a fundamental study of the entropic elasticity of circular chains; the second, a simple universal description of the effect of sequence on the elasticity of linear polymers such as DNA; the third, a model of the symmetric thermophoretic stretch of a nano-confined polymer; the fourth, a model that predicts the final sizes of vesicles obtained by pressure extrusion. These articles are preceded by an extensive introduction that covers all of the essential concepts and theories necessary to understand the work that has been done.

Effects of frequency- and direction-dependent elastic materials on linearly elastic MRE image reconstructions

NASA Astrophysics Data System (ADS)

Perreard, I. M.; Pattison, A. J.; Doyley, M.; McGarry, M. D. J.; Barani, Z.; Van Houten, E. E.; Weaver, J. B.; Paulsen, K. D.

2010-11-01

The mechanical model commonly used in magnetic resonance elastography (MRE) is linear elasticity. However, soft tissue may exhibit frequency- and direction-dependent (FDD) shear moduli in response to an induced excitation causing a purely linear elastic model to provide an inaccurate image reconstruction of its mechanical properties. The goal of this study was to characterize the effects of reconstructing FDD data using a linear elastic inversion (LEI) algorithm. Linear and FDD phantoms were manufactured and LEI images were obtained from time-harmonic MRE acquisitions with variations in frequency and driving signal amplitude. LEI responses to artificially imposed uniform phase shifts in the displacement data from both purely linear elastic and FDD phantoms were also evaluated. Of the variety of FDD phantoms considered, LEI appeared to tolerate viscoelastic data-model mismatch better than deviations caused by poroelastic and anisotropic mechanical properties in terms of visual image contrast. However, the estimated shear modulus values were substantially incorrect relative to independent mechanical measurements even in the successful viscoelastic cases and the variations in mean values with changes in experimental conditions associated with uniform phase shifts, driving signal frequency and amplitude were unpredictable. Overall, use of LEI to reconstruct data acquired in phantoms with FDD material properties provided biased results under the best conditions and significant artifacts in the worst cases. These findings suggest that the success with which LEI is applied to MRE data in tissue will depend on the underlying mechanical characteristics of the tissues and/or organs systems of clinical interest.

Effects of frequency- and direction-dependent elastic materials on linearly elastic MRE image reconstructions.

PubMed

Perreard, I M; Pattison, A J; Doyley, M; McGarry, M D J; Barani, Z; Van Houten, E E; Weaver, J B; Paulsen, K D

2010-11-21

The mechanical model commonly used in magnetic resonance elastography (MRE) is linear elasticity. However, soft tissue may exhibit frequency- and direction-dependent (FDD) shear moduli in response to an induced excitation causing a purely linear elastic model to provide an inaccurate image reconstruction of its mechanical properties. The goal of this study was to characterize the effects of reconstructing FDD data using a linear elastic inversion (LEI) algorithm. Linear and FDD phantoms were manufactured and LEI images were obtained from time-harmonic MRE acquisitions with variations in frequency and driving signal amplitude. LEI responses to artificially imposed uniform phase shifts in the displacement data from both purely linear elastic and FDD phantoms were also evaluated. Of the variety of FDD phantoms considered, LEI appeared to tolerate viscoelastic data-model mismatch better than deviations caused by poroelastic and anisotropic mechanical properties in terms of visual image contrast. However, the estimated shear modulus values were substantially incorrect relative to independent mechanical measurements even in the successful viscoelastic cases and the variations in mean values with changes in experimental conditions associated with uniform phase shifts, driving signal frequency and amplitude were unpredictable. Overall, use of LEI to reconstruct data acquired in phantoms with FDD material properties provided biased results under the best conditions and significant artifacts in the worst cases. These findings suggest that the success with which LEI is applied to MRE data in tissue will depend on the underlying mechanical characteristics of the tissues and/or organs systems of clinical interest.

Dynamic contraction behaviour of pneumatic artificial muscle

NASA Astrophysics Data System (ADS)

Doumit, Marc D.; Pardoel, Scott

2017-07-01

The development of a dynamic model for the Pneumatic Artificial Muscle (PAM) is an imperative undertaking for understanding and analyzing the behaviour of the PAM as a function of time. This paper proposes a Newtonian based dynamic PAM model that includes the modeling of the muscle geometry, force, inertia, fluid dynamic, static and dynamic friction, heat transfer and valve flow while ignoring the effect of bladder elasticity. This modeling contribution allows the designer to predict, analyze and optimize PAM performance prior to its development. Thus advancing successful implementations of PAM based powered exoskeletons and medical systems. To date, most muscle dynamic properties are determined experimentally, furthermore, no analytical models that can accurately predict the muscle's dynamic behaviour are found in the literature. Most developed analytical models adequately predict the muscle force in static cases but neglect the behaviour of the system in the transient response. This could be attributed to the highly challenging task of deriving such a dynamic model given the number of system elements that need to be identified and the system's highly non-linear properties. The proposed dynamic model in this paper is successfully simulated through MATLAB programing and validated the pressure, contraction distance and muscle temperature with experimental testing that is conducted with in-house built prototype PAM's.

New methodology for mechanical characterization of human superficial facial tissue anisotropic behaviour in vivo.

PubMed

Then, C; Stassen, B; Depta, K; Silber, G

2017-07-01

Mechanical characterization of human superficial facial tissue has important applications in biomedical science, computer assisted forensics, graphics, and consumer goods development. Specifically, the latter may include facial hair removal devices. Predictive accuracy of numerical models and their ability to elucidate biomechanically relevant questions depends on the acquisition of experimental data and mechanical tissue behavior representation. Anisotropic viscoelastic behavioral characterization of human facial tissue, deformed in vivo with finite strain, however, is sparse. Employing an experimental-numerical approach, a procedure is presented to evaluate multidirectional tensile properties of superficial tissue layers of the face in vivo. Specifically, in addition to stress relaxation, displacement-controlled multi-step ramp-and-hold protocols were performed to separate elastic from inelastic properties. For numerical representation, an anisotropic hyperelastic material model in conjunction with a time domain linear viscoelasticity formulation with Prony series was employed. Model parameters were inversely derived, employing finite element models, using multi-criteria optimization. The methodology provides insight into mechanical superficial facial tissue properties. Experimental data shows pronounced anisotropy, especially with large strain. The stress relaxation rate does not depend on the loading direction, but is strain-dependent. Preconditioning eliminates equilibrium hysteresis effects and leads to stress-strain repeatability. In the preconditioned state tissue stiffness and hysteresis insensitivity to strain rate in the applied range is evident. The employed material model fits the nonlinear anisotropic elastic results and the viscoelasticity model reasonably reproduces time-dependent results. Inversely deduced maximum anisotropic long-term shear modulus of linear elasticity is G ∞,max aniso =2.43kPa and instantaneous initial shear modulus at an applied rate of ramp loading is G 0,max aniso =15.38kPa. Derived mechanical model parameters constitute a basis for complex skin interaction simulation. Copyright © 2017. Published by Elsevier Ltd.

Molecular Dynamics Simulation Studies of Fracture in Two Dimensions

DTIC Science & Technology

1980-05-01

reversibility of trajectories. The microscopic elastic constants, dispersion relation and phonon spectrum of the system were determined by lattice dynamics. These... linear elasticity theory of a two-dimensional crack embedded in an infinite medium. System con- sists of 436 particles arranged in a tri- angular lattice ...satisfying these demands. In evaluating the mechanical energy of his model, Griffith used a result from linear elasticity theory, namely that for any body

Extracting real-crack properties from non-linear elastic behaviour of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson ratios

NASA Astrophysics Data System (ADS)

Zaitsev, Vladimir Y.; Radostin, Andrey V.; Pasternak, Elena; Dyskin, Arcady

2017-09-01

Results of examination of experimental data on non-linear elasticity of rocks using experimentally determined pressure dependences of P- and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects with explicitly introduced shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance (˜ 80 %) of cracks with the normal-to-shear compliance ratios that significantly exceed the values typical of conventionally used crack models (such as penny-shaped cuts or thin ellipsoidal cracks). Correspondingly, rocks with such cracks demonstrate a strongly decreased Poisson ratio including a significant (˜ 45 %) portion of rocks exhibiting negative Poisson ratios at lower pressures, for which the concentration of not yet closed cracks is maximal. The obtained results indicate the necessity for further development of crack models to account for the revealed numerous examples of cracks with strong domination of normal compliance. Discovering such a significant number of naturally auxetic rocks is in contrast to the conventional viewpoint that occurrence of a negative Poisson ratio is an exotic fact that is mostly discussed for artificial structures.

Numerical Simulation of Hysteretic Live Load Effect in a Soil-Steel Bridge

NASA Astrophysics Data System (ADS)

Sobótka, Maciej

2014-03-01

The paper presents numerical simulation of hysteretic live load effect in a soil-steel bridge. The effect was originally identified experimentally by Machelski [1], [2]. The truck was crossing the bridge one way and the other in the full-scale test performed. At the same time, displacements and stress in the shell were measured. The major conclusion from the research was that the measured quantities formed hysteretic loops. A numerical simulation of that effect is addressed in the present work. The analysis was performed using Flac finite difference code. The methodology of solving the mechanical problems implemented in Flac enables us to solve the problem concerning a sequence of load and non-linear mechanical behaviour of the structure. The numerical model incorporates linear elastic constitutive relations for the soil backfill, for the steel shell and the sheet piles, being a flexible substructure for the shell. Contact zone between the shell and the soil backfill is assumed to reflect elastic-plastic constitutive model. Maximum shear stress in contact zone is limited by the Coulomb condition. The plastic flow rule is described by dilation angle ψ = 0. The obtained results of numerical analysis are in fair agreement with the experimental evidence. The primary finding from the performed simulation is that the slip in the interface can be considered an explanation of the hysteresis occurrence in the charts of displacement and stress in the shell.

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.

Effect of Prestresses on the Dispersion of Quasi-Lamb Waves in the System Consisting of an Ideal Liquid Layer and a Compressible Elastic Layer

NASA Astrophysics Data System (ADS)

Bagno, A. M.

2017-03-01

The propagation of quasi-Lamb waves in a prestrained compressible elastic layer interacting with a layer of an ideal compressible fluid is studied. The three-dimensional equations of linearized elasticity and the assumption of finite strains for the elastic layer and the three-dimensional linearized Euler equations for the fluid are used. The dispersion curves for the quasi-Lamb modes are plotted over a wide frequency range. The effect of prestresses and the thickness of the elastic and liquid layers on the frequency spectrum of normal quasi-Lamb waves is analyzed. The localization properties of the lower quasi-Lamb modes in the elastic-fluid waveguides are studied. The numerical results are presented in the form of graphs and analyzed

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

NASA Technical Reports Server (NTRS)

Prosser, William H.

1987-01-01

The theoretical treatment of linear and nonlinear elasticity in a unidirectionally fiber reinforced composite as well as measurements for a unidirectional graphite/epoxy composite (T300/5208) are presented. Linear elastic properties were measured by both ultrasonic and strain gage measurements. The nonlinear properties were determined by measuring changes in ultrasonic natural phase velocity with a pulsed phase locked loop interferometer as a function of stress and temperature. These measurements provide the basis for further investigations into the relationship between nonlinear elastic properties and other important properties such as strength and fiber-matrix interfacial stength in graphite/epoxy composites.

Mechanical testing and modelling of carbon-carbon composites for aircraft disc brakes

NASA Astrophysics Data System (ADS)

Bradley, Luke R.

The objective of this study is to improve the understanding of the stress distributions and failure mechanisms experienced by carbon-carbon composite aircraft brake discs using finite element (FE) analyses. The project has been carried out in association with Dunlop Aerospace as an EPSRC CASE studentship. It therefore focuses on the carbon-carbon composite brake disc material produced by Dunlop Aerospace, although it is envisaged that the approach will have broader applications for modelling and mechanical testing of carbon-carbon composites in general. The disc brake material is a laminated carbon-carbon composite comprised of poly(acrylonitrile) (PAN) derived carbon fibres in a chemical vapour infiltration (CVI) deposited matrix, in which the reinforcement is present in both continuous fibre and chopped fibre forms. To pave the way for the finite element analysis, a comprehensive study of the mechanical properties of the carbon-carbon composite material was carried out. This focused largely, but not entirely, on model composite materials formulated using structural elements of the disc brake material. The strengths and moduli of these materials were measured in tension, compression and shear in several orientations. It was found that the stress-strain behaviour of the materials were linear in directions where there was some continuous fibre reinforcement, but non-linear when this was not the case. In all orientations, some degree of non-linearity was observed in the shear stress-strain response of the materials. However, this non-linearity was generally not large enough to pose a problem for the estimation of elastic moduli. Evidence was found for negative Poisson's ratio behaviour in some orientations of the material in tension. Additionally, the through-thickness properties of the composite, including interlaminar shear strength, were shown to be positively related to bulk density. The in-plane properties were mostly unrelated to bulk density over the range of densities of the tested specimens.Two types of FE model were developed using a commercially available program. The first type was designed to analyse the model composite materials for comparison with mechanical test data for the purpose of validation of the FE model. Elastic moduli predicted by this type of FE model showed good agreement with the experimentally measured elastic moduli of the model composite materials. This result suggested that the use of layered FE models, which rely upon an isostrain assumption between the layers, can be useful in predicting the elastic properties of different lay-ups of the disc brake material.The second type of FE model analysed disc brake segments, using the experimentally measured bulk mechanical properties of the disc brake material. This FE model approximated the material as a continuum with in-plane isotropy but with different properties in the through-thickness direction. In order to validate this modelling approach, the results of the FE analysis were compared with mechanical tests on disc brake segments, which were loaded by their drive tenons in a manner intended to simulate in-service loading. The FE model showed good agreement with in-plane strains measured on the disc tenon face close to the swept area of the disc, but predicted significantly higher strains than those experimentally measured on the tenon fillet curve. This discrepancy was attributed to the existence of a steep strain gradient on the fillet curve.

Strength and Deformation Behaviour of Cap Rocks Above the CO2SINK-Reservoir

NASA Astrophysics Data System (ADS)

Mutschler, T.; Triantafyllidis, T.; Balthasar, K.; Norden, B.

2009-04-01

The cap-rock of the CO2SINK storage site close to Ketzin consists of clay rich rocks which are typical for cap rock formations above CO2 storage reservoirs. The strength and deformation behaviour of such claystone samples are therefore of fundamental importance for the characterization of secure geological storage of CO2. The elastic and anelastic deformation behaviour limits the maximum injection pressure during CO2-injection and is part of the security measures for the long term storage of CO2. The laboratory experiments where performed on samples gathered from the injection well of the Ketzin pilot test site in Germany and are compared with the elastic and anelastic behaviour of samples from the same Keuper formation in a near-surface outcrop in the Southwest of Germany showing a similar lithology. The samples from the outcrop allowed drilling of samples with a standard size of 100 mm diameter and 200 mm height as well as large samples with a diameter of 550 mm and a height of 1200 mm. The investigations have a special emphasis on the viscous behaviour of the clay stones and its scaling behaviour. A special triaxial testing procedure is applied both on standard and large size samples allowing the determination of the strength, stiffness and viscosity behaviour of the rock in one experimental run. Multi-stage technique (stepwise variation of the confining pressure) gives the strength behaviour of each single sample while applying a constant deformation rate. Stepwise varied deformation rates on the other hand lead to steps in the stress-strain-curve from which the viscosity index is determined. The viscosity index is directly used in the Norton's constitutive relations for viscoplastic simulations. The combination of tests allows for the determination of a broad range of elastic and anelastic properties. The comparison of results - both for elastic and anelastic behaviour - from standard and large samples shows that for the examined rocks a scale effect is negligible. Transition from cataclastic to non-cataclastic behaviour - the transition limit - occurs in a similar range of applied levels of pressure and deformation rates even at room temperature. The obtained transition limit is very important for the judgment of the sealing capacity and integrity of the cap rock. The deformation rates predicted for the pressure and temperature conditions of the caprock at Ketzin test site are far beneath the determined transition limit during the injection and after stop of injection. As a 0° friction angle is used for pressure and deformation limit at Ketzin, the measured elastic and anelastic behaviour of the real caprock act as additional safety margin during injection and in the post injection phase. As the examined rocks are typical for many possible storage sites, the discussed results are of importance beyond the Ketzin Pilot Experiment CO2SINK.

Phase properties of elastic waves in systems constituted of adsorbed diatomic molecules on the (001) surface of a simple cubic crystal

NASA Astrophysics Data System (ADS)

Deymier, P. A.; Runge, K.

2018-03-01

A Green's function-based numerical method is developed to calculate the phase of scattered elastic waves in a harmonic model of diatomic molecules adsorbed on the (001) surface of a simple cubic crystal. The phase properties of scattered waves depend on the configuration of the molecules. The configurations of adsorbed molecules on the crystal surface such as parallel chain-like arrays coupled via kinks are used to demonstrate not only linear but also non-linear dependency of the phase on the number of kinks along the chains. Non-linear behavior arises for scattered waves with frequencies in the vicinity of a diatomic molecule resonance. In the non-linear regime, the variation in phase with the number of kinks is formulated mathematically as unitary matrix operations leading to an analogy between phase-based elastic unitary operations and quantum gates. The advantage of elastic based unitary operations is that they are easily realizable physically and measurable.

Biomechanically based simulation of brain deformations for intraoperative image correction: coupling of elastic and fluid models

NASA Astrophysics Data System (ADS)

Hagemann, Alexander; Rohr, Karl; Stiehl, H. Siegfried

2000-06-01

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images w.r.t. intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic, and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our approach has been tested using synthetic as well as tomographic images. It turns out from experiments, that the integrated treatment of rigid, elastic, and fluid regions significantly improves the prediction results in comparison to a pure linear elastic model.

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

ON THE DECOMPOSITION OF STRESS AND STRAIN TENSORS INTO SPHERICAL AND DEVIATORIC PARTS

PubMed Central

Augusti, G.; Martin, J. B.; Prager, W.

1969-01-01

It is well known that Hooke's law for a linearly elastic, isotropic solid may be written in the form of two relations that involve only the spherical or only the deviatoric parts of the tensors of stress and strain. The example of the linearly elastic, transversely isotropic solid is used to show that this decomposition is not, in general, feasible for linearly elastic, anisotropic solids. The discussion is extended to a large class of work-hardening rigid, plastic solids, and it is shown that the considered decomposition can only be achieved for the incompressible solids of this class. PMID:16591754

Wave propagation problem for a micropolar elastic waveguide

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-04-01

A propagation problem for coupled harmonic waves of translational displacements and microrotations along the axis of a long cylindrical waveguide is discussed at present study. Microrotations modeling is carried out within the linear micropolar elasticity frameworks. The mathematical model of the linear (or even nonlinear) micropolar elasticity is also expanded to a field theory model by variational least action integral and the least action principle. The governing coupled vector differential equations of the linear micropolar elasticity are given. The translational displacements and microrotations in the harmonic coupled wave are decomposed into potential and vortex parts. Calibrating equations providing simplification of the equations for the wave potentials are proposed. The coupled differential equations are then reduced to uncoupled ones and finally to the Helmholtz wave equations. The wave equations solutions for the translational and microrotational waves potentials are obtained for a high-frequency range.

Elastic metamaterial beam with remotely tunable stiffness

NASA Astrophysics Data System (ADS)

Qian, Wei; Yu, Zhengyue; Wang, Xiaole; Lai, Yun; Yellen, Benjamin B.

2016-02-01

We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ˜30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.

Solving the Problem of Bending of Multiply Connected Plates with Elastic Inclusions

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

This paper describes a method for determining the strain state of a thin anisotropic plate with elastic arbitrarily arranged elliptical inclusions. Complex potentials are used to reduce the problem to determining functions of generalized complex variables, which, in turn, comes down to an overdetermined system of linear algebraic equations, solved by singular expansions. This paper presents the results of numerical calculations that helped establish the influence of rigidity of elastic inclusions, distances between inclusions, and their geometric characteristics on the bending moments occurring in the plate. It is found that the specific properties of distribution of moments near the apexes of linear elastic inclusions, characterized by moment intensity coefficients, occur only in the case of sufficiently rigid and elastic inclusions.

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.

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

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.

A mathematical method for quantifying in vivo mechanical behaviour of heel pad under dynamic load.

PubMed

Naemi, Roozbeh; Chatzistergos, Panagiotis E; Chockalingam, Nachiappan

2016-03-01

Mechanical behaviour of the heel pad, as a shock attenuating interface during a foot strike, determines the loading on the musculoskeletal system during walking. The mathematical models that describe the force deformation relationship of the heel pad structure can determine the mechanical behaviour of heel pad under load. Hence, the purpose of this study was to propose a method of quantifying the heel pad stress-strain relationship using force-deformation data from an indentation test. The energy input and energy returned densities were calculated by numerically integrating the area below the stress-strain curve during loading and unloading, respectively. Elastic energy and energy absorbed densities were calculated as the sum of and the difference between energy input and energy returned densities, respectively. By fitting the energy function, derived from a nonlinear viscoelastic model, to the energy density-strain data, the elastic and viscous model parameters were quantified. The viscous and elastic exponent model parameters were significantly correlated with maximum strain, indicating the need to perform indentation tests at realistic maximum strains relevant to walking. The proposed method showed to be able to differentiate between the elastic and viscous components of the heel pad response to loading and to allow quantifying the corresponding stress-strain model parameters.

Two Propositions on the Application of Point Elasticities to Finite Price Changes.

ERIC Educational Resources Information Center

Daskin, Alan J.

1992-01-01

Considers counterintuitive propositions about using point elasticities to estimate quantity changes in response to price changes. Suggests that elasticity increases with price along a linear demand curve, but falling quantity demand offsets it. Argues that point elasticity with finite percentage change in price only approximates percentage change…

Nonlinear Acoustic and Ultrasonic NDT of Aeronautical Components

NASA Astrophysics Data System (ADS)

Van Den Abeele, Koen; Katkowski, Tomasz; Mattei, Christophe

2006-05-01

In response to the demand for innovative microdamage inspection systems, with high sensitivity and undoubted accuracy, we are currently investigating the use and robustness of several acoustic and ultrasonic NDT techniques based on Nonlinear Elastic Wave Spectroscopy (NEWS) for the characterization of microdamage in aeronautical components. In this report, we illustrate the results of an amplitude dependent analysis of the resonance behaviour, both in time (signal reverberation) and in frequency (sweep) domain. The technique is applied to intact and damaged samples of Carbon Fiber Reinforced Plastics (CFRP) composites after thermal loading or mechanical fatigue. The method shows a considerable gain in sensitivity and an incontestable interpretation of the results for nonlinear signatures in comparison with the linear characteristics. For highly fatigued samples, slow dynamical effects are observed.

Variational Theory of Motion of Curved, Twisted and Extensible Elastic Rods

DTIC Science & Technology

1993-01-18

nonlinear theory such as questions of existence of solutions and global behavior have been carried out by Antman (1976). His basic work entitled "The...Aerosp. Ens. Q017/018 16 REFERENCES Antman , S.S., "Ordinary Differential Equations of Non-Linear ElastIcity 1: Foundatious of the Theories of Non-Linearly...Elutic rods and Shells," A.R.M.A. 61 (1976), 307-351. Antman , S.S., "The Theory of Rods", Handbuch der Physik, Vol. Vla/2, Springer-Verlq, Berlin

Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

NASA Astrophysics Data System (ADS)

Geng, Jun; Shen, Zhongwei; Song, Liang

2017-06-01

This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L 2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).

Nonlocal integral elasticity in nanostructures, mixtures, boundary effects and limit behaviours

NASA Astrophysics Data System (ADS)

Romano, Giovanni; Luciano, Raimondo; Barretta, Raffaele; Diaco, Marina

2018-02-01

Nonlocal elasticity is addressed in terms of integral convolutions for structural models of any dimension, that is bars, beams, plates, shells and 3D continua. A characteristic feature of the treatment is the recourse to the theory of generalised functions (distributions) to provide a unified presentation of previous proposals. Local-nonlocal mixtures are also included in the analysis. Boundary effects of convolutions on bounded domains are investigated, and analytical evaluations are provided in the general case. Methods for compensation of boundary effects are compared and discussed with a comprehensive treatment. Estimates of limit behaviours for extreme values of the nonlocal parameter are shown to give helpful information on model properties, allowing for new comments on previous proposals. Strain-driven and stress-driven models are shown to emerge by swapping the mechanical role of input and output fields in the constitutive convolution, with stress-driven elastic model leading to well-posed problems. Computations of stress-driven nonlocal one-dimensional elastic models are performed to exemplify the theoretical results.

Towards an acoustic model-based poroelastic imaging method: I. Theoretical foundation.

PubMed

Berry, Gearóid P; Bamber, Jeffrey C; Armstrong, Cecil G; Miller, Naomi R; Barbone, Paul E

2006-04-01

The ultrasonic measurement and imaging of tissue elasticity is currently under wide investigation and development as a clinical tool for the assessment of a broad range of diseases, but little account in this field has yet been taken of the fact that soft tissue is porous and contains mobile fluid. The ability to squeeze fluid out of tissue may have implications for conventional elasticity imaging, and may present opportunities for new investigative tools. When a homogeneous, isotropic, fluid-saturated poroelastic material with a linearly elastic solid phase and incompressible solid and fluid constituents is subjected to stress, the behaviour of the induced internal strain field is influenced by three material constants: the Young's modulus (E(s)) and Poisson's ratio (nu(s)) of the solid matrix and the permeability (k) of the solid matrix to the pore fluid. New analytical expressions were derived and used to model the time-dependent behaviour of the strain field inside simulated homogeneous cylindrical samples of such a poroelastic material undergoing sustained unconfined compression. A model-based reconstruction technique was developed to produce images of parameters related to the poroelastic material constants (E(s), nu(s), k) from a comparison of the measured and predicted time-dependent spatially varying radial strain. Tests of the method using simulated noisy strain data showed that it is capable of producing three unique parametric images: an image of the Poisson's ratio of the solid matrix, an image of the axial strain (which was not time-dependent subsequent to the application of the compression) and an image representing the product of the aggregate modulus E(s)(1-nu(s))/(1+nu(s))(1-2nu(s)) of the solid matrix and the permeability of the solid matrix to the pore fluid. The analytical expressions were further used to numerically validate a finite element model and to clarify previous work on poroelastography.

Extending double modulation: combinatorial rules for identifying the modulations necessary for determining elasticities in metabolic pathways.

PubMed

Giersch, C; Cornish-Bowden, A

1996-10-07

The double modulation method for determining the elasticities of pathway enzymes, originally devised by Kacser & Burns (Biochem. Soc. Trans. 7, 1149-1160, 1979), is extended to pathways of complex topological structure, including branching and feedback loops. An explicit system of linear equations for the unknown elasticities is derived. The constraints imposed on this linear system imply that modulations of more than one enzyme are not necessarily independent. Simple combinatorial rules are described for identifying without using any algebra the set of independent modulations that allow the determination of the elasticities of any enzyme. By repeated application, the minimum numbers of modulations required to determine the elasticities of all enzymes of a given pathway can be determined. The procedure is illustrated with numerous examples.

Summer Research Program (1992). Summer Faculty Research Program (SFRP) Reports. Volume 2. Armstrong Laboratory

DTIC Science & Technology

1992-12-01

desirable. In this study, the proposed model consists of a thick-walled, highly deformable elastic tube in which the blood flow is described by linearized ...presented a mechanical model consisting of linearized Navier-Stokes and finite elasticity equations to predict blood pooling under acceleration stress... linear multielement model of the cardiovascular system which can calculate blood pressures and flows at any point in the cardio- vascular system. It

Dynamics of an elastic sphere containing a thin creeping region and immersed in an acoustic region for similar viscous-elastic and acoustic time- and length-scales

NASA Astrophysics Data System (ADS)

Gat, Amir; Friedman, Yonathan

2017-11-01

The characteristic time of low-Reynolds number fluid-structure interaction scales linearly with the ratio of fluid viscosity to solid Young's modulus. For sufficiently large values of Young's modulus, both time- and length-scales of the viscous-elastic dynamics may be similar to acoustic time- and length-scales. However, the requirement of dominant viscous effects limits the validity of such regimes to micro-configurations. We here study the dynamics of an acoustic plane wave impinging on the surface of a layered sphere, immersed within an inviscid fluid, and composed of an inner elastic sphere, a creeping fluid layer and an external elastic shell. We focus on configurations with similar viscous-elastic and acoustic time- and length-scales, where the viscous-elastic speed of interaction between the creeping layer and the elastic regions is similar to the speed of sound. By expanding the linearized spherical Reynolds equation into the relevant spectral series solution for the hyperbolic elastic regions, a global stiffness matrix of the layered elastic sphere was obtained. This work relates viscous-elastic dynamics to acoustic scattering and may pave the way to the design of novel meta-materials with unique acoustic properties. ISF 818/13.

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

NASA Astrophysics Data System (ADS)

Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.

2014-08-01

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

Modeling of Soft Poroelastic Tissue in Time-Harmonic MR Elastography

PubMed Central

Perriñez, Phillip R.; Kennedy, Francis E.; Van Houten, Elijah E. W.; Weaver, John B.; Paulsen, Keith D.

2010-01-01

Elastography is an emerging imaging technique that focuses on assessing the resistance to deformation of soft biological tissues in vivo. Magnetic resonance elastography (MRE) uses measured displacement fields resulting from low-amplitude, low-frequency (10 Hz–1 kHz) time-harmonic vibration to recover images of the elastic property distribution of tissues including breast, liver, muscle, prostate, and brain. While many soft tissues display complex time-dependent behavior not described by linear elasticity, the models most commonly employed in MRE parameter reconstructions are based on elastic assumptions. Further, elasticity models fail to include the interstitial fluid phase present in vivo. Alternative continuum models, such as consolidation theory, are able to represent tissue and other materials comprising two distinct phases, generally consisting of a porous elastic solid and penetrating fluid. MRE reconstructions of simulated elastic and poroelastic phantoms were performed to investigate the limitations of current-elasticity-based methods in producing accurate elastic parameter estimates in poroelastic media. The results indicate that linearly elastic reconstructions of fluid-saturated porous media at amplitudes and frequencies relevant to steady-state MRE can yield misleading effective property distributions resulting from the complex interaction between their solid and fluid phases. PMID:19272864

Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

NASA Astrophysics Data System (ADS)

Pepi, John W.

2017-08-01

Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

Modelling strong seismic ground motion: three-dimensional loading path versus wavefield polarization

NASA Astrophysics Data System (ADS)

Santisi d'Avila, Maria Paola; Lenti, Luca; Semblat, Jean-François

2012-09-01

Seismic waves due to strong earthquakes propagating in surficial soil layers may both reduce soil stiffness and increase the energy dissipation into the soil. To investigate seismic wave amplification in such cases, past studies have been devoted to one-directional shear wave propagation in a soil column (1D-propagation) considering one motion component only (1C-polarization). Three independent purely 1C computations may be performed ('1D-1C' approach) and directly superimposed in the case of weak motions (linear behaviour). This research aims at studying local site effects by considering seismic wave propagation in a 1-D soil profile accounting for the influence of the 3-D loading path and non-linear hysteretic behaviour of the soil. In the proposed '1D-3C' approach, the three components (3C-polarization) of the incident wave are simultaneously propagated into a horizontal multilayered soil. A 3-D non-linear constitutive relation for the soil is implemented in the framework of the Finite Element Method in the time domain. The complex rheology of soils is modelled by mean of a multisurface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan type. The great advantage of this choice is that the only data needed to describe the model is the modulus reduction curve. A parametric study is carried out to characterize the changes in the seismic motion of the surficial layers due to both incident wavefield properties and soil non-linearities. The numerical simulations show a seismic response depending on several parameters such as polarization of seismic waves, material elastic and dynamic properties, as well as on the impedance contrast between layers and frequency content and oscillatory character of the input motion. The 3-D loading path due to the 3C-polarization leads to multi-axial stress interaction that reduces soil strength and increases non-linear effects. The non-linear behaviour of the soil may have beneficial or detrimental effects on the seismic response at the free surface, depending on the energy dissipation rate. Free surface time histories, stress-strain hysteresis loops and in-depth profiles of octahedral stress and strain are estimated for each soil column. The combination of three separate 1D-1C non-linear analyses is compared to the proposed 1D-3C approach, evidencing the influence of the 3C-polarization and the 3-D loading path on strong seismic motions.

Effect of wire size on maxillary arch force/couple systems for a simulated high canine malocclusion.

PubMed

Major, Paul W; Toogood, Roger W; Badawi, Hisham M; Carey, Jason P; Seru, Surbhi

2014-12-01

To better understand the effects of copper nickel titanium (CuNiTi) archwire size on bracket-archwire mechanics through the analysis of force/couple distributions along the maxillary arch. The hypothesis is that wire size is linearly related to the forces and moments produced along the arch. An Orthodontic Simulator was utilized to study a simplified high canine malocclusion. Force/couple distributions produced by passive and elastic ligation using two wire sizes (Damon 0.014 and 0.018 inch) measured with a sample size of 144. The distribution and variation in force/couple loading around the arch is a complicated function of wire size. The use of a thicker wire increases the force/couple magnitudes regardless of ligation method. Owing to the non-linear material behaviour of CuNiTi, this increase is less than would occur based on linear theory as would apply for stainless steel wires. The results demonstrate that an increase in wire size does not result in a proportional increase of applied force/moment. This discrepancy is explained in terms of the non-linear properties of CuNiTi wires. This non-proportional force response in relation to increased wire size warrants careful consideration when selecting wires in a clinical setting. © 2014 British Orthodontic Society.

Small vibrations of a linearly elastic body surrounded by heavy, incompressible, non-Newtonian fluids with free surfaces

NASA Astrophysics Data System (ADS)

Licht, Christian; Tran Thu Ha

2005-02-01

We consider the small transient motions of a coupled system constituted by a linearly elastic body and two heavy, incompressible, non-Newtonian fluids.Through a formulation in terms of non-linear evolution equations in Hilbert spaces of possible states with finite mechanical energy, we obtain existence and uniqueness results and study the influence of gravity. To cite this article: C. Licht, Tran Thu Ha, C. R. Mecanique 333 (2005).

Mechanical properties and flexure behaviour of lightweight foamed concrete incorporating coir fibre

NASA Astrophysics Data System (ADS)

Mohamad, Noridah; Afif Iman, Muhamad; Othuman Mydin, M. A.; Samad, A. A. A.; Rosli, J. A.; Noorwirdawati, A.

2018-04-01

This paper presents an experimental investigation on the mechanical properties and flexural behaviour of lightweight foamed concrete (LFC) with added coir fibre as filler. The compressive strength (Pt), tensile strength (Ft), modulus of elasticity (E), ultimate load and crack pattern of the foamed concrete were determined. The coir fibre was added to the foamed concrete mixture at 0.1%, 0.2% and 0.3% of the total weight of cement. Effects of various percentage of coir fibre used on foam concrete’s mechanical and properties and flexural behaviour were studied and analysed. It was found that the increase percentage of fibre resulted in increase in compressive strength, tensile strength and modulus of elasticity of LFC mixture. LFC with added coir of 0.3% experienced the smallest crack propagation.

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

NASA Technical Reports Server (NTRS)

Jacquotte, Olivier P.; Oden, J. Tinsley

1994-01-01

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Elastic-Brittle-Plastic Behaviour of Shale Reservoirs and Its Implications on Fracture Permeability Variation: An Analytical Approach

NASA Astrophysics Data System (ADS)

Masoudian, Mohsen S.; Hashemi, Mir Amid; Tasalloti, Ali; Marshall, Alec M.

2018-05-01

Shale gas has recently gained significant attention as one of the most important unconventional gas resources. Shales are fine-grained rocks formed from the compaction of silt- and clay-sized particles and are characterised by their fissured texture and very low permeability. Gas exists in an adsorbed state on the surface of the organic content of the rock and is freely available within the primary and secondary porosity. Geomechanical studies have indicated that, depending on the clay content of the rock, shales can exhibit a brittle failure mechanism. Brittle failure leads to the reduced strength of the plastic zone around a wellbore, which can potentially result in wellbore instability problems. Desorption of gas during production can cause shrinkage of the organic content of the rock. This becomes more important when considering the use of shales for CO2 sequestration purposes, where CO2 adsorption-induced swelling can play an important role. These phenomena lead to changes in the stress state within the rock mass, which then influence the permeability of the reservoir. Thus, rigorous simulation of material failure within coupled hydro-mechanical analyses is needed to achieve a more systematic and accurate representation of the wellbore. Despite numerous modelling efforts related to permeability, an adequate representation of the geomechanical behaviour of shale and its impact on permeability and gas production has not been achieved. In order to achieve this aim, novel coupled poro-elastoplastic analytical solutions are developed in this paper which take into account the sorption-induced swelling and the brittle failure mechanism. These models employ linear elasticity and a Mohr-Coulomb failure criterion in a plane-strain condition with boundary conditions corresponding to both open-hole and cased-hole completions. The post-failure brittle behaviour of the rock is defined using residual strength parameters and a non-associated flow rule. Swelling and shrinkage are considered to be elastic and are defined using a Langmuir-like curve, which is directly related to the reservoir pressure. The models are used to evaluate the stress distribution and the induced change in permeability within a reservoir. Results show that development of a plastic zone near the wellbore can significantly impact fracture permeability and gas production. The capabilities and limitations of the models are discussed and potential future developments related to modelling of permeability in brittle shales under elastoplastic deformations are identified.

Generation of wavy structure on lipid membrane by peripheral proteins: a linear elastic analysis.

PubMed

Mahata, Paritosh; Das, Sovan Lal

2017-05-01

We carry out a linear elastic analysis to study wavy structure generation on lipid membrane by peripheral membrane proteins. We model the lipid membrane as linearly elastic and anisotropic material. The hydrophobic insertion by proteins into the lipid membrane has been idealized as penetration of rigid rod-like inclusions into the membrane and the electrostatic interaction between protein and membrane has been modeled by a distributed surface traction acting on the membrane surface. With the proposed model we study curvature generation by several binding domains of peripheral membrane proteins containing BAR domains and amphipathic alpha-helices. It is observed that electrostatic interaction is essential for curvature generation by the BAR domains. © 2017 Federation of European Biochemical Societies.

Muscle-spring dynamics in time-limited, elastic movements.

PubMed

Rosario, M V; Sutton, G P; Patek, S N; Sawicki, G S

2016-09-14

Muscle contractions that load in-series springs with slow speed over a long duration do maximal work and store the most elastic energy. However, time constraints, such as those experienced during escape and predation behaviours, may prevent animals from achieving maximal force capacity from their muscles during spring-loading. Here, we ask whether animals that have limited time for elastic energy storage operate with springs that are tuned to submaximal force production. To answer this question, we used a dynamic model of a muscle-spring system undergoing a fixed-end contraction, with parameters from a time-limited spring-loader (bullfrog: Lithobates catesbeiana) and a non-time-limited spring-loader (grasshopper: Schistocerca gregaria). We found that when muscles have less time to contract, stored elastic energy is maximized with lower spring stiffness (quantified as spring constant). The spring stiffness measured in bullfrog tendons permitted less elastic energy storage than was predicted by a modelled, maximal muscle contraction. However, when muscle contractions were modelled using biologically relevant loading times for bullfrog jumps (50 ms), tendon stiffness actually maximized elastic energy storage. In contrast, grasshoppers, which are not time limited, exhibited spring stiffness that maximized elastic energy storage when modelled with a maximal muscle contraction. These findings demonstrate the significance of evolutionary variation in tendon and apodeme properties to realistic jumping contexts as well as the importance of considering the effect of muscle dynamics and behavioural constraints on energy storage in muscle-spring systems. © 2016 The Author(s).

Temperature dependence of elastic and strength properties of T300/5208 graphite-epoxy

NASA Technical Reports Server (NTRS)

Milkovich, S. M.; Herakovich, C. T.

1984-01-01

Experimental results are presented for the elastic and strength properties of T300/5208 graphite-epoxy at room temperature, 116K (-250 F), and 394K (+250 F). Results are presented for unidirectional 0, 90, and 45 degree laminates, and + or - 30, + or - 45, and + or - 60 degree angle-ply laminates. The stress-strain behavior of the 0 and 90 degree laminates is essentially linear for all three temperatures and that the stress-strain behavior of all other laminates is linear at 116K. A second-order curve provides the best fit for the temperature is linear at 116K. A second-order curve provides the best fit for the temperature dependence of the elastic modulus of all laminates and for the principal shear modulus. Poisson's ratio appears to vary linearly with temperature. all moduli decrease with increasing temperature except for E (sub 1) which exhibits a small increase. The strength temperature dependence is also quadratic for all laminates except the 0 degree - laminate which exhibits linear temperature dependence. In many cases the temperature dependence of properties is nearly linear.

On the shock response of PCTFE (Kel-F 81¯)

NASA Astrophysics Data System (ADS)

Wood, D. C.; Appleby-Thomas, G. J.; Fitzmaurice, B. C.; Hameed, A.; Millett, J. C. F.; Hazell, P. J.

2017-01-01

The polymeric material PCTFE (Kel-F 81®) has found a useful niche in explosive research due to its use not only an explosive binder but also as a explosive simulant. Knowledge of shock propagation in explosives is of paramount importance primarily from a safety perspective both in terms of reaction to a designed stimulus and to off-normal (accident) events. To this end, as part of a more general investigation into the relationship between polymeric structure and high strain-rate response, the dynamic response of PCFTE (more commonly known as Kel-F 81®) has been investigated via a series of plate-impact experiments. Using this technique both the shock and release behaviour of PCTFE have been investigated. The data obtained for the shock response agreed with previously obtained data from the literature. Deviation from the Hugoniot was seen in the pressure-particle velocity plane, a response attributed here to material strength. With regards to the behaviour of the release Hugoniot, a two-tiered response was observed. Initially a tensile elastic wave with an approximate velocity of 3.00 mm μs-1 was noted until a particle velocity of 0.36 mm μs-1. After this initial region a linear release Hugoniot was apparent, a response comparable to behaviour seen in other polymers.

Stability Analysis of an Encapsulated Microbubble against Gas Diffusion

PubMed Central

Katiyar, Amit; Sarkar, Kausik

2009-01-01

Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although, bubbles, containing gases other than air is considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided. PMID:20005522

Locality and rapidity of the ultra-large elastic deformation of Nb nanowires in a NiTi phase-transforming matrix

DOE PAGES

Wang, Shan; Cui, Lishan; Hao, Shijie; ...

2014-10-24

This study investigated the elastic deformation behaviour of Nb nanowires embedded in a NiTi matrix. The Nb nanowires exhibited an ultra-large elastic deformation, which is found to be dictated by the martensitic transformation of the NiTi matrix, thus exhibiting unique characteristics of locality and rapidity. These are in clear contrast to our conventional observation of elastic deformations of crystalline solids, which is a homogeneous lattice distortion with a strain rate controlled by the applied strain. The Nb nanowires are also found to exhibit elastic-plastic deformation accompanying the martensitic transformation of the NiTi matrix in the case when the transformation strainmore » of the matrix over-matches the elastic strain limit of the nanowires, or exhibit only elastic deformation in the case of under-matching. Such insight provides an important opportunity for elastic strain engineering and composite design.« less

A model for compression-weakening materials and the elastic fields due to contractile cells

NASA Astrophysics Data System (ADS)

Rosakis, Phoebus; Notbohm, Jacob; Ravichandran, Guruswami

2015-12-01

We construct a homogeneous, nonlinear elastic constitutive law that models aspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers in such networks buckle when in compression. We model this as a loss of stiffness in compression in the stress-strain relations of the homogeneous constitutive model. Problems that model a contracting biological cell in a finite matrix are solved. It is found that matrix displacements and stresses induced by cell contraction decay slower (with distance from the cell) in a compression weakening material than linear elasticity would predict. This points toward a mechanism for long-range cell mechanosensing. In contrast, an expanding cell would induce displacements that decay faster than in a linear elastic matrix.

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

Wang, Shan; Cui, Lishan; Hao, Shijie

This study investigated the elastic deformation behaviour of Nb nanowires embedded in a NiTi matrix. The Nb nanowires exhibited an ultra-large elastic deformation, which is found to be dictated by the martensitic transformation of the NiTi matrix, thus exhibiting unique characteristics of locality and rapidity. These are in clear contrast to our conventional observation of elastic deformations of crystalline solids, which is a homogeneous lattice distortion with a strain rate controlled by the applied strain. The Nb nanowires are also found to exhibit elastic-plastic deformation accompanying the martensitic transformation of the NiTi matrix in the case when the transformation strainmore » of the matrix over-matches the elastic strain limit of the nanowires, or exhibit only elastic deformation in the case of under-matching. Such insight provides an important opportunity for elastic strain engineering and composite design.« less

Elastic and thermal expansion asymmetry in dense molecular materials.

PubMed

Burg, Joseph A; Dauskardt, Reinhold H

2016-09-01

The elastic modulus and coefficient of thermal expansion are fundamental properties of elastically stiff molecular materials and are assumed to be the same (symmetric) under both tension and compression loading. We show that molecular materials can have a marked asymmetric elastic modulus and coefficient of thermal expansion that are inherently related to terminal chemical groups that limit molecular network connectivity. In compression, terminal groups sterically interact to stiffen the network, whereas in tension they interact less and disconnect the network. The existence of asymmetric elastic and thermal expansion behaviour has fundamental implications for computational approaches to molecular materials modelling and practical implications on the thermomechanical strains and associated elastic stresses. We develop a design space to control the degree of elastic asymmetry in molecular materials, a vital step towards understanding their integration into device technologies.

Modeling Elastic Wave Propagation from an Underground Chemical Explosion Using Higher Order Finite Difference Approximation: Theory, Validation and Application to SPE

NASA Astrophysics Data System (ADS)

Hirakawa, E. T.; Ezzedine, S. M.; Petersson, A.; Sjogreen, B.; Vorobiev, O.; Pitarka, A.; Antoun, T.; Walter, W. R.

2016-12-01

Motions from underground explosions are governed by non-linear hydrodynamic response of material. However, the numerical calculation of this non-linear constitutive behavior is computationally intensive in contrast to the elastic and acoustic linear wave propagation solvers. Here, we develop a hybrid modeling approach with one-way hydrodynamic-to-elastic coupling in three dimensions in order to propagate explosion generated ground motions from the non-linear near-source region to the far-field. Near source motions are computed using GEODYN-L, a Lagrangian hydrodynamics code for high-energy loading of earth materials. Motions on a dense grid of points sampled on two nested shells located beyond the non-linear damaged zone are saved, and then passed to SW4, an anelastic anisotropic fourth order finite difference code for seismic wave modeling. Our coupling strategy is based on the decomposition and uniqueness theorems where motions are introduced into SW4 as a boundary source and continue to propagate as elastic waves at a much lower computational cost than by using GEODYN-L to cover the entire near- and the far-field domain. The accuracy of the numerical calculations and the coupling strategy is demonstrated in cases with a purely elastic medium as well as non-linear medium. Our hybrid modeling approach is applied to SPE-4' and SPE-5 which are the most recent underground chemical explosions conducted at the Nevada National Security Site (NNSS) where the Source Physics Experiments (SPE) are performed. Our strategy by design is capable of incorporating complex non-linear effects near the source as well as volumetric and topographic material heterogeneity along the propagation path to receiver, and provides new prospects for modeling and understanding explosion generated seismic waveforms. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-698608.

The demand for sports and exercise: results from an illustrative survey.

PubMed

Anokye, Nana Kwame; Pokhrel, Subhash; Buxton, Martin; Fox-Rushby, Julia

2012-06-01

There is a paucity of empirical evidence on the extent to which price and perceived benefits affect the level of participation in sports and exercise. Using an illustrative sample of 60 adults at Brunel University, West London, we investigate the determinants of demand for sports and exercise. The data were collected through face-to-face interviews that covered indicators of sports and exercise behaviour; money/time price and perceived benefits of participation; and socio-economic/demographic details. Count, linear and probit regression models were fitted as appropriate. Seventy eight per cent of the sample participated in sports and exercise and spent an average of £27 per month and an average of 20 min travelling per occasion of sports and exercise. The demand for sport and exercise was negatively associated with time (travel or access time) and 'variable' price and positively correlated with 'fixed' price. Demand was price inelastic, except in the case of meeting the UK government's recommended level of participation, which is time price elastic (elasticity = -2.2). The implications of data from a larger nationally representative sample as well as the role of economic incentives in influencing uptake of sports and exercise are discussed.

On the nature of the excess heat capacity of mixing

NASA Astrophysics Data System (ADS)

Benisek, Artur; Dachs, Edgar

2011-03-01

The excess vibrational entropy (Δ S {vib/ex}) of several silicate solid solutions are found to be linearly correlated with the differences in end-member volumes (Δ V i ) and end-member bulk moduli (Δκ i ). If a substitution produces both, larger and elastically stiffer polyhedra, then the substituted ion will find itself in a strong enlarged structure. The frequency of its vibration is decreased because of the increase in bond lengths. Lowering of frequencies produces larger heat capacities, which give rise to positive excess vibrational entropies. If a substitution produces larger but elastically softer polyhedra, then increase and decrease of mean bond lengths may be similar in magnitude and their effect on the vibrational entropy tends to be compensated. The empirical relationship between Δ S {vib/ex}, Δ V i and Δκ i , as described by Δ S {vib/ex} = (Δ V i + mΔκ i ) f, was calibrated on six silicate solid solutions (analbite-sanidine, pyrope-grossular, forsterite-fayalite, analbite-anorthite, anorthite-sanidine, CaTs-diopside) yielding m = 0.0246 and f = 2.926. It allows the prediction of Δ S {vib/ex} behaviour of a solid solution based on its volume and bulk moduli end-member data.

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

NASA Technical Reports Server (NTRS)

Hsu, Su-Yuen; Chang, Chau-Lyan

2007-01-01

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

QUANTITATIVE NON-DESTRUCTIVE EVALUATION (QNDE) OF THE ELASTIC MODULI OF POROUS TIAL ALLOYS

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

Yeheskel, O.

2008-02-28

The elastic moduli of {gamma}-TiA1 were studied in porous samples consolidated by various techniques e.g. cold isostatic pressing (CIP), pressure-less sintering, or hot isostatic pressing (HIP). Porosity linearly affects the dynamic elastic moduli of samples. The results indicate that the sound wave velocities and the elastic moduli affected by the processing route and depend not only on the attained density but also on the consolidation temperature. In this paper we show that there is linear correlation between the shear and the longitudinal sound velocities in porous TiA1. This opens the way to use a single sound velocity as a toolmore » for quantitative non-destructive evaluation (QNDE) of porous TiA1 alloys. Here we demonstrate the applicability of an equation derived from the elastic theory and used previously for porous cubic metals.« less

Mapping forces in a 3D elastic assembly of grains

NASA Astrophysics Data System (ADS)

Saadatfar, Mohammad; Sheppard, Adrian P.; Senden, Tim J.; Kabla, Alexandre J.

2012-01-01

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterise their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the material's microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems.

Engineered elastomeric proteins with dual elasticity can be controlled by a molecular regulator.

PubMed

Cao, Yi; Li, Hongbin

2008-08-01

Elastomeric proteins are molecular springs that confer excellent mechanical properties to many biological tissues and biomaterials. Depending on the role performed by the tissue or biomaterial, elastomeric proteins can behave as molecular springs or shock absorbers. Here we combine single-molecule atomic force microscopy and protein engineering techniques to create elastomeric proteins that can switch between two distinct types of mechanical behaviour in response to the binding of a molecular regulator. The proteins are mechanically labile by design and behave as entropic springs with an elasticity that is governed by their configurational entropy. However, when a molecular regulator binds to the protein, it switches into a mechanically stable state and can act as a shock absorber. These engineered proteins effectively mimic and combine the two extreme forms of elastic behaviour found in natural elastomeric proteins, and thus represent a new type of smart nanomaterial that will find potential applications in nanomechanics and material sciences.

Instability of fiber-reinforced viscoelastic composite plates to in-plane compressive loads

NASA Technical Reports Server (NTRS)

Chandiramani, N. K.; Librescu, L.

1990-01-01

This study analyzes the stability behavior of unidirectional fiber-reinforced composite plates with viscoelastic material behavior subject to in-plane biaxial compressive edge loads. To predict the effective time-dependent material properties, elastic fibers embedded in a linearly viscoelastic matrix are examined. The micromechanical relations developed for a transversely isotropic medium are discussed along with the correspondence principle of linear viscoelasticity. It is concluded that the stability boundary obtained for a viscoelastic plate is lower (more critical) than its elastic counterpart, and the transverse shear deformation effects are more pronounced in viscoelastic plates than in their elastic counterparts.

Dynamic energy release rate in couple-stress elasticity

NASA Astrophysics Data System (ADS)

Morini, L.; Piccolroaz, A.; Mishuris, G.

2013-07-01

This paper is concerned with energy release rate for dynamic steady state crack problems in elastic materials with microstructures. A Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behaviour of the material is described by the theory of couple-stress elasticity developed by Koiter. A general expression for the dynamic J-integral including both traslational and micro-rotational inertial contributions is derived, and the conservation of this integral on a path surrounding the crack tip is demonstrated.

Contact mechanics at nanometric scale using nanoindentation technique for brittle and ductile materials.

PubMed

Roa, J J; Rayon, E; Morales, M; Segarra, M

2012-06-01

In the last years, Nanoindentation or Instrumented Indentation Technique has become a powerful tool to study the mechanical properties at micro/nanometric scale (commonly known as hardness, elastic modulus and the stress-strain curve). In this review, the different contact mechanisms (elastic and elasto-plastic) are discussed, the recent patents for each mechanism (elastic and elasto-plastic) are summarized in detail, and the basic equations employed to know the mechanical behaviour for brittle and ductile materials are described.

Couple stress theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

Improved Indentation Test for Measuring Nonlinear Elasticity

NASA Technical Reports Server (NTRS)

Eldridge, Jeffrey I.

2004-01-01

A cylindrical-punch indentation technique has been developed as a means of measuring the nonlinear elastic responses of materials -- more specifically, for measuring the moduli of elasticity of materials in cases in which these moduli vary with applied loads. This technique offers no advantage for characterizing materials that exhibit purely linear elastic responses (constant moduli of elasticity, independent of applied loads). However, the technique offers a significant advantage for characterizing such important materials as plasma-sprayed thermal-barrier coatings, which, in cyclic loading, exhibit nonlinear elasticity with hysteresis related to compaction and sliding within their microstructures.

The relationship between the instantaneous velocity field and the rate of moment release in the lithosphere

USGS Publications Warehouse

Pollitz, F.F.

2003-01-01

Instantaneous velocity gradients within the continental lithosphere are often related to the tectonic driving forces. This relationship is direct if the forces are secular, as for the case of loading of a locked section of a subduction interface by the downgoing plate. If the forces are static, as for the case of lateral variations in gravitational potential energy, then velocity gradients can be produced only if the lithosphere has, on average, zero strength. The static force model may be related to the long-term velocity field but not the instantaneous velocity field (typically measured geodetically over a period of several years) because over short time intervals the upper lithosphere behaves elastically. In order to describe both the short- and long-term behaviour of an (elastic) lithosphere-(viscoelastic) asthenosphere system in a self-consistent manner, I construct a deformation model termed the expected interseismic velocity (EIV) model. Assuming that the lithosphere is populated with faults that rupture continually, each with a definite mean recurrence time, and that the Earth is well approximated as a linear elastic-viscoelastic coupled system, I derive a simple relationship between the instantaneous velocity field and the average rate of moment release in the lithosphere. Examples with synthetic fault networks demonstrate that velocity gradients in actively deforming regions may to a large extent be the product of compounded viscoelastic relaxation from past earthquakes on hundreds of faults distributed over large ( ≥106 km2) areas.

Time-dependent strains and stresses in a pumpkin balloon

NASA Technical Reports Server (NTRS)

Gerngross, T.; Xu, Y.; Pellegrino, S.

2006-01-01

This paper presents a study of pumpkin-shaped superpressure balloons, consisting of gores made from a thin polymeric film attached to high stiffness, meridional tendons. This type of design is being used for the NASA ULDB balloons. The gore film shows considerable time-dependent stress relaxation, whereas the behaviour of the tendons is essentially time-independent. Upon inflation and pressurization, the "instantaneous", i.e. linear-elastic strain and stress distribution in the film show significantly higher values in the meridional direction. However, over time, and due to the biaxial visco-elastic stress relaxation of the the material, the hoop strains increase and the meridional stresses decrease, whereas the remaining strain and stress components remain substantially unchanged. These results are important for a correct assessment of the structural integrity of a pumpkin balloon in a long-duration mission, both in terms of the material performance and the overall stability of the shape of the balloon. An experimental investigation of the time dependence of the biaxial strain distribution in the film of a 4 m diameter, 48 gore pumpkin balloon is presented. The inflated shape of selected gores has been measured using photogrammetry and the time variation in strain components at some particular points of these gores has been measured under constant pressure and temperature. The results show good correlation with a numerical study, using the ABAQUS finite-element package, that includes a widely used model of the visco-elastic response of the gore material:

Application of high-speed photography to the study of high-strain-rate materials testing

NASA Astrophysics Data System (ADS)

Ruiz, D.; Harding, John; Noble, J. P.; Hillsdon, Graham K.

1991-04-01

There is a growing interest in material behaviour at strain rates greater than 104sec1, for instance in the design of aero-engine turbine blades. It is necessary therefore, to develop material testing techniques that give well-defined information on mechanical behaviour in this very high strain-rate regime. A number of techniques are available, including the expanding ring test1, a miniaturised compression Hopkinson bar technique using direct impact and the double-notch shear test3 which has been described by Nicholas4 as "one of the most promising for future studies in dynamic plasticity". However, although it is believed to be a good test for determining the flow stress at shear strain rates of 104sec and above, the design of specimen used makes an accurate determination of strain extremely difficult while, in the later stages of the test the deformation mode involves rotation as well as shear. If this technique is to be used, therefore, it is necessary to examine in detail the progressive deformation and state of stress within the specimen during the impact process. An attempt can then be made to assess how far the data obtained is a reliable measure of the specimen material response and the test can be calibrated. An extensive three stage analysis has been undertaken. In the first stage, reported in a previous paper5, the initial elastic behaviour was studied. Dynamic photoelastic experiments were used to support linear elastic numerical results derived by the finite element method. Good qualitative agreement was obtained between the photoelastic experiment and the numerical model and the principal source of error in the elastic region of the double-notch shear test was identified as the assumption that all deformation of the specimen is concentrated in the two shear zones. For the epoxy (photoelastic) specimen a calibration factor of 5.3 was determined. This factor represents the ratio between the defined (nominal) gauge length and the effective gauge length. The second stage of the analysis of the double-notch shear (DNS) specimen is described in this paper. This consists of the use of ultra-high speed photography to provide information on the plastic deformation behaviour of the specimen. Two different high speed cine cameras were used for this work, a Hadland "Imacon" 792 electronic image converter camera and a Cordin 377 rotating mirror-drum optical camera. Implementation of the two cameras and photographic results are briefly compared and contrasted here. Stage three of this work consists of an advanced numerical analysis of the elasto-plastic, strain rate dependent behaviour of the DNS specimen. The principle intention of the authors was to use the physical data collected from high speed photographs for correlation with this work. Full details of the numerical work are presented elsewhere6 but some salient results will be given here for completeness.

A Galerkin approximation for linear elastic shallow shells

NASA Astrophysics Data System (ADS)

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

Influence of stretch-shortening cycle on mechanical behaviour of triceps surae during hopping.

PubMed

Belli, A; Bosco, C

1992-04-01

Six subjects performed a first series of vertical plantar flexions and a second series of vertical rebounds, both involving muscle triceps surae exclusively. Vertical displacements, vertical forces and ankle angles were recorded during the entire work period of 60 seconds per series. In addition, expired gases were collected during the test and recovery for determination of the energy expenditure. Triceps surae was mechanically modelled with a contractile component and with an elastic component. Mechanical behaviour and work of the different muscle components were determined in both series. The net muscular efficiency calculated from the work performed by the centre of gravity was 17.5 +/- 3.0% (mean +/- SD) in plantar flexions and 29.9 +/- 4.8% in vertical rebounds. The net muscle efficiency calculated from the work performed by the contractile component was 17.4 +/- 2.9% in plantar flexions and 16.1 +/- 1.4% in vertical rebounds. These results suggest that the muscular efficiency differences do not reflect muscle contractile component efficiency but essentially the storage and recoil of elastic energy. This is supported by the relationship (P less than 0.01) found in vertical rebounds between the extra work and the elastic component work. A detailed observation of the mechanical behaviour of muscle mechanical components showed that the strategy to maximize the elastic work depends also on the force-velocity characteristics of the movement and that the eccentric-concentric work of the contractile component does not always correspond respectively to the ankle extension-flexion.

ZIP2DL: An Elastic-Plastic, Large-Rotation Finite-Element Stress Analysis and Crack-Growth Simulation Program

NASA Technical Reports Server (NTRS)

Deng, Xiaomin; Newman, James C., Jr.

1997-01-01

ZIP2DL is a two-dimensional, elastic-plastic finte element program for stress analysis and crack growth simulations, developed for the NASA Langley Research Center. It has many of the salient features of the ZIP2D program. For example, ZIP2DL contains five material models (linearly elastic, elastic-perfectly plastic, power-law hardening, linear hardening, and multi-linear hardening models), and it can simulate mixed-mode crack growth for prescribed crack growth paths under plane stress, plane strain and mixed state of stress conditions. Further, as an extension of ZIP2D, it also includes a number of new capabilities. The large-deformation kinematics in ZIP2DL will allow it to handle elastic problems with large strains and large rotations, and elastic-plastic problems with small strains and large rotations. Loading conditions in terms of surface traction, concentrated load, and nodal displacement can be applied with a default linear time dependence or they can be programmed according to a user-defined time dependence through a user subroutine. The restart capability of ZIP2DL will make it possible to stop the execution of the program at any time, analyze the results and/or modify execution options and resume and continue the execution of the program. This report includes three sectons: a theoretical manual section, a user manual section, and an example manual secton. In the theoretical secton, the mathematics behind the various aspects of the program are concisely outlined. In the user manual section, a line-by-line explanation of the input data is given. In the example manual secton, three types of examples are presented to demonstrate the accuracy and illustrate the use of this program.

Inelastic behaviour of collagen networks in cell-matrix interactions and mechanosensation.

PubMed

Mohammadi, Hamid; Arora, Pamma D; Simmons, Craig A; Janmey, Paul A; McCulloch, Christopher A

2015-01-06

The mechanical properties of extracellular matrix proteins strongly influence cell-induced tension in the matrix, which in turn influences cell function. Despite progress on the impact of elastic behaviour of matrix proteins on cell-matrix interactions, little is known about the influence of inelastic behaviour, especially at the large and slow deformations that characterize cell-induced matrix remodelling. We found that collagen matrices exhibit deformation rate-dependent behaviour, which leads to a transition from pronounced elastic behaviour at fast deformations to substantially inelastic behaviour at slow deformations (1 μm min(-1), similar to cell-mediated deformation). With slow deformations, the inelastic behaviour of floating gels was sensitive to collagen concentration, whereas attached gels exhibited similar inelastic behaviour independent of collagen concentration. The presence of an underlying rigid support had a similar effect on cell-matrix interactions: cell-induced deformation and remodelling were similar on 1 or 3 mg ml(-1) attached collagen gels while deformations were two- to fourfold smaller in floating gels of high compared with low collagen concentration. In cross-linked collagen matrices, which did not exhibit inelastic behaviour, cells did not respond to the presence of the underlying rigid foundation. These data indicate that at the slow rates of collagen compaction generated by fibroblasts, the inelastic responses of collagen gels, which are influenced by collagen concentration and the presence of an underlying rigid foundation, are important determinants of cell-matrix interactions and mechanosensation. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Inelastic behaviour of collagen networks in cell–matrix interactions and mechanosensation

PubMed Central

Mohammadi, Hamid; Arora, Pamma D.; Simmons, Craig A.; Janmey, Paul A.; McCulloch, Christopher A.

2015-01-01

The mechanical properties of extracellular matrix proteins strongly influence cell-induced tension in the matrix, which in turn influences cell function. Despite progress on the impact of elastic behaviour of matrix proteins on cell–matrix interactions, little is known about the influence of inelastic behaviour, especially at the large and slow deformations that characterize cell-induced matrix remodelling. We found that collagen matrices exhibit deformation rate-dependent behaviour, which leads to a transition from pronounced elastic behaviour at fast deformations to substantially inelastic behaviour at slow deformations (1 μm min−1, similar to cell-mediated deformation). With slow deformations, the inelastic behaviour of floating gels was sensitive to collagen concentration, whereas attached gels exhibited similar inelastic behaviour independent of collagen concentration. The presence of an underlying rigid support had a similar effect on cell–matrix interactions: cell-induced deformation and remodelling were similar on 1 or 3 mg ml−1 attached collagen gels while deformations were two- to fourfold smaller in floating gels of high compared with low collagen concentration. In cross-linked collagen matrices, which did not exhibit inelastic behaviour, cells did not respond to the presence of the underlying rigid foundation. These data indicate that at the slow rates of collagen compaction generated by fibroblasts, the inelastic responses of collagen gels, which are influenced by collagen concentration and the presence of an underlying rigid foundation, are important determinants of cell–matrix interactions and mechanosensation. PMID:25392399

Myelin basic protein reduces molecular motions in DMPA, an elastic neutron scattering study

NASA Astrophysics Data System (ADS)

Natali, F.; Gliozzi, A.; Rolandi, R.; Cavatorta, P.; Deriu, A.; Fasano, A.; Riccio, P.

2001-07-01

We have studied the effect of physiological amounts of myelin basic protein (MBP) on pure dimyristoyl L- α-phosphatidic acid (DMPA) vesicles using the elastic neutron scattering technique. Elastic scans have been performed in a wide temperature range (20-300 K). In the lower temperature region the behaviour of the integrated elastic intensity was the typical one of harmonic systems. The analysis of the Q and T dependence performed in terms of an asymmetric double well potential clearly showed that the effect of the protein consisted in a significant reduction of the conformational mobility of the DMPA bilayers and in the stabilisation of the membrane.

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

A new Hysteretic Nonlinear Energy Sink (HNES)

NASA Astrophysics Data System (ADS)

Tsiatas, George C.; Charalampakis, Aristotelis E.

2018-07-01

The behavior of a new Hysteretic Nonlinear Energy Sink (HNES) coupled to a linear primary oscillator is investigated in shock mitigation. Apart from a small mass and a nonlinear elastic spring of the Duffing oscillator, the HNES is also comprised of a purely hysteretic and a linear elastic spring of potentially negative stiffness, connected in parallel. The Bouc-Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. Coupling the primary oscillator with the HNES, three nonlinear equations of motion are derived in terms of the two displacements and the dimensionless hysteretic variable, which are integrated numerically using the analog equation method. The performance of the HNES is examined by quantifying the percentage of the initially induced energy in the primary system that is passively transferred and dissipated by the HNES. Remarkable results are achieved for a wide range of initial input energies. The great performance of the HNES is mostly evidenced when the linear spring stiffness takes on negative values.

Developing ultrasensitive pressure sensor based on graphene nanoribbon: Molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Kwon, Oh Kuen; Lee, Jun Ha; Kim, Ki-Sub; Kang, Jeong Won

2013-01-01

We propose schematics for an ultra-sensitive pressure sensor based on graphene-nanoribbon (GNR) and investigate its electromechanical properties using classical molecular dynamics simulations and piezo-electricity theory. Since the top plate applied to the actual pressure is large whereas the contact area on the GNR is very small, both the sensitivity and the sensing range can be adjusted by controlling the aspect ratio between the top plate and the contact point areas. Our calculation shows that the electrical conductivity of GNRs can be tuned by the applied pressure and the electric conductance of the deflected GNR linearly increases with increasing applied pressure for the linear elastic region in low pressure below the cut-off point. In the curves for both the deflection and potential energy, the linear elastic regime in low pressure was explicitly separated with the non-linear elastic regime in high pressure. The proposed GNR-based nanoelectromechanical devices have great potential for application as electromechanical memory, relay or switching devices.

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

Muscle shear elastic modulus is linearly related to muscle torque over the entire range of isometric contraction intensity.

PubMed

Ateş, Filiz; Hug, François; Bouillard, Killian; Jubeau, Marc; Frappart, Thomas; Couade, Mathieu; Bercoff, Jeremy; Nordez, Antoine

2015-08-01

Muscle shear elastic modulus is linearly related to muscle torque during low-level contractions (<60% of Maximal Voluntary Contraction, MVC). This measurement can therefore be used to estimate changes in individual muscle force. However, it is not known if this relationship remains valid for higher intensities. The aim of this study was to determine: (i) the relationship between muscle shear elastic modulus and muscle torque over the entire range of isometric contraction and (ii) the influence of the size of the region of interest (ROI) used to average the shear modulus value. Ten healthy males performed two incremental isometric little finger abductions. The joint torque produced by Abductor Digiti Minimi was considered as an index of muscle torque and elastic modulus. A high coefficient of determination (R(2)) (range: 0.86-0.98) indicated that the relationship between elastic modulus and torque can be accurately modeled by a linear regression over the entire range (0% to 100% of MVC). The changes in shear elastic modulus as a function of torque were highly repeatable. Lower R(2) values (0.89±0.13 for 1/16 of ROI) and significantly increased absolute errors were observed when the shear elastic modulus was averaged over smaller ROI, half, 1/4 and 1/16 of the full ROI) than the full ROI (mean size: 1.18±0.24cm(2)). It suggests that the ROI should be as large as possible for accurate measurement of muscle shear modulus. Copyright © 2015 Elsevier Ltd. All rights reserved.

Study of critical behavior in concrete during curing by application of dynamic linear and nonlinear means.

PubMed

Lacouture, Jean-Christoph; Johnson, Paul A; Cohen-Tenoudji, Frederic

2003-03-01

The monitoring of both linear and nonlinear elastic properties of a high performance concrete during curing is presented by application of compressional and shear waves. To follow the linear elastic behavior, both compressional and shear waves are used in wide band pulse echo mode. Through the value of the complex reflection coefficient between the cell material (Lucite) and the concrete within the cell, the elastic moduli are calculated. Simultaneously, the transmission of a continuous compressional sine wave at progressively increasing drive levels permits us to calculate the nonlinear properties by extracting the harmonics amplitudes of the signal. Information regarding the chemical evolution of the concrete based upon the reaction of hydration of cement is obtained by monitoring the temperature inside the sample. These different types of measurements are linked together to interpret the critical behavior.

Non-linear programming in shakedown analysis with plasticity and friction

NASA Astrophysics Data System (ADS)

Spagnoli, A.; Terzano, M.; Barber, J. R.; Klarbring, A.

2017-07-01

Complete frictional contacts, when subjected to cyclic loading, may sometimes develop a favourable situation where slip ceases after a few cycles, an occurrence commonly known as frictional shakedown. Its resemblance to shakedown in plasticity has prompted scholars to apply direct methods, derived from the classical theorems of limit analysis, in order to assess a safe limit to the external loads applied on the system. In circumstances where zones of plastic deformation develop in the material (e.g., because of the large stress concentrations near the sharp edges of a complete contact), it is reasonable to expect an effect of mutual interaction of frictional slip and plastic strains on the load limit below which the global behaviour is non dissipative, i.e., both slip and plastic strains go to zero after some dissipative load cycles. In this paper, shakedown of general two-dimensional discrete systems, involving both friction and plasticity, is discussed and the shakedown limit load is calculated using a non-linear programming algorithm based on the static theorem of limit analysis. An illustrative example related to an elastic-plastic solid containing a frictional crack is provided.

Stiffness map of the grasping contact areas of the human hand.

PubMed

Pérez-González, Antonio; Vergara, Margarita; Sancho-Bru, Joaquin L

2013-10-18

The elasticity and damping of the soft tissues of the hand contribute to dexterity while grasping and also help to stabilise the objects in manipulation tasks. Although some previous works have studied the force-displacement response of the fingertips, the responses in all other regions of the hand that usually participate in grasping have not been analysed to date. In this work we performed experimental measurements in 20 subjects to obtain a stiffness map of the different grasping contact areas of the human hand. A force-displacement apparatus was used to simultaneously measure force and displacement at 39 different points on the hand at six levels of force ranging from 1N to 6N. A non-linear force-displacement response was found for all points, with stiffness increasing with the amount of force applied. Mean stiffness for the different points and force levels was within the range from 0.2N/mm to 7.7N/mm. However, the stiffness range and variation with level of force were found to be different from point to point. A total of 13 regions with similar stiffness behaviours were identified. The stiffness in the fingertips increased linearly with the amount of force applied, while in the palm it remained more constant for the range of forces considered. It is hypothesised that the differences in the stiffness behaviour from one region to another allow these regions to play different roles during grasping. © 2013 Elsevier Ltd. All rights reserved.

Analysis of laminated plates under thermal environment

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

Iyenger, N.G.R.; Shankara, C.A.

1995-12-31

Use of composites in advanced aircrafts and spacecraft structures calls for a thorough understanding of their behaviour under various types of loads. In the present paper, an attempt has been made to study the effect of thermal loads on the flexural response of composite laminated plates. Most of the studies in this area are either based on Classical Lamination Theory or First Order Shear Deformation Theory. In the present investigation, analysis has been carried out using a Higher Order Shear Deformation Theory, that allows for a parabolic variation of transverse shear stress through the thickness. The displacement model presented bymore » Reddy has been transformed so that only C{degrees} continuous element is required. This, however, increases the Degree of freedom per node from 5 to 7. Nine-noded isoparametric Legrangian elements are used for computing the results. The results were found to be very stable and comparable with those of exact elasticity solutions. The temperature is assumed to remain constant or vary linearly through the thickness. However, it varies sinusoidally in the plane of the plate. Effect of various parameters like material, fiber orientation, number of layers and boundary conditions on the response of the laminate has been investigated. The present study indicates that the flexural behaviour of laminates under thermal loads is very much different from that when subjected only to mechanical loads. Further, the variation of plate deflection with increase in temperature is not linear.« less

Elastic and mechanical softening in boron-doped diamond

PubMed Central

Liu, Xiaobing; Chang, Yun-Yuan; Tkachev, Sergey N.; Bina, Craig R.; Jacobsen, Steven D.

2017-01-01

Alternative approaches to evaluating the hardness and elastic properties of materials exhibiting physical properties comparable to pure diamond have recently become necessary. The classic linear relationship between shear modulus (G) and Vickers hardness (HV), along with more recent non-linear formulations based on Pugh’s modulus extending into the superhard region (HV > 40 GPa) have guided synthesis and identification of novel superabrasives. These schemes rely on accurately quantifying HV of diamond-like materials approaching or potentially exceeding the hardness of the diamond indenter, leading to debate about methodology and the very definition of hardness. Elasticity measurements on such materials are equally challenging. Here we used a high-precision, GHz-ultrasonic interferometer in conjunction with a newly developed optical contact micrometer and 3D optical microscopy of indentations to evaluate elasticity-hardness relations in the ultrahard range (HV > 80 GPa) by examining single-crystal boron-doped diamond (BDD) with boron contents ranging from 50–3000 ppm. We observe a drastic elastic-mechanical softening in highly doped BDD relative to the trends observed for superhard materials, providing insight into elasticity-hardness relations for ultrahard materials. PMID:28233808

Creeping gaseous flows through elastic tube and annulus micro-configurations

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2016-11-01

Gaseous flows in elastic micro-configurations is relevant to biological systems (e.g. alveolar ducts in the lungs) as well as to applications such as gas actuated soft micro-robots. We here examine the effect of low-Mach-number compressibility on creeping gaseous axial flows through linearly elastic tube and annulus micro-configurations. For steady flows, the leading-order effects of elasticity on the pressure distribution and mass-flux are obtained. For transient flow in a tube with small deformations, elastic effects are shown to be negligible in leading order due to compressibility. We then examine transient flows in annular configurations where the deformation is significant compared with the gap between the inner and outer cylinders defining the annulus. Both compressibility and elasticity are obtained as dominant terms interacting with viscosity. For a sudden flux impulse, the governing non-linear leading order diffusion equation is initially approximated by a porous-medium-equation of order 2.5 for the pressure square. However, as the fluid expand and the pressure decreases, the governing equation degenerates to a porous-medium-equation of order 2 for the pressure.

Elastic and mechanical softening in boron-doped diamond

NASA Astrophysics Data System (ADS)

Liu, Xiaobing; Chang, Yun-Yuan; Tkachev, Sergey N.; Bina, Craig R.; Jacobsen, Steven D.

2017-02-01

Alternative approaches to evaluating the hardness and elastic properties of materials exhibiting physical properties comparable to pure diamond have recently become necessary. The classic linear relationship between shear modulus (G) and Vickers hardness (HV), along with more recent non-linear formulations based on Pugh’s modulus extending into the superhard region (HV > 40 GPa) have guided synthesis and identification of novel superabrasives. These schemes rely on accurately quantifying HV of diamond-like materials approaching or potentially exceeding the hardness of the diamond indenter, leading to debate about methodology and the very definition of hardness. Elasticity measurements on such materials are equally challenging. Here we used a high-precision, GHz-ultrasonic interferometer in conjunction with a newly developed optical contact micrometer and 3D optical microscopy of indentations to evaluate elasticity-hardness relations in the ultrahard range (HV > 80 GPa) by examining single-crystal boron-doped diamond (BDD) with boron contents ranging from 50-3000 ppm. We observe a drastic elastic-mechanical softening in highly doped BDD relative to the trends observed for superhard materials, providing insight into elasticity-hardness relations for ultrahard materials.

On the residual properties of damaged FRC

NASA Astrophysics Data System (ADS)

Zerbino, R.; Torrijos, M. C.; Giaccio, G.

2017-09-01

A discussion on the residual behaviour of Fibre Reinforced Concrete (FRC) is performed based on two selected cases of concrete degradation: the exposure at High Temperatures and the development of Alkali Silica Reactions. In addition, and taking in mind that the failure mechanism in FRC is strongly related with the fibre pull-out strength, the bond strength in damaged matrices was shown concluding that the residual bond strength is less affected than the matrix strength. As the damage increases, the compressive strength and the modulus of elasticity decrease, being the modulus of elasticity the most affected. There were no significant changes produced by the incorporation of fibres on the residual behaviour when compared with previous experience on plain damage concrete. Regarding the tensile behaviour although the first peak decreases as the damage increases, even for a severely damage FRC the residual stresses remain almost unaffected.

Elastic band prediction equations for combined free-weight and elastic band bench presses and squats.

PubMed

Shoepe, Todd C; Ramirez, David A; Almstedt, Hawley C

2010-01-01

Elastic bands added to traditional free-weight techniques have become a part of suggested training routines in recent years. Because of the variable loading patterns of elastic bands (i.e., greater stretch produces greater resistance), it is necessary to quantify the exact loading patterns of bands to identify the volume and intensity of training. The purpose of this study was to determine the length vs. tension properties of multiple sizes of a set of commonly used elastic bands to quantify the resistance that would be applied to free-weight plus elastic bench presses (BP) and squats (SQ). Five elastic bands of varying thickness were affixed to an overhead support beam. Dumbbells of varying weights were progressively added to the free end while the linear deformation was recorded with each subsequent weight increment. The resistance was plotted as a factor of linear deformation, and best-fit nonlinear logarithmic regression equations were then matched to the data. For both the BP and SQ loading conditions and all band thicknesses tested, R values were greater than 0.9623. These data suggest that differences in load exist as a result of the thickness of the elastic band, attachment technique, and type of exercise being performed. Facilities should adopt their own form of loading quantification to match their unique set of circumstances when acquiring, researching, and implementing elastic band and free-weight exercises into the training programs.

A Conforming Multigrid Method for the Pure Traction Problem of Linear Elasticity: Mixed Formulation

NASA Technical Reports Server (NTRS)

Lee, Chang-Ock

1996-01-01

A multigrid method using conforming P-1 finite element is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

NASA Technical Reports Server (NTRS)

Hodges, D. H., Roberta.

1976-01-01

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Achieving large linear elasticity and high strength in bulk nanocompsite via synergistic effect

DOE PAGES

Hao, Shijie; Cui, Lishan; Guo, Fangmin; ...

2015-03-09

Elastic strain in bulk metallic materials is usually limited to only a fraction of 1%. Developing bulk metallic materials showing large linear elasticity and high strength has proven to be difficult. Here, based on the synergistic effect between nanowires and orientated martensite NiTi shape memory alloy, we developed an in-situ Nb nanowires-orientated martensitic NiTi matrix composite showing an ultra-large linear elastic strain of 4% and an ultrahigh yield strength of 1.8 GPa. This material also has a high mechanical energy storage efficiency of 96% and a high energy storage density of 36 J/cm 3 that is almost one order ofmore » larger than that of spring steel. It is demonstrated that the synergistic effect allows the exceptional mechanical properties of nanowires to be harvested at macro scale and the mechanical properties of matrix to be greatly improved, resulting in these superior properties. This research provides new avenues for developing advanced composites with superior properties by using effective synergistic effect between components.« less

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Experiment study and FEM simulation on erythrocytes under linear stretching of optical micromanipulation

NASA Astrophysics Data System (ADS)

Liu, Ying; Song, Huadong; Zhu, Panpan; Lu, Hao; Tang, Qi

2017-08-01

The elasticity of erythrocytes is an important criterion to evaluate the quality of blood. This paper presents a novel research on erythrocytes' elasticity with the application of optical tweezers and the finite element method (FEM) during blood storage. In this work, the erythrocytes with different in vitro times were linearly stretched by trapping force using optical tweezers and the time dependent elasticity of erythrocytes was investigated. The experimental results indicate that the membrane shear moduli of erythrocytes increased with the increasing in vitro time, namely the elasticity was decreasing. Simultaneously, an erythrocyte shell model with two parameters (membrane thickness h and membrane shear modulus H) was built to simulate the linear stretching states of erythrocytes by the FEM, and the simulations conform to the results obtained in the experiment. The evolution process was found that the erythrocytes membrane thicknesses were decreasing. The analysis assumes that the partial proteins and lipid bilayer of erythrocyte membrane were decomposed during the in vitro preservation of blood, which results in thin thickness, weak bending resistance, and losing elasticity of erythrocyte membrane. This study implies that the FEM can be employed to investigate the inward mechanical property changes of erythrocyte in different environments, which also can be a guideline for studying the erythrocyte mechanical state suffered from different diseases.

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.

Investigation on the Crack Behaviour in Kevlar 49 Based Composite Materials using Extended Finite Element Method for Aerospace Applications

NASA Astrophysics Data System (ADS)

Handa, Danish; Sekhar Dondapati, Raja; Kumar, Abhinav

2017-08-01

Ductile to brittle transition (DTBT) is extensively observed in materials under cryogenic temperatures, thereby observing brittle failure due to the non-resistance of crack propagation. Owing to its outstanding mechanical and thermal properties, Kevlar 49 composites are widely used in aerospace applications under cryogenic temperatures. Therefore, in this paper, involving the assumption of linear elastic fracture mechanics (LEFM), mechanical characterization of Kevlar 49 composite is done using Extended Finite Element Method (X-FEM) technique in Abaqus/CAE software. Further, the failure of Kevlar 49 composites due to the propagation of crack at room temperature and the cryogenic temperature is investigated. Stress, strain and strain energy density as a function of the width of the Kevlar specimen is predicted, indicates that Kevlar 49 composites are suitable for use under cryogenic temperatures.

Soft actuators and soft actuating devices

DOEpatents

Yang, Dian; Whitesides, George M.

2017-10-17

A soft buckling linear actuator is described, including: a plurality of substantially parallel bucklable, elastic structural components each having its longest dimension along a first axis; and a plurality of secondary structural components each disposed between and bridging two adjacent bucklable, elastic structural components; wherein every two adjacent bucklable, elastic structural components and the secondary structural components in-between define a layer comprising a plurality of cells each capable of being connected with a fluid inflation or deflation source; the secondary structural components from two adjacent layers are not aligned along a second axis perpendicular to the first axis; and the secondary structural components are configured not to buckle, the bucklable, elastic structural components are configured to buckle along the second axis to generate a linear force, upon the inflation or deflation of the cells. Methods of actuation using the same are also described.

Setting behaviour of luting cements monitored by an ultrasonic method.

PubMed

Tsubota, Keishi; Mori, Kentarou; Yasuda, Genta; Kawamoto, Ryo; Yoshida, Takeshi; Yamaguchi, Kanako; Kurokawa, Hiroyasu; Miyazaki, Masashi

2008-06-01

The purpose of this study was to monitor the setting behaviour and elastic modulus of luting cements using an ultrasonic device. The ultrasonic equipment comprised a pulser-receiver, transducers and an oscilloscope. The transit time through the cement disk was multiplied by the thickness of the specimen, and the sonic velocity within the material was then calculated. The sonic velocities of the longitudinal and shear waves were used to determine the elastic modulus. Analysis of variance and the Tukey HSD test were used to compare the elastic moduli of the set cements. In the earliest stages of the setting process, most of the ultrasound energy was absorbed by the cements and the sound waves were relatively weak. As the cements hardened, the sound velocities increased and this tendency differed among the luting cements used. The mean elastic moduli of the specimens ranged from 2.9 to 9.9 GPa after 15 min, from 14.4 to 20.3 GPa after 24 h and from 12.1 to 15.9 GPa after 1 month. The setting processes of the luting cements were thus clearly defined by using the present ultrasonic method.

Nonlocal theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-09-01

New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

Ultrasonic Characterization of the Linear Elastic Properties of Myocardium and Other Anisotropic Soft Tissues

NASA Astrophysics Data System (ADS)

Hoffmeister, Brentley Keith

1995-01-01

This thesis seeks to contribute to a better understanding of the physics of interaction of ultrasonic waves with inhomogeneous and anisotropic media, one example of which is the human heart. The clinical success of echocardiography has generated a considerable interest in the development of ultrasonic techniques to measure the elastic properties of heart tissue. It is hypothesized that the elastic properties of myocardium are influenced by the interstitial content and organization of collagen. Collagen, which is the main component of tendon, interconnects the muscle cells of the heart to form locally unidirectional myofibers. This thesis therefore employs ultrasonic techniques to characterize the linear elastic properties of both heart and tendon. The linear elastic properties of tissues possessing a unidirectional arrangement of fibers may be described in terms of five independent elastic stiffness coefficients. Three of these coefficients were determined for formalin fixed specimens of bovine Achilles tendon and human myocardium by measuring the velocity of longitudinal mode ultrasonic pulses as a function of angle of propagation relative to the fiber axis of the tissue. The remaining two coefficients were determined by measuring the velocity of transverse mode ultrasonic waves through these tissues. To overcome technical difficulties associated with the extremely high attenuation of transverse mode waves at low megahertz frequencies, a novel measurement system was developed based on the sampled continuous wave technique. Results of these measurements were used to assess the influence of interstitial collagen, and to model the mechanical properties of heart wall.

A global assessment of climate-water quality relationships in large rivers: an elasticity perspective.

PubMed

Jiang, Jiping; Sharma, Ashish; Sivakumar, Bellie; Wang, Peng

2014-01-15

To uncover climate-water quality relationships in large rivers on a global scale, the present study investigates the climate elasticity of river water quality (CEWQ) using long-term monthly records observed at 14 large rivers. Temperature and precipitation elasticities of 12 water quality parameters, highlighted by N- and P-nutrients, are assessed. General observations on elasticity values show the usefulness of this approach to describe the magnitude of stream water quality responses to climate change, which improves that of simple statistical correlation. Sensitivity type, intensity and variability rank of CEWQ are reported and specific characteristics and mechanism of elasticity of nutrient parameters are also revealed. Among them, the performance of ammonia, total phosphorus-air temperature models, and nitrite, orthophosphorus-precipitation models are the best. Spatial and temporal assessment shows that precipitation elasticity is more variable in space than temperature elasticity and that seasonal variation is more evident for precipitation elasticity than for temperature elasticity. Moreover, both anthropogenic activities and environmental factors are found to impact CEWQ for select variables. The major relationships that can be inferred include: (1) human population has a strong linear correlation with temperature elasticity of turbidity and total phosphorus; and (2) latitude has a strong linear correlation with precipitation elasticity of turbidity and N nutrients. As this work improves our understanding of the relation between climate factors and surface water quality, it is potentially helpful for investigating the effect of climate change on water quality in large rivers, such as on the long-term change of nutrient concentrations. © 2013.

Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?

PubMed

Claessens, T E; Georgakopoulos, D; Afanasyeva, M; Vermeersch, S J; Millar, H D; Stergiopulos, N; Westerhof, N; Verdonck, P R; Segers, P

2006-04-01

The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) < 0.75) during isovolumic relaxation and early filling; and 4) logarithmic regression is superior in estimating the fixed volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.

Dynamical theory of stability for elastic rods with nonlinear curvature and twist

NASA Technical Reports Server (NTRS)

Wauer, J.

1977-01-01

Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.

Coulomb-like elastic interaction induced by symmetry breaking in nematic liquid crystal colloids.

PubMed

Lee, Beom-Kyu; Kim, Sung-Jo; Kim, Jong-Hyun; Lev, Bohdan

2017-11-21

It is generally thought that colloidal particles in a nematic liquid crystal do not generate the first multipole term called deformation elastic charge as it violates the mechanical equilibrium. Here, we demonstrate theoretically and experimentally that this is not the case, and deformation elastic charges, as well as dipoles and quadrupoles, can be induced through anisotropic boundary conditions. We report the first direct observation of Coulomb-like elastic interactions between colloidal particles in a nematic liquid crystal. The behaviour of two spherical colloidal particles with asymmetric anchoring conditions induced by asymmetric alignment is investigated experimentally; the interaction of two particles located at the boundary of twist and parallel aligned regions is observed. We demonstrate that such particles produce deformation elastic charges and interact by Coulomb-like interactions.

Applying the transtheoretical model to promote functional fitness of community older adults participating in elastic band exercises.

PubMed

Yang, Hui-Ju; Chen, Kuei-Min; Chen, Ming-De; Wu, Hui-Chuan; Chang, Wen-Jane; Wang, Yueh-Chin; Huang, Hsin-Ting

2015-10-01

The transtheoretical model was applied to promote behavioural change and test the effects of a group senior elastic band exercise programme on the functional fitness of community older adults in the contemplation and preparation stages of behavioural change. Forming regular exercise habits is challenging for older adults. The transtheoretical model emphasizes using different strategies in various stages to facilitate behavioural changes. Quasi-experimental design with pre-test and post-tests on two groups. Six senior activity centres were randomly assigned to either the experimental or control group. The data were collected during 2011. A total of 199 participants were recruited and 169 participants completed the study (experimental group n = 84, control group n = 85). The elastic band exercises were performed for 40 minutes, three times per week for 6 months. The functional fitness of the participants was evaluated at baseline and at the third and sixth month of the intervention. Statistical analyses included a two-way mixed design analysis of variance, one-way repeated measures analysis of variance and an analysis of covariance. All of the functional fitness indicators had significant changes at post-tests from pre-test in the experimental group. The experimental group had better performances than the control group in all of the functional fitness indicators after three months and 6 months of the senior elastic band exercises. The exercise programme provided older adults with appropriate strategies for maintaining functional fitness, which improved significantly after the participants exercising regularly for 6 months. © 2015 John Wiley & Sons Ltd.

Using an elastic magnifier to increase power output and performance of heart-beat harvesters

NASA Astrophysics Data System (ADS)

Galbier, Antonio C.; Karami, M. Amin

2017-09-01

Embedded piezoelectric energy harvesting (PEH) systems in medical pacemakers have been a growing and innovative research area. The goal of these systems, at present, is to remove the pacemaker battery, which makes up 60%-80% of the unit, and replace it with a sustainable power source. This requires that energy harvesting systems provide sufficient power, 1-3 μW, for operating a pacemaker. The goal of this work is to develop, test, and simulate cantilevered energy harvesters with a linear elastic magnifier (LEM). This research hopes to provide insight into the interaction between pacemaker energy harvesters and the heart. By introducing the elastic magnifier into linear and nonlinear systems oscillations of the tip are encouraged into high energy orbits and large tip deflections. A continuous nonlinear model is presented for the bistable piezoelectric energy harvesting (BPEH) system and a one-degree-of-freedom linear mass-spring-damper model is presented for the elastic magnifier. The elastic magnifier will not consider the damping negligible, unlike most models. A physical model was created for the bistable structure and formed to an elastic magnifier. A hydrogel was designed for the experimental model for the LEM. Experimental results show that the BPEH coupled with a LEM (BPEH + LEM) produces more power at certain input frequencies and operates a larger bandwidth than a PEH, BPEH, and a standard piezoelectric energy harvester with the elastic magnifier (PEH + LEM). Numerical simulations are consistent with these results. It was observed that the system enters high-energy and high orbit oscillations and that, ultimately, BPEH systems implemented in medical pacemakers can, if designed properly, have enhanced performance if positioned over the heart.

Inelastic response of silicon to shock compression.

PubMed

Higginbotham, A; Stubley, P G; Comley, A J; Eggert, J H; Foster, J M; Kalantar, D H; McGonegle, D; Patel, S; Peacock, L J; Rothman, S D; Smith, R F; Suggit, M J; Wark, J S

2016-04-13

The elastic and inelastic response of [001] oriented silicon to laser compression has been a topic of considerable discussion for well over a decade, yet there has been little progress in understanding the basic behaviour of this apparently simple material. We present experimental x-ray diffraction data showing complex elastic strain profiles in laser compressed samples on nanosecond timescales. We also present molecular dynamics and elasticity code modelling which suggests that a pressure induced phase transition is the cause of the previously reported 'anomalous' elastic waves. Moreover, this interpretation allows for measurement of the kinetic timescales for transition. This model is also discussed in the wider context of reported deformation of silicon to rapid compression in the literature.

Blocky inversion of multichannel elastic impedance for elastic parameters

NASA Astrophysics Data System (ADS)

Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

2018-04-01

Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.

Lifelong modelling of properties for materials with technological memory

NASA Astrophysics Data System (ADS)

Falaleev, AP; Meshkov, VV; Vetrogon, AA; Ogrizkov, SV; Shymchenko, AV

2016-10-01

An investigation of real automobile parts produced from dual phase steel during standard periods of life cycle is presented, which considers such processes as stamping, exploitation, automobile accident, and further repair. The development of the phenomenological model of the mechanical properties of such parts was based on the two surface plastic theory of Chaboche. As a consequence of the composite structure of dual phase steel, it was shown that local mechanical properties of parts produced from this material change significantly their during their life cycle, depending on accumulated plastic deformations and thermal treatments. Such mechanical property changes have a considerable impact on the accuracy of the computer modelling of automobile behaviour. The most significant errors of modelling were obtained at the critical operating conditions, such as crashes and accidents. The model developed takes into account the kinematics (Bauschinger effect), isotropic hardening, non-linear elastic steel behaviour and changes caused by the thermal treatment. Using finite element analysis, the model allows the evaluation of the passive safety of a repaired car body, and enables increased restoration accuracy following an accident. The model was confirmed experimentally for parts produced from dual phase steel DP780.

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

PubMed

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

A Lagrangian meshfree method applied to linear and nonlinear elasticity

PubMed Central

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code. PMID:29045443

Variation of nanostructures, molecular interactions, and anisotropic elastic moduli of lignocellulosic cell walls with moisture

Treesearch

S. Youssefian; J. E. Jakes; N. Rahbar

2017-01-01

A combination of experimental, theoretical and numerical studies is used to investigate the variation of elastic moduli of lignocellulosic (bamboo) fiber cell walls with moisture content (MC). Our Nanoindentation results show that the longitudinal elastic modulus initially increased to a maximum value at about 3% MC and then decreased linearly with increasing MC. In...

Mechanical and corrosion resistance of a new nanostructured Ti-Zr-Ta-Nb alloy.

PubMed

Raducanu, D; Vasilescu, E; Cojocaru, V D; Cinca, I; Drob, P; Vasilescu, C; Drob, S I

2011-10-01

In this work, a multi-elementary Ti-10Zr-5Nb-5Ta alloy, with non-toxic alloying elements, was used to develop an accumulative roll bonding, ARB-type procedure in order to improve its structural and mechanical properties. The alloy was obtained by cold crucible semi-levitation melting technique and then was ARB deformed following a special route. After three ARB cycles, the total deformation degree per layer is about 86%; the calculated medium layer thickness is about 13 μm. The ARB processed alloy has a low Young's modulus of 46 GPa, a value very close to the value of the natural cortical bone (about 20 GPa). Data concerning ultimate tensile strength obtained for ARB processed alloy is rather high, suitable to be used as a material for bone substitute. Hardness of the ARB processed alloy is higher than that of the as-cast alloy, ensuring a better behaviour as a implant material. The tensile curve for the as-cast alloy shows an elastoplastic behaviour with a quite linear elastic behaviour and the tensile curve for the ARB processed alloy is quite similar with a strain-hardening elastoplastic body. Corrosion behaviour of the studied alloy revealed the improvement of the main electrochemical parameters, as a result of the positive influence of ARB processing. Lower corrosion and ion release rates for the ARB processed alloy than for the as-cast alloy, due to the favourable effect of ARB thermo-mechanical processing were obtained. Copyright © 2011 Elsevier Ltd. All rights reserved.

A Review of the Proposed KIsi Offset-Secant Method for Size-Insensitive Linear-Elastic Fracture Toughness Evaluation

NASA Technical Reports Server (NTRS)

James, Mark; Wells, Doug; Allen, Phillip; Wallin, Kim

2017-01-01

Recently proposed modifications to ASTM E399 would provide a new size-insensitive approach to analyzing the force-displacement test record. The proposed size-insensitive linear-elastic fracture toughness, KIsi, targets a consistent 0.5mm crack extension for all specimen sizes by using an offset secant that is a function of the specimen ligament length. The KIsi evaluation also removes the Pmax/PQ criterion and increases the allowable specimen deformation. These latter two changes allow more plasticity at the crack tip, prompting the review undertaken in this work to ensure the validity of this new interpretation of the force-displacement curve. This paper provides a brief review of the proposed KIsi methodology and summarizes a finite element study into the effects of increased crack tip plasticity on the method given the allowance for additional specimen deformation. The study has two primary points of investigation: the effect of crack tip plasticity on compliance change in the force-displacement record and the continued validity of linear-elastic fracture mechanics to describe the crack front conditions. The analytical study illustrates that linear-elastic fracture mechanics assumptions remain valid at the increased deformation limit; however, the influence of plasticity on the compliance change in the test record is problematic. A proposed revision to the validity criteria for the KIsi test method is briefly discussed.

Deformations of a pre-stretched and lubricated finite elastic membrane driven by non-uniform external forcing

NASA Astrophysics Data System (ADS)

Boyko, Evgeniy; Gat, Amir; Bercovici, Moran

2017-11-01

We study viscous-elastic dynamics of a fluid confined between a rigid plate and a finite pre-stretched circular elastic membrane, pinned at its boundaries. The membrane is subjected to forces acting either directly on the membrane or through a pressure distribution in the fluid. Under the assumptions of strong pre-stretching and small deformations of the elastic sheet, and by applying the lubrication approximation for the flow, we derive the Green's function for the resulting linearized 4th order diffusion equation governing the deformation field in cylindrical coordinates. In addition, defining an asymptotic expansion with the ratio of the induced to prescribed tension serving as the small parameter, we reduce the coupled Reynolds and non-linear von-Karman equations to a set of three one-way coupled linear equations. The solutions to these equations provide insight onto the effects of induced tension, and enable simplified prediction of the correction for the deformation field. Funded by the European Research Council (ERC) under the European Union'sHorizon 2020 Research and Innovation Programme, Grant Agreement No. 678734 (MetamorphChip). E.B. is supported by the Adams Fellowship Program.

Estimation of the behavior factor of existing RC-MRF buildings

NASA Astrophysics Data System (ADS)

Vona, Marco; Mastroberti, Monica

2018-01-01

In recent years, several research groups have studied a new generation of analysis methods for seismic response assessment of existing buildings. Nevertheless, many important developments are still needed in order to define more reliable and effective assessment procedures. Moreover, regarding existing buildings, it should be highlighted that due to the low knowledge level, the linear elastic analysis is the only analysis method allowed. The same codes (such as NTC2008, EC8) consider the linear dynamic analysis with behavior factor as the reference method for the evaluation of seismic demand. This type of analysis is based on a linear-elastic structural model subject to a design spectrum, obtained by reducing the elastic spectrum through a behavior factor. The behavior factor (reduction factor or q factor in some codes) is used to reduce the elastic spectrum ordinate or the forces obtained from a linear analysis in order to take into account the non-linear structural capacities. The behavior factors should be defined based on several parameters that influence the seismic nonlinear capacity, such as mechanical materials characteristics, structural system, irregularity and design procedures. In practical applications, there is still an evident lack of detailed rules and accurate behavior factor values adequate for existing buildings. In this work, some investigations of the seismic capacity of the main existing RC-MRF building types have been carried out. In order to make a correct evaluation of the seismic force demand, actual behavior factor values coherent with force based seismic safety assessment procedure have been proposed and compared with the values reported in the Italian seismic code, NTC08.

Bessel smoothing filter for spectral-element mesh

NASA Astrophysics Data System (ADS)

Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.

2017-06-01

Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the efficiency and flexibility of the approach proposed.

Inelastic response of silicon to shock compression

DOE PAGES

Higginbotham, Andrew; Stubley, P. G.; Comley, A. J.; ...

2016-04-13

The elastic and inelastic response of [001] oriented silicon to laser compression has been a topic of considerable discussion for well over a decade, yet there has been little progress in understanding the basic behaviour of this apparently simple material. We present experimental x-ray diffraction data showing complex elastic strain profiles in laser compressed samples on nanosecond timescales. We also present molecular dynamics and elasticity code modelling which suggests that a pressure induced phase transition is the cause of the previously reported ‘anomalous’ elastic waves. Moreover, this interpretation allows for measurement of the kinetic timescales for transition. Lastly, this modelmore » is also discussed in the wider context of reported deformation of silicon to rapid compression in the literature.« less

Inelastic response of silicon to shock compression

PubMed Central

Higginbotham, A.; Stubley, P. G.; Comley, A. J.; Eggert, J. H.; Foster, J. M.; Kalantar, D. H.; McGonegle, D.; Patel, S.; Peacock, L. J.; Rothman, S. D.; Smith, R. F.; Suggit, M. J.; Wark, J. S.

2016-01-01

The elastic and inelastic response of [001] oriented silicon to laser compression has been a topic of considerable discussion for well over a decade, yet there has been little progress in understanding the basic behaviour of this apparently simple material. We present experimental x-ray diffraction data showing complex elastic strain profiles in laser compressed samples on nanosecond timescales. We also present molecular dynamics and elasticity code modelling which suggests that a pressure induced phase transition is the cause of the previously reported ‘anomalous’ elastic waves. Moreover, this interpretation allows for measurement of the kinetic timescales for transition. This model is also discussed in the wider context of reported deformation of silicon to rapid compression in the literature. PMID:27071341

Shape memory effect and super elasticity. Its dental applications.

PubMed

Kotian, R

2001-01-01

The shape memory alloys are quite fascinating materials characterized by a shape memory effect and super elasticity which ordinary metals do not have. This unique behaviour was first found in a Au-47.5 at % Cd alloy in 1951, and was published in 1963 by the discovery of Ti-Ni alloy. Shape memory alloys now being practically used as new functional alloys for various dental and medical applications.

Elastic constants and dynamics in nematic liquid crystals

NASA Astrophysics Data System (ADS)

Humpert, Anja; Allen, Michael P.

2015-09-01

In this paper, we present molecular dynamics calculations of the Frank elastic constants, and associated time correlation functions, in nematic liquid crystals. We study two variants of the Gay-Berne potential, and use system sizes of half a million molecules, significantly larger than in previous studies of elastic behaviour. Equilibrium orientational fluctuations in reciprocal (k-) space were calculated, to determine the elastic constants by fitting at low |k|; our results indicate that small system size may be a source of inaccuracy in previous work. Furthermore, the dynamics of the Gay-Berne nematic were studied by calculating time correlation functions of components of the order tensor, together with associated components of the velocity field, for a set of wave vectors k. Confirming our earlier work, we found exponential decay for splay and twist correlations, and oscillatory exponential decay for the bend correlation. In this work, we confirm similar behaviour for the corresponding velocity components. In all cases, the decay rates, and oscillation frequencies, were found to be accurately proportional to k2 for small k, as predicted by the equations of nematodynamics. However, the observation of oscillatory bend fluctuations, and corresponding oscillatory shear flow decay, is in contradiction to the usual assumptions appearing in the literature, and in standard texts. We discuss the advantages and drawbacks of using large systems in these calculations.

Linear elastic fracture mechanics primer

NASA Technical Reports Server (NTRS)

Wilson, Christopher D.

1992-01-01

This primer is intended to remove the blackbox perception of fracture mechanics computer software by structural engineers. The fundamental concepts of linear elastic fracture mechanics are presented with emphasis on the practical application of fracture mechanics to real problems. Numerous rules of thumb are provided. Recommended texts for additional reading, and a discussion of the significance of fracture mechanics in structural design are given. Griffith's criterion for crack extension, Irwin's elastic stress field near the crack tip, and the influence of small-scale plasticity are discussed. Common stress intensities factor solutions and methods for determining them are included. Fracture toughness and subcritical crack growth are discussed. The application of fracture mechanics to damage tolerance and fracture control is discussed. Several example problems and a practice set of problems are given.

Linear elastic properties derivation from microstructures representative of transport parameters.

PubMed

Hoang, Minh Tan; Bonnet, Guy; Tuan Luu, Hoang; Perrot, Camille

2014-06-01

It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

Gaseous Viscous Peeling of Linearly Elastic Substrates

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2017-11-01

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

The Dynamic Response and Vibration of Functionally Graded Carbon Nanotube-Reinforced Composite (FG-CNTRC) Truncated Conical Shells Resting on Elastic Foundations

PubMed Central

Nguyen Dinh, Duc; Nguyen, Pham Dinh

2017-01-01

Based on the classical shell theory, the linear dynamic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) truncated conical shells resting on elastic foundations subjected to dynamic loads is presented. The truncated conical shells are reinforced by single-walled carbon nanotubes (SWCNTs) that vary according to the linear functions of the shell thickness. The motion equations are solved by the Galerkin method and the fourth-order Runge–Kutta method. In numerical results, the influences of geometrical parameters, elastic foundations, natural frequency parameters, and nanotube volume fraction of FG-CNTRC truncated conical shells are investigated. The proposed results are validated by comparing them with those of other authors. PMID:29057821

Modelling deformation and fracture in confectionery wafers

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

Mohammed, Idris K.; Charalambides, Maria N.; Williams, J. Gordon

2015-01-22

The aim of this research is to model the deformation and fracture behaviour of brittle wafers often used in chocolate confectionary products. Three point bending and compression experiments were performed on beam and circular disc samples respectively to determine the 'apparent' stress-strain curves in bending and compression. The deformation of the wafer for both these testing types was observed in-situ within an SEM. The wafer is modeled analytically and numerically as a composite material with a core which is more porous than the skins. X-ray tomography was used to generate a three dimensional volume of the wafer microstructure which wasmore » then meshed and used for quantitative analysis. A linear elastic material model, with a damage function and element deletion, was used and the XMT generated architecture was loaded in compression. The output from the FE simulations correlates closely to the load-deflection deformation observed experimentally.« less

Lattice Boltzmann simulation of antiplane shear loading of a stationary crack

NASA Astrophysics Data System (ADS)

Schlüter, Alexander; Kuhn, Charlotte; Müller, Ralf

2018-01-01

In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61-69, 2000) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu's work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.

Modelling deformation and fracture in confectionery wafers

NASA Astrophysics Data System (ADS)

Mohammed, Idris K.; Charalambides, Maria N.; Williams, J. Gordon; Rasburn, John

2015-01-01

The aim of this research is to model the deformation and fracture behaviour of brittle wafers often used in chocolate confectionary products. Three point bending and compression experiments were performed on beam and circular disc samples respectively to determine the 'apparent' stress-strain curves in bending and compression. The deformation of the wafer for both these testing types was observed in-situ within an SEM. The wafer is modeled analytically and numerically as a composite material with a core which is more porous than the skins. X-ray tomography was used to generate a three dimensional volume of the wafer microstructure which was then meshed and used for quantitative analysis. A linear elastic material model, with a damage function and element deletion, was used and the XMT generated architecture was loaded in compression. The output from the FE simulations correlates closely to the load-deflection deformation observed experimentally.

Free-form reticulated shell structures searched for maximum buckling strength

NASA Astrophysics Data System (ADS)

Takiuchi, Yuji; Kato, Shiro; Nakazawa, Shoji

2017-10-01

In this paper, a scheme of shape optimization is proposed for maximum buckling strength of free-form steel reticulated shells. In order to discuss the effectiveness of objective functions with respect to maximizing buckling strength, several different optimizations are applied to shallow steel single layer reticulated shells targeting rigidly jointed tubular members. The objective functions to be compared are linear buckling load, strain energy, initial yield load, and elasto-plastic buckling strength evaluated based on Modified Dunkerley Formula. With respect to obtained free-forms based on the four optimization schemes, both of their elastic buckling and elasto-plastic buckling behaviour are investigated and compared considering geometrical imperfections. As a result, it is concluded that the first and fourth optimization methods are effective from a viewpoint of buckling strength. And the relation between generalized slenderness ratio and appropriate objective function applied in buckling strength maximization is made clear.

Fe-Mg substitution in aluminate spinels: effects on elastic properties investigated by Brillouin scattering

NASA Astrophysics Data System (ADS)

Bruschini, Enrico; Speziale, Sergio; Bosi, Ferdinando; Andreozzi, Giovanni B.

2018-03-01

We investigated by a multi-analytical approach (Brillouin scattering, X-ray diffraction and electron microprobe) the dependence of the elastic properties on the chemical composition of six spinels in the series (Mg1-x ,Fe x )Al2O4 (0 ≤ x ≤ 0.5). With the exception of C 12, all the elastic moduli (C 11, C 44, K S0 and G) are insensitive to chemical composition for low iron concentration, while they decrease linearly for higher Fe2+ content. Only C 12 shows a continuous linear increase with increasing Fe2+ across the whole compositional range under investigation. The high cation disorder showed by the sample with x = 0.202 has little or no influence on the elastic parameters. The range 0.202 < x < 0.388 bounds the percolation threshold (p c) for nearest neighbor interaction of Fe in the cation sublattices of the spinel structure. Below x = 0.202, the iron atoms are diluted in the system and far from each other, and the elastic moduli are nearly constant. Above x = 0.388, Fe atoms form extended interconnected clusters and show a cooperative behavior thus affecting the single-crystal elastic moduli. The elastic anisotropy largely increases with the introduction of Fe2+ in substitution of magnesium in spinel. This behavior is different with respect to other spinels containing transition metals such as Mn2+ and Co2+.

Kelvin-Voigt model of wave propagation in fragmented geomaterials with impact damping

NASA Astrophysics Data System (ADS)

Khudyakov, Maxim; Pasternak, Elena; Dyskin, Arcady

2017-04-01

When a wave propagates through real materials, energy dissipation occurs. The effect of loss of energy in homogeneous materials can be accounted for by using simple viscous models. However, a reliable model representing the effect in fragmented geomaterials has not been established yet. The main reason for that is a mechanism how vibrations are transmitted between the elements (fragments) in these materials. It is hypothesised that the fragments strike against each other, in the process of oscillation, and the impacts lead to the energy loss. We assume that the energy loss is well represented by the restitution coefficient. The principal element of this concept is the interaction of two adjacent blocks. We model it by a simple linear oscillator (a mass on an elastic spring) with an additional condition: each time the system travels through the neutral point, where the displacement is equal to zero, the velocity reduces by multiplying itself by the restitution coefficient, which characterises an impact of the fragments. This additional condition renders the system non-linear. We show that the behaviour of such a model averaged over times much larger than the system period can approximately be represented by a conventional linear oscillator with linear damping characterised by a damping coefficient expressible through the restitution coefficient. Based on this the wave propagation at times considerably greater than the resonance period of oscillations of the neighbouring blocks can be modelled using the Kelvin-Voigt model. The wave velocities and the dispersion relations are obtained.

First principles study of hydrogen bond symmetrization in δ-AlOOH

NASA Astrophysics Data System (ADS)

Pillai, Sharad Babu; Jha, Prafulla K.; Padmalal, Akash; Maurya, D. M.; Chamyal, L. S.

2018-03-01

The high pressure behaviour of the hydrous mineral δ-AlOOH has been investigated by many experimental and theoretical studies, but the discrepancy in predicting the value of hydrogen symmetrization pressure was not resolved. Here, we investigated the high pressure behaviour of δ-AlOOH using first principles calculations and found that with proper optimization using pressure routine control, local density approximation (LDA) predicts the hydrogen symmetrization pressure as 15 GPa which is in good agreement with the experimentally predicted value which resolves the existing discrepancy and hence proving the validity of LDA in predicting the hydrogen symmetrization pressure. We further studied the compressibility behaviour of δ-AlOOH at low pressures and confirmed the P21nm to Pnnm transition of δ-AlOOH shown by the experimental work [Kuribayashi et al., Phys. Chem. Miner. 41, 303-312 (2014)]. We have also analysed the dependence of elastic constants, elastic moduli, sound velocities, and Raman spectrum of δ-AlOOH with pressure and found that a subtle change in the position of the hydrogen atom at hydrogen symmetrization pressure results into drastic changes in elastic and vibrational properties. Further, this study has been used to discuss the seismic anomalies observed in the upper mantle beneath the Deccan Volcanic Province in India and the Java subduction zone in the eastern flank of the Indian Ocean.

Linear Elastic Waves - Series: Cambridge Texts in Applied Mathematics (No. 26)

NASA Astrophysics Data System (ADS)

Harris, John G.

2001-10-01

Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers. Aimed at beginning graduate students Includes examples and exercises Has application in a wide range of disciplines

Towards a Model of Reactive-Cracking: the Role of Reactions, Elasticity and Surface Energy Driven Flow in Poro-elastic Media

NASA Astrophysics Data System (ADS)

Evans, O.; Spiegelman, M. W.; Wilson, C. R.; Kelemen, P. B.

2016-12-01

Many critical processes can be described by reactive fluid flow in brittle media, including hydration/alteration of oceanic plates near spreading ridges, chemical weathering, and dehydration/decarbonation of subducting plates. Such hydration reactions can produce volume changes that may induce stresses large enough to drive fracture in the rock, in turn exposing new reactive surface and modifying the permeability. A better understanding of this potentially rich feedback could also be critical in the design of engineered systems for geologic carbon sequestration. To aid understanding of these processes we have developed a macroscopic continuum description of reactive fluid flow in an elastically deformable porous media. We explore the behaviour of this model by considering a simplified hydration reaction (e.g. olivine + H20 -> serpentine + brucite). In a closed system, these hydration reactions will continue to consume available fluids until the permeability reaches zero, leaving behind it a highly stressed residuum. Our model demonstrates this limiting behaviour, and that the elastic stresses generated are large enough to cause failure/fracture of the host rock. Whilst it is understood that `reactive fracture' is an important mechanism for the continued evolution of this process, it is also proposed that imbibition/surface energy driven flow may play a role. Through a simplified set of computational experiments, we investigate the relative roles of elasticity and surface energy in both a non-reactive purely poro-elastic framework, and then in the presence of reaction. We demonstrate that surface energy can drive rapid diffusion of porosity, thus allowing the reaction to propagate over larger areas. As we expect both surface energy and fracture/failure to be of importance in these processes, we plan to integrate the current model into one that allows for fracture once critical stresses are exceeded.

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

Peeling without precursors

NASA Astrophysics Data System (ADS)

Lister, John; Skinner, Dominic; Large, Tim

2017-11-01

The peeling by fluid injection of an elastic sheet away from a substrate is often regularised by invoking a thin prewetting film or a low-viscosity phase in the tip. Here we analyse fluid-driven peeling without such precursors, and consider an elastic sheet either bonded to, or simply laid on, an elastic substrate. To resolve the `elastic contact-line problem' that arises from viscous flow and beam theory, we determine the near-tip behaviour from lubrication theory coupled to the full equations of elasticity and fracture. The result is a law for the tip propagation speed in terms of the remote loading and the toughness of the sheet-substrate bonding (which might be zero). There are distinct modes of failure, according to whether there is slip ahead of the fluid front. The propagation-speed law gives rise to new similarity solutions for the spread of a fluid-filled blister in different regimes.

Spatio-Temporal Modelling of the Pre-Eruptive Strain Localization in a Volcanic Edifice Using a Maxwell-Elasto-Brittle Rheology

NASA Astrophysics Data System (ADS)

Dansereau, V.; Got, J. L.

2017-12-01

Before a volcanic eruption, the pressurization of the volcanic edifice by a magma reservoir induces earthquakes and damage in the edifice; damage lowers the strength of the edifice and decreases its elastic properties. Anelastic deformations cumulate and lead to rupture and eruption. These deformations translate into surface displacements, measurable via GPS or InSAR (e.g., Kilauea, southern flank, or Piton de la Fournaise, eastern flank).Attempts to represent these processes are usually based on a linear-elastic rheology. More recently, linear elastic-perfectly plastic or elastic-brittle damage approaches were used to explain the time evolution of the surface displacements in basaltic volcanoes before an eruption. However these models are non-linear elastic, and can not account for the anelastic deformation that occurs during the pre-eruptive process. Therefore, they can not be used to represent the complete eruptive cycle, comprising loading and unloading phases. Here we present a new rheological approach for modelling the eruptive cycle called Maxwell-Elasto-Brittle, which incorporates a viscous-like relaxation of the stresses in an elastic-brittle damage framework. This mechanism allows accounting for the anelastic deformations that cumulate and lead to rupture and eruption. The inclusion of healing processes in this model is another step towards a complete spatio-temporal representation of the eruptive cycle. Plane-strain Maxwell-EB modelling of the deformation of a magma reservoir and volcanic edifice will be presented. The model represents the propagation of damage towards the surface and the progressive localization of the deformation along faults under the pressurization of the magma reservoir. This model allows a complete spatio-temporal representation of the rupture process. We will also discuss how available seismicity records and time series of surface displacements could be used jointly to constrain the model.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Polycrystalline gamma plutonium's elastic moduli versus temperature

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

Migliori, Albert; Betts, J; Trugman, A

2009-01-01

Resonant ultrasound spectroscopy was used to measure the elastic properties of pure polycrystalline {sup 239}Pu in the {gamma} phase. Shear and longitudinal elastic moduli were measured simultaneously and the bulk modulus was computed from them. A smooth, linear, and large decrease of all elastic moduli with increasing temperature was observed. They calculated the Poisson ratio and found that it increases from 0.242 at 519 K to 0.252 at 571 K. These measurements on extremely well characterized pure Pu are in agreement with other reported results where overlap occurs.

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.

Ultrastructure of the bovine nuchal ligament.

PubMed Central

Morocutti, M; Raspanti, M; Ottani, V; Govoni, P; Ruggeri, A

1991-01-01

Nuchal ligament is composed almost exclusively of elastic fibres and collagen fibrils, interwoven very closely and lying parallel to the main ligament axis. Elastic fibres are very large, straight and roughly cylindrical; the collagenous matrix consists of septa of diminishing size forming a 3-dimensional matrix that envelops fibre bundles as well as individual elastic fibres. In all areas examined, collagen fibrils are of very uniform size and, on replicas, they reveal a spiral subfibrillar arrangement with an inclination angle of 17 degrees. Collagen fibrils appear to adhere to the elastic fibres very closely, conforming to their irregular shape. Sometimes they impinge directly upon the elastic fibres, while in other cases a space is visible between collagen fibrils and elastic fibres that contains a rich fabric of intermediate filaments. The collagen-elastin complex of the ligamentum nuchae may be considered a fibre-reinforced composite material comprising tough fibres immersed in an amorphous elastic matrix. Its mechanical behaviour is the result of the combined properties of its components and their interactions. Images Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 PMID:1810923

High elastic modulus polymer electrolytes

DOEpatents

Balsara, Nitash Pervez; Singh, Mohit; Eitouni, Hany Basam; Gomez, Enrique Daniel

2013-10-22

A polymer that combines high ionic conductivity with the structural properties required for Li electrode stability is useful as a solid phase electrolyte for high energy density, high cycle life batteries that do not suffer from failures due to side reactions and dendrite growth on the Li electrodes, and other potential applications. The polymer electrolyte includes a linear block copolymer having a conductive linear polymer block with a molecular weight of at least 5000 Daltons, a structural linear polymer block with an elastic modulus in excess of 1.times.10.sup.7 Pa and an ionic conductivity of at least 1.times.10.sup.-5 Scm.sup.-1. The electrolyte is made under dry conditions to achieve the noted characteristics.

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

PubMed

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

Mechanical and histological characterization of the abdominal muscle. A previous step to modelling hernia surgery.

PubMed

Hernández, B; Peña, E; Pascual, G; Rodríguez, M; Calvo, B; Doblaré, M; Bellón, J M

2011-04-01

The aims of this study are to experimentally characterize the passive elastic behaviour of the rabbit abdominal wall and to develop a mechanical constitutive law which accurately reproduces the obtained experimental results. For this purpose, tissue samples from New Zealand White rabbits 2150±50 (g) were mechanically tested in vitro. Mechanical tests, consisting of uniaxial loading on tissue samples oriented along the craneo-caudal and the perpendicular directions, respectively, revealed the anisotropic non-linear mechanical behaviour of the abdominal tissues. Experiments were performed considering the composite muscle (including external oblique-EO, internal oblique-IO and transverse abdominis-TA muscle layers), as well as separated muscle layers (i.e., external oblique, and the bilayer formed by internal oblique and transverse abdominis). Both the EO muscle layer and the IO-TA bilayer demonstrated a stiffer behaviour along the transversal direction to muscle fibres than along the longitudinal one. The fibre arrangement was measured by means of a histological study which confirmed that collagen fibres are mainly responsible for the passive mechanical strength and stiffness. Furthermore, the degree of anisotropy of the abdominal composite muscle turned out to be less pronounced than those obtained while studying the EO and IO-TA separately. Moreover, a phenomenological constitutive law was used to capture the measured experimental curves. A Levenberg-Marquardt optimization algorithm was used to fit the model constants to reproduce the experimental curves. Copyright © 2010 Elsevier Ltd. All rights reserved.

Classical and sequential limit analysis revisited

NASA Astrophysics Data System (ADS)

Leblond, Jean-Baptiste; Kondo, Djimédo; Morin, Léo; Remmal, Almahdi

2018-04-01

Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic-plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity - in the absence of hardening and within a linearized geometrical framework -, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity - although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic-plastic coupling in the specific case considered.

Effects of aging on the architecture of the ileocecal junction in rats

PubMed Central

de Brito, Maria Cícera; Chopard, Renato Paulo; Cury, Diego Pulzatto; Watanabe, Ii Sei; Mendes, Cristina Eusébio; Castelucci, Patricia

2016-01-01

AIM: To evaluate the structural organization of the elastic and collagen fibers in the region of the ileocecal transition in 30 young and old male Wistar rats. METHODS: Histology, immunohistochemistry (IHC), transmission electron microscopy and scanning electron microscopy were employed in this study. The results demonstrated that there was a demarcation of the ileocecal region between the ileum and the cecum in both groups. RESULTS: The connective tissue fibers had different distribution patterns in the two groups. IHC revealed the presence of nitric oxide synthase, enteric neurons and smooth muscle fibers in the ileocecal junctions (ICJs) of both groups. Compared to the young group, the elderly group exhibited an increase in collagen type I fibers, a decrease in collagen type III fibers, a decreased linear density of oxytalan elastic fibers, and a greater linear density of elaunin and mature elastic fibers. CONCLUSION: The results revealed changes in the patterns of distribution of collagen and elastic fibers that may lead to a possible decrease in ICJ functionality. PMID:27602243

Functional forms and price elasticities in a discrete continuous choice model of the residential water demand

NASA Astrophysics Data System (ADS)

Vásquez Lavín, F. A.; Hernandez, J. I.; Ponce, R. D.; Orrego, S. A.

2017-07-01

During recent decades, water demand estimation has gained considerable attention from scholars. From an econometric perspective, the most used functional forms include log-log and linear specifications. Despite the advances in this field and the relevance for policymaking, little attention has been paid to the functional forms used in these estimations, and most authors have not provided justifications for their selection of functional forms. A discrete continuous choice model of the residential water demand is estimated using six functional forms (log-log, full-log, log-quadratic, semilog, linear, and Stone-Geary), and the expected consumption and price elasticity are evaluated. From a policy perspective, our results highlight the relevance of functional form selection for both the expected consumption and price elasticity.

Elastic Scattering of 65 MeV Protons from Several Nuclei between 16O and 209Bi

NASA Astrophysics Data System (ADS)

Ahmed, Syed; Akther, Parvin; Ferdous, Nasima; Begum, Amena; Gupta, Hiranmay

1997-10-01

Elastic scattering of 65 MeV polarized protons from twenty five nuclei ranging from 16O to 209Bi have been analysed within the framework of the nine parameter optical model. A set of optical model parameters has been obtained which shows the systematic behaviour of the target mass dependence of the real potential, volume integral and the r.m.s. radius. The isotopic spin dependence of the real potential has also been studied. Parameters obtained by fitting the elastic scattering data have been able to reproduce the pickup and stripping reaction cross sections as studied in a few cases.

Substrate stress relaxation regulates cell spreading

NASA Astrophysics Data System (ADS)

Chaudhuri, Ovijit; Gu, Luo; Darnell, Max; Klumpers, Darinka; Bencherif, Sidi A.; Weaver, James C.; Huebsch, Nathaniel; Mooney, David J.

2015-02-01

Studies of cellular mechanotransduction have converged upon the idea that cells sense extracellular matrix (ECM) elasticity by gauging resistance to the traction forces they exert on the ECM. However, these studies typically utilize purely elastic materials as substrates, whereas physiological ECMs are viscoelastic, and exhibit stress relaxation, so that cellular traction forces exerted by cells remodel the ECM. Here we investigate the influence of ECM stress relaxation on cell behaviour through computational modelling and cellular experiments. Surprisingly, both our computational model and experiments find that spreading for cells cultured on soft substrates that exhibit stress relaxation is greater than cells spreading on elastic substrates of the same modulus, but similar to that of cells spreading on stiffer elastic substrates. These findings challenge the current view of how cells sense and respond to the ECM.

High-energy transmission Laue micro-beam X-ray diffraction: a probe for intra-granular lattice orientation and elastic strain in thicker samples.

PubMed

Hofmann, Felix; Song, Xu; Abbey, Brian; Jun, Tea-Sung; Korsunsky, Alexander M

2012-05-01

An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load-bearing components in high-performance safety-critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'-type mechanisms. It is strongly dependent on the anisotropic single-crystal elastic-plastic behaviour, local morphology and microstructure, and grain-to-grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro-scale is key. The diffraction of highly penetrating synchrotron X-rays is well suited to this purpose and micro-beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5-25 keV, limiting penetration into the material, so that only thin samples or near-surface regions can be studied. In this paper the development of high-energy transmission Laue (HETL) micro-beam X-ray diffraction is described, extending the micro-beam Laue technique to significantly higher photon energies (50-150 keV). It allows the probing of thicker sample sections, with the potential for grain-level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large-grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is studied using a pattern-matching approach. The results highlight the inability of a simple Schmid-factor model to capture the behaviour of individual grains and illustrate the need for complementary mechanical modelling.

Comparison of the DeWitt metric in general relativity with the fourth-rank constitutive tensors in electrodynamics and in elasticity theory

NASA Astrophysics Data System (ADS)

Hehl, Friedrich W.; Kiefer, Claus

2018-01-01

We perform a short comparison between the local and linear constitutive tensor χ ^{λ ν σ κ } in four-dimensional electrodynamics, the elasticity tensor c^{ijkl} in three-dimensional elasticity theory, and the DeWitt metric G^{abcd} in general relativity, with {a,b,\\ldots =1,2,3}. We find that the DeWitt metric has only six independent components.

An Experimental and Finite Element Investigation into the Nonlinear Material Behavior of Pin-Loaded Composite Laminates

DTIC Science & Technology

1991-01-01

their midsurface counterparts due to the nature of the pin deflection and resulting load transfer. Linear elastic coupon radial stresses also followed... midsurface counterparts. The effects of the nonlinear elastic material behavior were quite evident when viewing the [(0/90)3,01, coupon intralaminar...to the midsurface of the coupon. The nonlinear elastic intralaminar shear stress-strain assumption acted to increase through thickness stresses

Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

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

Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.

1993-11-01

Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.

Series elastic actuation of an elbow rehabilitation exoskeleton with axis misalignment adaptation.

PubMed

Wu, Kuan-Yi; Su, Yin-Yu; Yu, Ying-Lung; Lin, Kuei-You; Lan, Chao-Chieh

2017-07-01

Powered exoskeletons can facilitate rehabilitation of patients with upper limb disabilities. Designs using rotary motors usually result in bulky exoskeletons to reduce the problem of moving inertia. This paper presents a new linearly actuated elbow exoskeleton that consists of a slider crank mechanism and a linear motor. The linear motor is placed beside the upper arm and closer to shoulder joint. Thus better inertia properties can be achieved while lightweight and compactness are maintained. A passive joint is introduced to compensate for the exoskeleton-elbow misalignment and intersubject size variation. A linear series elastic actuator (SEA) is proposed to obtain accurate force and impedance control at the exoskeleton-elbow interface. Bidirectional actuation between exoskeleton and forearm is verified, which is required for various rehabilitation processes. We expect this exoskeleton can provide a means of robot-aided elbow rehabilitation.

Perception of Elasticity in the Kinetic Illusory Object with Phase Differences in Inducer Motion

PubMed Central

Masuda, Tomohiro; Sato, Kazuki; Murakoshi, Takuma; Utsumi, Ken; Kimura, Atsushi; Shirai, Nobu; Kanazawa, So; Yamaguchi, Masami K.; Wada, Yuji

2013-01-01

Background It is known that subjective contours are perceived even when a figure involves motion. However, whether this includes the perception of rigidity or deformation of an illusory surface remains unknown. In particular, since most visual stimuli used in previous studies were generated in order to induce illusory rigid objects, the potential perception of material properties such as rigidity or elasticity in these illusory surfaces has not been examined. Here, we elucidate whether the magnitude of phase difference in oscillation influences the visual impressions of an object's elasticity (Experiment 1) and identify whether such elasticity perceptions are accompanied by the shape of the subjective contours, which can be assumed to be strongly correlated with the perception of rigidity (Experiment 2). Methodology/Principal Findings In Experiment 1, the phase differences in the oscillating motion of inducers were controlled to investigate whether they influenced the visual impression of an illusory object's elasticity. The results demonstrated that the impression of the elasticity of an illusory surface with subjective contours was systematically flipped with the degree of phase difference. In Experiment 2, we examined whether the subjective contours of a perceived object appeared linear or curved using multi-dimensional scaling analysis. The results indicated that the contours of a moving illusory object were perceived as more curved than linear in all phase-difference conditions. Conclusions/Significance These findings suggest that the phase difference in an object's motion is a significant factor in the material perception of motion-related elasticity. PMID:24205281

Deformation of compound shells under action of internal shock wave loading

NASA Astrophysics Data System (ADS)

Chernobryvko, Marina; Kruszka, Leopold; Avramov, Konstantin

2015-09-01

The compound shells under the action of internal shock wave loading are considered. The compound shell consists of a thin cylindrical shell and two thin parabolic shells at the edges. The boundary conditions in the shells joints satisfy the equality of displacements. The internal shock wave loading is modelled as the surplus pressure surface. This pressure is a function of the shell coordinates and time. The strain rate deformation of compound shell takes place in both the elastic and in plastic stages. In the elastic stage the equations of the structure motions are obtained by the assumed-modes method, which uses the kinetic and potential energies of the cylindrical and two parabolic shells. The dynamic behaviour of compound shells is treated. In local plastic zones the 3-D thermo-elastic-plastic model is used. The deformations are described by nonlinear model. The stress tensor elements are determined using dynamic deformation theory. The deformation properties of materials are influenced by the strain rate behaviour, the influence of temperature parameters, and the elastic-plastic properties of materials. The dynamic yield point of materials and Pisarenko-Lebedev's criterion of destruction are used. The modified adaptive finite differences method of numerical analysis is suggested for those simulations. The accuracy of the numerical simulation is verified on each temporal step of calculation and in the case of large deformation gradients.

The Application of Simulation Method in Isothermal Elastic Natural Gas Pipeline

NASA Astrophysics Data System (ADS)

Xing, Chunlei; Guan, Shiming; Zhao, Yue; Cao, Jinggang; Chu, Yanji

2018-02-01

This Elastic pipeline mathematic model is of crucial importance in natural gas pipeline simulation because of its compliance with the practical industrial cases. The numerical model of elastic pipeline will bring non-linear complexity to the discretized equations. Hence the Newton-Raphson method cannot achieve fast convergence in this kind of problems. Therefore A new Newton Based method with Powell-Wolfe Condition to simulate the Isothermal elastic pipeline flow is presented. The results obtained by the new method aregiven based on the defined boundary conditions. It is shown that the method converges in all cases and reduces significant computational cost.

Optimal mechanical design of anatomical post-systems for endodontic restoration.

PubMed

Maceri, Franco; Martignoni, Marco; Vairo, Giuseppe

2009-02-01

This paper analyses the mechanical behaviour of a new reinforced anatomical post-systems (RAPS) for endodontic restoration. The composite restorative material (CRM) completely fills the root canal (as do the commonly used cast metal posts) and multiple prefabricated composite posts (PCPs) are employed as reinforcements. Numerical simulations based on 3D linearly elastic finite element models under parafunctional loads were performed in order to investigate the influence of the stiffness of the CRM and of the number of PCPs. Periodontal ligament effects were taken into account using a discretised anisotropic nonlinearly elastic spring system, and the full discrete model was validated by comparing the resulting stress fields with those obtained with conventional restorations (cast gold-alloy post, homogeneous anatomical post and cemented single PCP) and with the natural tooth. Analysis of the results shows that stresses at the cervical/middle region decrease as CRM stiffness increases and, for large and irregular root cavities that apical stress peaks disappear when multiple PCPs are used. Accordingly, from a mechanical point of view, an optimal RAPS will use multiple PCPs when CRM stiffness is equal to or at most twice that of the dentin. This restorative solution minimises stress differences with respect to the natural tooth, mechanical inhomogeneities, stress concentrations on healthy tissues, volumes subject to shrinkage phenomena, fatigue effects and risks of both root fracture and adhesive/cohesive interfacial failure.

An analysis of hypercritical states in elastic and inelastic systems

NASA Astrophysics Data System (ADS)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

Elastic and viscoelastic mechanical properties of brain tissues on the implanting trajectory of sub-thalamic nucleus stimulation.

PubMed

Li, Yan; Deng, Jianxin; Zhou, Jun; Li, Xueen

2016-11-01

Corresponding to pre-puncture and post-puncture insertion, elastic and viscoelastic mechanical properties of brain tissues on the implanting trajectory of sub-thalamic nucleus stimulation are investigated, respectively. Elastic mechanical properties in pre-puncture are investigated through pre-puncture needle insertion experiments using whole porcine brains. A linear polynomial and a second order polynomial are fitted to the average insertion force in pre-puncture. The Young's modulus in pre-puncture is calculated from the slope of the two fittings. Viscoelastic mechanical properties of brain tissues in post-puncture insertion are investigated through indentation stress relaxation tests for six interested regions along a planned trajectory. A linear viscoelastic model with a Prony series approximation is fitted to the average load trace of each region using Boltzmann hereditary integral. Shear relaxation moduli of each region are calculated using the parameters of the Prony series approximation. The results show that, in pre-puncture insertion, needle force almost increases linearly with needle displacement. Both fitting lines can perfectly fit the average insertion force. The Young's moduli calculated from the slope of the two fittings are worthy of trust to model linearly or nonlinearly instantaneous elastic responses of brain tissues, respectively. In post-puncture insertion, both region and time significantly affect the viscoelastic behaviors. Six tested regions can be classified into three categories in stiffness. Shear relaxation moduli decay dramatically in short time scales but equilibrium is never truly achieved. The regional and temporal viscoelastic mechanical properties in post-puncture insertion are valuable for guiding probe insertion into each region on the implanting trajectory.

Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation.

PubMed

Yamakov, V; Wolf, D; Phillpot, S R; Mukherjee, A K; Gleiter, H

2004-01-01

Molecular-dynamics simulations have recently been used to elucidate the transition with decreasing grain size from a dislocation-based to a grain-boundary-based deformation mechanism in nanocrystalline f.c.c. metals. This transition in the deformation mechanism results in a maximum yield strength at a grain size (the 'strongest size') that depends strongly on the stacking-fault energy, the elastic properties of the metal, and the magnitude of the applied stress. Here, by exploring the role of the stacking-fault energy in this crossover, we elucidate how the size of the extended dislocations nucleated from the grain boundaries affects the mechanical behaviour. Building on the fundamental physics of deformation as exposed by these simulations, we propose a two-dimensional stress-grain size deformation-mechanism map for the mechanical behaviour of nanocrystalline f.c.c. metals at low temperature. The map captures this transition in both the deformation mechanism and the related mechanical behaviour with decreasing grain size, as well as its dependence on the stacking-fault energy, the elastic properties of the material, and the applied stress level.

The elastic properties of woven polymeric fabric

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

Warren, W.E.

1989-01-01

The in-plane linear elastic constants of woven fabric are determined in terms of the specific fabric microstructure. The fabric is assumed to be a spatially periodic interlaced network of orthogonal yarns and the individual yarns are modeled as extensible elastica. These results indicate that a significant coupling of bending and stretching effects occurs during deformation. Results of this theoretical analysis compare favorable with measured in-plane elastic constants for Vincel yarn fabrics. 17 refs., 2 figs., 1 tab.

Calculation of skin-stiffener interface stresses in stiffened composite panels

NASA Technical Reports Server (NTRS)

Cohen, David; Hyer, Michael W.

1987-01-01

A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.

Structure-Property Relations in Aluminum-Lithium Alloys

DTIC Science & Technology

1989-01-01

adsorbed ( Mughrabi et al , 1983). Such dislocations could not re-enter the grain during the reverse cycle of stress and the associated slip would be...ASTM STP 601, ASTM, 33 Mughrabi , H., Wang, R., Differt, D., Essmann, U. (1983) ASTM STP 811, ASTM, 5 Muller, W. et al (1986) Aluminium-Lithium Alloys...behaviour of Al -Li-Cu-Mg-Zr alloys ...... 34 2.4 Mechanical behaviour ......................................... 35 2.4.1 Elastic modulus

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress

NASA Astrophysics Data System (ADS)

Tchitchekova, Deyana S.; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-01

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ˜3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress.

PubMed

Tchitchekova, Deyana S; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-21

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ∼3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

Elastic membranes in confinement.

PubMed

Bostwick, J B; Miksis, M J; Davis, S H

2016-07-01

An elastic membrane stretched between two walls takes a shape defined by its length and the volume of fluid it encloses. Many biological structures, such as cells, mitochondria and coiled DNA, have fine internal structure in which a membrane (or elastic member) is geometrically 'confined' by another object. Here, the two-dimensional shape of an elastic membrane in a 'confining' box is studied by introducing a repulsive confinement pressure that prevents the membrane from intersecting the wall. The stage is set by contrasting confined and unconfined solutions. Continuation methods are then used to compute response diagrams, from which we identify the particular membrane mechanics that generate mitochondria-like shapes. Large confinement pressures yield complex response diagrams with secondary bifurcations and multiple turning points where modal identities may change. Regions in parameter space where such behaviour occurs are then mapped. © 2016 The Author(s).

On the Impact of a Quadratic Acceleration Term in the Analysis of Position Time Series

NASA Astrophysics Data System (ADS)

Bogusz, Janusz; Klos, Anna; Bos, Machiel Simon; Hunegnaw, Addisu; Teferle, Felix Norman

2016-04-01

The analysis of Global Navigation Satellite System (GNSS) position time series generally assumes that each of the coordinate component series is described by the sum of a linear rate (velocity) and various periodic terms. The residuals, the deviations between the fitted model and the observations, are then a measure of the epoch-to-epoch scatter and have been used for the analysis of the stochastic character (noise) of the time series. Often the parameters of interest in GNSS position time series are the velocities and their associated uncertainties, which have to be determined with the highest reliability. It is clear that not all GNSS position time series follow this simple linear behaviour. Therefore, we have added an acceleration term in the form of a quadratic polynomial function to the model in order to better describe the non-linear motion in the position time series. This non-linear motion could be a response to purely geophysical processes, for example, elastic rebound of the Earth's crust due to ice mass loss in Greenland, artefacts due to deficiencies in bias mitigation models, for example, of the GNSS satellite and receiver antenna phase centres, or any combination thereof. In this study we have simulated 20 time series with different stochastic characteristics such as white, flicker or random walk noise of length of 23 years. The noise amplitude was assumed at 1 mm/y-/4. Then, we added the deterministic part consisting of a linear trend of 20 mm/y (that represents the averaged horizontal velocity) and accelerations ranging from minus 0.6 to plus 0.6 mm/y2. For all these data we estimated the noise parameters with Maximum Likelihood Estimation (MLE) using the Hector software package without taken into account the non-linear term. In this way we set the benchmark to then investigate how the noise properties and velocity uncertainty may be affected by any un-modelled, non-linear term. The velocities and their uncertainties versus the accelerations for different types of noise are determined. Furthermore, we have selected 40 globally distributed stations that have a clear non-linear behaviour from two different International GNSS Service (IGS) analysis centers: JPL (Jet Propulsion Laboratory) and BLT (British Isles continuous GNSS Facility and University of Luxembourg Tide Gauge Benchmark Monitoring (TIGA) Analysis Center). We obtained maximum accelerations of -1.8±1.2 mm2/y and -4.5±3.3 mm2/y for the horizontal and vertical components, respectively. The noise analysis tests have shown that the addition of the non-linear term has significantly whitened the power spectra of the position time series, i.e. shifted the spectral index from flicker towards white noise.

Elasticity modulated Electrowetting of a sessile liquid droplet

NASA Astrophysics Data System (ADS)

Kumar, Sumit; Subramanian, Sri Ganesh; Dasgupta, Sunando; Chakraborty, Suman

2017-11-01

The sessile liquid droplets on the elastic and soft deformable surface produce strong deformation near the three-phase contact line (TPCL). The capillary and elastic forces play an important role during this deformation, and deteriorate the wetting behaviour of a sessile drop. The present work combines the effects of liquid viscosity and substrate elasticity on the dynamics of EWOD. The influence of decreasing film elasticity and viscosity on the electrowetting response of a sessile drop is experimentally investigated by delineating the changes in equilibrium apparent contact angles on substrates with varying Young's modulus of elasticity. The increase in viscosity of the liquid leads to greater electrowetting for non-deformable substrates whereas; the dynamics are not greatly affected in case of soft substrates. Although the viscosity appears to be an influential factor, the dynamics are more skewed towards the substrate rigidity. The vertical component of Young's force creates a wetting ridge at the three-phase contact line, the height of which is a direct function of the substrate rigidity. The produced ridges reduce the overall wettability of the droplet.

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

NASA Astrophysics Data System (ADS)

Spannenberg, Jescica; Atangana, Abdon; Vermeulen, P. D.

2017-09-01

Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

Seismic waves in heterogeneous material: subcell resolution of the discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Castro, Cristóbal E.; Käser, Martin; Brietzke, Gilbert B.

2010-07-01

We present an important extension of the arbitrary high-order discontinuous Galerkin (DG) finite-element method to model 2-D elastic wave propagation in highly heterogeneous material. In this new approach we include space-variable coefficients to describe smooth or discontinuous material variations inside each element using the same numerical approximation strategy as for the velocity-stress variables in the formulation of the elastic wave equation. The combination of the DG method with a time integration scheme based on the solution of arbitrary accuracy derivatives Riemann problems still provides an explicit, one-step scheme which achieves arbitrary high-order accuracy in space and time. Compared to previous formulations the new scheme contains two additional terms in the form of volume integrals. We show that the increasing computational cost per element can be overcompensated due to the improved material representation inside each element as coarser meshes can be used which reduces the total number of elements and therefore computational time to reach a desired error level. We confirm the accuracy of the proposed scheme performing convergence tests and several numerical experiments considering smooth and highly heterogeneous material. As the approximation of the velocity and stress variables in the wave equation and of the material properties in the model can be chosen independently, we investigate the influence of the polynomial material representation on the accuracy of the synthetic seismograms with respect to computational cost. Moreover, we study the behaviour of the new method on strong material discontinuities, in the case where the mesh is not aligned with such a material interface. In this case second-order linear material approximation seems to be the best choice, with higher-order intra-cell approximation leading to potential instable behaviour. For all test cases we validate our solution against the well-established standard fourth-order finite difference and spectral element method.

Large poroelastic deformation of a soft material

NASA Astrophysics Data System (ADS)

MacMinn, Christopher W.; Dufresne, Eric R.; Wettlaufer, John S.

2014-11-01

Flow through a porous material will drive mechanical deformation when the fluid pressure becomes comparable to the stiffness of the solid skeleton. This has applications ranging from hydraulic fracture for recovery of shale gas, where fluid is injected at high pressure, to the mechanics of biological cells and tissues, where the solid skeleton is very soft. The traditional linear theory of poroelasticity captures this fluid-solid coupling by combining Darcy's law with linear elasticity. However, linear elasticity is only volume-conservative to first order in the strain, which can become problematic when damage, plasticity, or extreme softness lead to large deformations. Here, we compare the predictions of linear poroelasticity with those of a large-deformation framework in the context of two model problems. We show that errors in volume conservation are compounded and amplified by coupling with the fluid flow, and can become important even when the deformation is small. We also illustrate these results with a laboratory experiment.

Long-term elasticity in the continental lithosphere; modelling the Aden Ridge propagation and the Anatolian extrusion process

NASA Astrophysics Data System (ADS)

Hubert-Ferrari, Aurélia; King, Geoffrey; Manighetti, Isabelle; Armijo, Rolando; Meyer, Bertrand; Tapponnier, Paul

2003-04-01

The evolution of the Gulf of Aden and the Anatolian Fault systems are modelled using the principles of elastic fracture mechanics usually applied to smaller scale cracks or faults. The lithosphere is treated as a plate, and simple boundary conditions are applied that correspond to the known plate boundary geometry and slip vectors. The models provide a simple explanation for many observed geological features. For the Gulf of Aden the model predicts why the ridge propagated from east to west from the Owen Fracture Zone towards the Afar and the overall form of its path. The smaller en echelon offsets can be explained by upward propagation from the initially created mantle dyke while the larger ones may be attributed to the propagating rupture interacting with pre-existing structures. For Anatolia the modelling suggests that the East Anatolian Fault was created before the North Anatolian Fault could form. Once both faults were formed however, activity could switch between them. The time scales over which this should take place are not known, but evidence for switching can be found in the historical seismicity. For Aden and Anatolia pre-existing structures or inhomogeneous stress fields left from earlier orogenic events have modified the processes of propagation and without an understanding of the existence of such features the propagation processes cannot be fully understood. Furthermore a propagating fault can extend into an active region where it would not have initiated. The North Anatolian Fault encountered slow but active extension when it entered the Aegean about 5 Ma and the stress field associated with the extending fault has progressively modified Aegean extension. In the central Aegean activity has been reduced while to the north-west on features such as the Gulfs of Evvia and Corinth activity has been increased. The field observation that major structures propagate and the success of simple elastic models suggest that the continental crust behaves in an elastic-brittle or elastic-plastic fashion even though laboratory tests may be interpreted to suggest viscous behaviour. There are major problems in scaling from the behaviour of small homogeneous samples to the large heterogeneous mantle and large-scale observations should be treated more seriously than extrapolations of the behaviour of laboratory experiments over many orders of magnitude in space and time. The retention of long-term elasticity and localised failure suggests a similar gross rheology for the oceanic and continental lithospheres. Even though it is incorrect to attribute differences in behaviour to the former being rigid (i.e. elastic) and the latter viscous, oceanic and continental lithosphere behave in different ways. Unlike oceanic crust, continental crust is buoyant and cannot be simply created or destroyed. The process of thickening or thinning works against gravity preventing large displacements on extensional or contractional features in the upper mantle. The equivalents of ridge or subduction systems are suppressed before they can accommodate large displacements and activity must shift elsewhere. On the other hand, strike-slip boundaries and extrusion processes are favoured.

Importance of elastic finite-size effects: Neutral defects in ionic compounds

NASA Astrophysics Data System (ADS)

Burr, P. A.; Cooper, M. W. D.

2017-09-01

Small system sizes are a well-known source of error in density functional theory (DFT) calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite-size effects have been well characterized, but self-interaction of charge-neutral defects is often discounted or assumed to follow an asymptotic behavior and thus easily corrected with linear elastic theory. Here we show that elastic effects are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequately small supercells are used; moreover, the spurious self-interaction does not follow the behavior predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground-state structure of (charge-neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768, and 1500 atoms), and careful analysis determines that elastic, not electrostatic, effects are responsible. The spurious self-interaction was also observed in nonoxide ionic compounds irrespective of the computational method used, thereby resolving long-standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects is a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g., hybrid functionals) or when modeling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studied oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells: greater than 96 atoms.

Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities

NASA Astrophysics Data System (ADS)

Balthazar, J. M.; Brasil, R. M. L. F.; Felix, J. L. P.; Tusset, A. M.; Picirillo, V.; Iluik, I.; Rocha, R. T.; Nabarrete, A.; Oliveira, C.

2016-05-01

This paper overviews recent developments on some problems related to elastic structures, such as portal frames, taking into account the full interactions of the vibrating systems, with an energy source of limited power supply (small motors, electro-mechanical shakers). We include a discussion on fractional (rational) damping and stiffness effects on the adopted modelling. This was a plenary lecture, delivered in the event titled: Mechanics of Slender Structures, organized in Northampton, England from 21-22, September 2015.

The Role of Evolutive Elastic Properties in the Performance of a Sheet Formed Spring Applied in Multimedia Car Industry

NASA Astrophysics Data System (ADS)

Faria, J.; Silva, J.; Bernardo, P.; Araújo, M.; Alves, J. L.

2016-08-01

The manufacturing process and the behaviour of a spring manufactured from an aluminium sheet is described and investigated in this work considering the specifications for the in-service conditions. The spring is intended to be applied in car multimedia industry to replace bolted connections. Among others, are investigated the roles of the constitutive parameters and the hypothesis of evolutive elastic properties with the plastic work in the multistep forming process and in working conditions.

Effect of ripples on the finite temperature elastic properties of hexagonal boron nitride using strain-fluctuation method

NASA Astrophysics Data System (ADS)

Thomas, Siby; Ajith, K. M.; Valsakumar, M. C.

2017-11-01

This work intents to put forth the results of a classical molecular dynamics study to investigate the temperature dependent elastic constants of monolayer hexagonal boron nitride (h-BN) between 100 and 1000 K for the first time using strain fluctuation method. The temperature dependence of out-of-plane fluctuations (ripples) is quantified and is explained using continuum theory of membranes. At low temperatures, negative in-plane thermal expansion is observed and at high temperatures, a transition to positive thermal expansion has been observed due to the presence of thermally excited ripples. The decrease of Young's modulus, bulk modulus, shear modulus and Poisson's ratio with increase in temperature has been analyzed. The thermal rippling in h-BN leads to strong anharmonic behaviour that causes large deviation from the isotropic elasticity. A detailed study shows that the strong thermal rippling in large systems is also responsible for the softening of elastic constants in h-BN. From the determined values of elastic constants and elastic moduli, it has been elucidated that 2D h-BN sheets meet the Born's mechanical stability criterion in the investigated temperature range. The variation of longitudinal and shear velocities with temperature is also calculated from the computed values of elastic constants and elastic moduli.

Fillet Weld Stress Using Finite Element Methods

NASA Technical Reports Server (NTRS)

Lehnhoff, T. F.; Green, G. W.

1985-01-01

Average elastic Von Mises equivalent stresses were calculated along the throat of a single lap fillet weld. The average elastic stresses were compared to initial yield and to plastic instability conditions to modify conventional design formulas is presented. The factor is a linear function of the thicknesses of the parent plates attached by the fillet weld.

Wave-front singularities for two-dimensional anisotropic elastic waves.

NASA Technical Reports Server (NTRS)

Payton, R. G.

1972-01-01

Wavefront singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d to the -1/2 power, where d measures distance away from the front. However, in certain exceptional cases singularities of order d to the -n power, where n = 1/4, 2/3, 3/4, may be encountered.

Finite Deformations and Internal Forces in Elastic-Plastic Crystals: Interpretations From Nonlinear Elasticity and Anharmonic Lattice Statics

DTIC Science & Technology

2009-09-01

Sec. 2, while the latter ase—which implicitly includes the effects of image forces of efects in neighboring volume elements—may be more practical rom...versetzungen und eigenspannungen,” Arch . Ration. Mech. Anal., 4, pp. 273–334. 25 Lee, E. H., 1969, “Elastic-Plastic Deformation at Finite Strains,” ASME J...Rev., 73, pp. 373–382. 27 Kroner, E., and Seeger, A., 1959, “Nicht-Lineare Elastizitatstheorie der Verset- zungen und Eigenspannungen,” Arch . Ration

Ab-initio study of electronic structure and elastic properties of ZrC

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

Mund, H. S., E-mail: hmoond@gmail.com; Ahuja, B. L.

2016-05-23

The electronic and elastic properties of ZrC have been investigated using the linear combination of atomic orbitals method within the framework of density functional theory. Different exchange-correlation functionals are taken into account within generalized gradient approximation. We have computed energy bands, density of states, elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, lattice parameters and pressure derivative of the bulk modulus by calculating ground state energy of the rock salt structure type ZrC.

How tall can gelatin towers be? An introduction to elasticity and buckling

NASA Astrophysics Data System (ADS)

Taberlet, Nicolas; Ferrand, Jérémy; Camus, Élise; Lachaud, Léa; Plihon, Nicolas

2017-12-01

The stability of elastic towers is studied through simple hands-on experiments. Using gelatin-based stackable bricks, one can investigate the maximum height a simple structure can reach before collapsing. We show through experiments and by using the classical linear elastic theory that the main limitation to the height of such towers is the buckling of the elastic structures under their own weight. Moreover, the design and architecture of the towers can be optimized to greatly improve their resistance to self-buckling. To this aim, the maximum height of hollow and tapered towers is investigated. The experimental and theoretical developments presented in this paper can help students grasp the fundamental concepts in elasticity and mechanical stability.

Emergence of linear elasticity from the atomistic description of matter

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

Cakir, Abdullah, E-mail: acakir@ntu.edu.sg; Pica Ciamarra, Massimo; Dipartimento di Scienze Fisiche, CNR–SPIN, Università di Napoli Federico II, I-80126 Napoli

2016-08-07

We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of themore » fluctuations of the local elastic constants close to the jamming transition.« less

Micromechanical analysis on anisotropy of structured magneto-rheological elastomer

NASA Astrophysics Data System (ADS)

Li, R.; Zhang, Z.; Chen, S. W.; Wang, X. J.

2015-07-01

This paper investigates the equivalent elastic modulus of structured magneto-rheological elastomer (MRE) in the absence of magnetic field. We assume that both matrix and ferromagnetic particles are linear elastic materials, and ferromagnetic particles are embedded in matrix with layer-like structure. The structured composite could be divided into matrix layer and reinforced layer, in which the reinforced layer is composed of matrix and the homogenously distributed ferromagnetic particles in matrix. The equivalent elastic modulus of reinforced layer is analysed by the Mori-Tanaka method. Finite Element Method (FEM) is also carried out to illustrate the relationship between the elastic modulus and the volume fraction of ferromagnetic particles. The results show that the anisotropy of elastic modulus becomes noticeable, as the volume fraction of particles increases.

Envelope of coda waves for a double couple source due to non-linear elasticity

NASA Astrophysics Data System (ADS)

Calisto, Ignacia; Bataille, Klaus

2014-10-01

Non-linear elasticity has recently been considered as a source of scattering, therefore contributing to the coda of seismic waves, in particular for the case of explosive sources. This idea is analysed further here, theoretically solving the expression for the envelope of coda waves generated by a point moment tensor in order to compare with earthquake data. For weak non-linearities, one can consider each point of the non-linear medium as a source of scattering within a homogeneous and linear medium, for which Green's functions can be used to compute the total displacement of scattered waves. These sources of scattering have specific radiation patterns depending on the incident and scattered P or S waves, respectively. In this approach, the coda envelope depends on three scalar parameters related to the specific non-linearity of the medium; however these parameters only change the scale of the coda envelope. The shape of the coda envelope is sensitive to both the source time function and the intrinsic attenuation. We compare simulations using this model with data from earthquakes in Taiwan, with a good fit.

Elastic and Photoelastic Properties of M(NO3)2, MO (M = Mg, Ca, Sr, Ba)

NASA Astrophysics Data System (ADS)

Zhuravlev, Yu. N.; Korabel'nikov, D. V.

2017-05-01

The paper deals with ab initio investigations of elastic and photoelastic properties of oxides and nitrates of alkaline-earth metals. In gradient approximation of the density functional theory (DFT), these properties are studied with the use of the linear combination of the atomic orbital technique. DFT calculations are done with the CRYSTAL 14 software package. The paper introduces the elastic and photoelastic constants, anisotropy parameters for single-crystalline phases and the elastic modules, hardness, Poisson ratio for polycrystalline phases. Such parameters as sonic speed, Debye temperature, thermal conductivity, and Gruneisen parameter are estimated herein. For the fist time, mechanical stability, anisotropy of elastic and photoelastic properties and their dependences are investigated ab initio in this paper. Experimental results on elastic and photoelastic properties of oxides and nitrates are in good agreement with theoretical calculations.

Relationship between tendon stiffness and failure: a metaanalysis

PubMed Central

LaCroix, Andrew S.; Duenwald-Kuehl, Sarah E.; Lakes, Roderic S.

2013-01-01

Tendon is a highly specialized, hierarchical tissue designed to transfer forces from muscle to bone; complex viscoelastic and anisotropic behaviors have been extensively characterized for specific subsets of tendons. Reported mechanical data consistently show a pseudoelastic, stress-vs.-strain behavior with a linear slope after an initial toe region. Many studies report a linear, elastic modulus, or Young's modulus (hereafter called elastic modulus) and ultimate stress for their tendon specimens. Individually, these studies are unable to provide a broader, interstudy understanding of tendon mechanical behavior. Herein we present a metaanalysis of pooled mechanical data from a representative sample of tendons from different species. These data include healthy tendons and those altered by injury and healing, genetic modification, allograft preparation, mechanical environment, and age. Fifty studies were selected and analyzed. Despite a wide range of mechanical properties between and within species, elastic modulus and ultimate stress are highly correlated (R2 = 0.785), suggesting that tendon failure is highly strain-dependent. Furthermore, this relationship was observed to be predictable over controlled ranges of elastic moduli, as would be typical of any individual species. With the knowledge gained through this metaanalysis, noninvasive tools could measure elastic modulus in vivo and reasonably predict ultimate stress (or structural compromise) for diseased or injured tendon. PMID:23599401

Phase field benchmark problems for dendritic growth and linear elasticity

DOE PAGES

Jokisaari, Andrea M.; Voorhees, P. W.; Guyer, Jonathan E.; ...

2018-03-26

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem formore » solidifiication and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. As a result, these numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.« less

Micropolar curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer-Viscous-Liquid-Layer System

NASA Astrophysics Data System (ADS)

Guz, A. N.; Bagno, A. M.

2017-07-01

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier -Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.

Experimental investigation of Rayleigh Taylor instability in elastic-plastic materials

NASA Astrophysics Data System (ADS)

Haley, Aaron Alan; Banerjee, Arindam

2010-11-01

The interface of an elastic-plastic plate accelerated by a fluid of lower density is Rayleigh Taylor (RT) unstable, the growth being mitigated by the mechanical strength of the plate. The instability is observed when metal plates are accelerated by high explosives, in explosive welding, and in volcanic island formation due to the strength of the inner crust. In contrast to the classical case involving Newtonian fluids, RT instability in accelerated solids is not well understood. The difficulties for constructing a theory for the linear growth phase in solids is essentially due to the character of elastic-plastic constitutive properties which has a nonlinear dependence on the magnitude of the rate of deformation. Experimental investigation of the phenomena is difficult due to the exceedingly small time scales (in high energy density experiments) and large measurement uncertainties of material properties. We performed experiments on our Two-Wheel facility to study the linear stage of the incompressible RT instability in elastic-plastic materials (yogurt) whose properties were well characterized. Rotation of the wheels imparted a constant centrifugal acceleration on the material interface that was cut with a small sinusoidal ripple. The controlled initial conditions and precise acceleration amplitudes are levied to investigate transition from elastic to plastic deformation and allow accurate and detailed measurements of flow properties.

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2014-01-01

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

Phase field benchmark problems for dendritic growth and linear elasticity

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

Jokisaari, Andrea M.; Voorhees, P. W.; Guyer, Jonathan E.

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem formore » solidifiication and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. As a result, these numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.« less

Theoretical investigations on structural, elastic and electronic properties of thallium halides

NASA Astrophysics Data System (ADS)

Singh, Rishi Pal; Singh, Rajendra Kumar; Rajagopalan, Mathrubutham

2011-04-01

Theoretical investigations on structural, elastic and electronic properties, viz. ground state lattice parameter, elastic moduli and density of states, of thallium halides (viz. TlCl and TlBr) have been made using the full potential linearized augmented plane wave method within the generalized gradient approximation (GGA). The ground state lattice parameter and bulk modulus and its pressure derivative have been obtained using optimization method. Young's modulus, shear modulus, Poisson ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature and Grüneisen parameter have also been calculated for these compounds. Calculated structural, elastic and other parameters are in good agreement with the available data.

Approximate formulas for elasticity of the Tornquist functions and some their advantages

NASA Astrophysics Data System (ADS)

Issin, Meyram

2017-09-01

In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.

Nanoparticle amount, and not size, determines chain alignment and nonlinear hardening in polymer nanocomposites

PubMed Central

Varol, H. Samet; Meng, Fanlong; Hosseinkhani, Babak; Malm, Christian; Bonn, Daniel; Bonn, Mischa; Zaccone, Alessio

2017-01-01

Polymer nanocomposites—materials in which a polymer matrix is blended with nanoparticles (or fillers)—strengthen under sufficiently large strains. Such strain hardening is critical to their function, especially for materials that bear large cyclic loads such as car tires or bearing sealants. Although the reinforcement (i.e., the increase in the linear elasticity) by the addition of filler particles is phenomenologically understood, considerably less is known about strain hardening (the nonlinear elasticity). Here, we elucidate the molecular origin of strain hardening using uniaxial tensile loading, microspectroscopy of polymer chain alignment, and theory. The strain-hardening behavior and chain alignment are found to depend on the volume fraction, but not on the size of nanofillers. This contrasts with reinforcement, which depends on both volume fraction and size of nanofillers, potentially allowing linear and nonlinear elasticity of nanocomposites to be tuned independently. PMID:28377517

ELASTIC NET FOR COX'S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM.

PubMed

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox's proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox's proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems.

First-principles study of structural stability, electronic, optical and elastic properties of binary intermetallic: PtZr

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

Pagare, Gitanjali, E-mail: gita-pagare@yahoo.co.in; Jain, Ekta, E-mail: jainekta05@gmail.com; Sanyal, S. P., E-mail: sps.physicsbu@gmail.com

2016-05-06

Structural, electronic, optical and elastic properties of PtZr have been studied using the full-potential linearized augmented plane wave (FP-LAPW) method within density functional theory (DFT). The energy against volume and enthalpy vs. pressure variation in three different structures i.e. B{sub 1}, B{sub 2} and B{sub 3} for PtZr has been presented. The equilibrium lattice parameter, bulk modulus and its pressure derivative have been obtained using optimization method for all the three phases. Furthermore, electronic structure was discussed to reveal the metallic character of the present compound. The linear optical properties are also studied under zero pressure for the first time.more » Results on elastic properties are obtained using generalized gradient approximation (GGA) for exchange correlation potentials. Ductile nature of PtZr compound is predicted in accordance with Pugh’s criteria.« less

Calculation of open and closed system elastic coefficients for multicomponent solids

NASA Astrophysics Data System (ADS)

Mishin, Y.

2015-06-01

Thermodynamic equilibrium in multicomponent solids subject to mechanical stresses is a complex nonlinear problem whose exact solution requires extensive computations. A few decades ago, Larché and Cahn proposed a linearized solution of the mechanochemical equilibrium problem by introducing the concept of open system elastic coefficients [Acta Metall. 21, 1051 (1973), 10.1016/0001-6160(73)90021-7]. Using the Ni-Al solid solution as a model system, we demonstrate that open system elastic coefficients can be readily computed by semigrand canonical Monte Carlo simulations in conjunction with the shape fluctuation approach. Such coefficients can be derived from a single simulation run, together with other thermodynamic properties needed for prediction of compositional fields in solid solutions containing defects. The proposed calculation approach enables streamlined solutions of mechanochemical equilibrium problems in complex alloys. Second order corrections to the linear theory are extended to multicomponent systems.

Force sensing using 3D displacement measurements in linear elastic bodies

NASA Astrophysics Data System (ADS)

Feng, Xinzeng; Hui, Chung-Yuen

2016-07-01

In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.

Low-temperature anomalies in the dynamic elastic moduli of cubic AIIBVI crystals with 3d-transition metal impurities

NASA Astrophysics Data System (ADS)

Lonchakov, A. T.

2011-04-01

A negative paramagnetic contribution to the dynamic elastic moduli is identified in AIIBVI:3d wide band-gap compounds for the first time. It appears as a paramagnetic elastic, or, briefly, paraelastic, susceptibility. These compounds are found to have a linear temperature dependence for the inverse paraelastic susceptibility. This is explained by a contribution from the diagonal matrix elements of the orbit-lattice interaction operators in the energy of the spin-orbital states of the 3d-ion as a function of applied stress (by analogy with the Curie contribution to the magnetic susceptibility). The inverse paraelastic susceptibility of AIIBVI crystals containing non-Kramers 3d-ions is found to deviate from linearity with decreasing temperature and reaches saturation. This effect is explained by a contribution from nondiagonal matrix elements (analogous to the well known van Vleck contribution to the magnetic susceptibility of paramagnets).

Spall behaviour of single crystal aluminium at three principal orientations

NASA Astrophysics Data System (ADS)

Owen, G. D.; Chapman, D. J.; Whiteman, G.; Stirk, S. M.; Millett, J. C. F.; Johnson, S.

2017-10-01

A series of plate impact experiments have been conducted to study the spall strength of the three principal crystallographic orientations of single crystal aluminium ([100], [110] and, [111]) and ultra-pure polycrystalline aluminium. The samples have been shock loaded at two impact stresses (4 GPa and 10 GPa). Significant differences have been observed in the elastic behaviour, the pullback velocities, and the general shape of the wave profiles, which can be accounted for by considerations of the microscale homogeneity, the dislocation density, and the absence of grain boundaries in the single crystal materials. The data have shown that there is a consistent order of spall strength measured for the four sample materials. The [111] orientation has the largest spall strength and elastic limit, followed closely by [110], [100], and then the polycrystalline material. This order is consistent with both quasi-static data and geometrical consideration of Schmid factors.

Systematic Breakdown of Amontons' Law of Friction for an Elastic Object Locally Obeying Amontons' Law

PubMed Central

Otsuki, Michio; Matsukawa, Hiroshi

2013-01-01

In many sliding systems consisting of solid object on a solid substrate under dry condition, the friction force does not depend on the apparent contact area and is proportional to the loading force. This behaviour is called Amontons' law and indicates that the friction coefficient, or the ratio of the friction force to the loading force, is constant. Here, however, using numerical and analytical methods, we show that Amontons' law breaks down systematically under certain conditions for an elastic object experiencing a friction force that locally obeys Amontons' law. The macroscopic static friction coefficient, which corresponds to the onset of bulk sliding of the object, decreases as pressure or system length increases. This decrease results from precursor slips before the onset of bulk sliding, and is consistent with the results of certain previous experiments. The mechanisms for these behaviours are clarified. These results will provide new insight into controlling friction. PMID:23545778

Theoretical investigation of the structural, elastic, electronic and optical properties of the ternary indium sulfide layered structures AInS2 (A = K, Rb and Cs)

NASA Astrophysics Data System (ADS)

Bouchenafa, M.; Sidoumou, M.; Halit, M.; Benmakhlouf, A.; Bouhemadou, A.; Maabed, S.; Bentabet, A.; Bin-Omran, S.

2018-02-01

Ab initio calculations were performed to investigate the structural, elastic, electronic and optical properties of the ternary layered systems AInS2 (A = K, Rb and Cs). The calculated structural parameters are in good agreement with the existing experimental data. Analysis of the electronic band structure shows that the three studied materials are direct band-gap semiconductors. Density of states, charge transfers and charge density distribution maps were computed and analyzed. Numerical estimations of the elastic moduli and their related properties for single-crystal and polycrystalline aggregates were predicted. The optical properties were calculated for incident radiation polarized along the [100], [010] and [001] crystallographic directions. The studied materials exhibit a noticeable anisotropic behaviour in the elastic and optical properties, which is expected due to the symmetry and the layered nature of these compounds.

Elastic-plastic models for multi-site damage

NASA Technical Reports Server (NTRS)

Actis, Ricardo L.; Szabo, Barna A.

1994-01-01

This paper presents recent developments in advanced analysis methods for the computation of stress site damage. The method of solution is based on the p-version of the finite element method. Its implementation was designed to permit extraction of linear stress intensity factors using a superconvergent extraction method (known as the contour integral method) and evaluation of the J-integral following an elastic-plastic analysis. Coarse meshes are adequate for obtaining accurate results supported by p-convergence data. The elastic-plastic analysis is based on the deformation theory of plasticity and the von Mises yield criterion. The model problem consists of an aluminum plate with six equally spaced holes and a crack emanating from each hole. The cracks are of different sizes. The panel is subjected to a remote tensile load. Experimental results are available for the panel. The plasticity analysis provided the same limit load as the experimentally determined load. The results of elastic-plastic analysis were compared with the results of linear elastic analysis in an effort to evaluate how plastic zone sizes influence the crack growth rates. The onset of net-section yielding was determined also. The results show that crack growth rate is accelerated by the presence of adjacent damage, and the critical crack size is shorter when the effects of plasticity are taken into consideration. This work also addresses the effects of alternative stress-strain laws: The elastic-ideally-plastic material model is compared against the Ramberg-Osgood model.

Slackline dynamics and the Helmholtz-Duffing oscillator

NASA Astrophysics Data System (ADS)

Athanasiadis, Panos J.

2018-01-01

Slacklining is a new, rapidly expanding sport, and understanding its physics is paramount for maximizing fun and safety. Yet, compared to other sports, very little has been published so far on slackline dynamics. The equations of motion describing a slackline are fundamentally nonlinear, and assuming linear elasticity, they lead to a form of the Duffing equation. Following this approach, characteristic examples of slackline motion are simulated, including trickline bouncing, leash falls and longline surfing. The time-dependent solutions of the differential equations describing the system are acquired by numerical integration. A simple form of energy dissipation (linear drag) is added in some cases. It is recognized in this study that geometric nonlinearity is a fundamental aspect characterizing the dynamics of slacklines. Sports, and particularly slackline, is an excellent way of engaging young people with physics. A slackline is a simple yet insightful example of a nonlinear oscillator. It is very easy to model in the laboratory, as well as to rig and try on a university campus. For instructive purposes, its behaviour can be explored by numerically integrating the respective equations of motion. A form of the Duffing equation emerges naturally in the analysis and provides a powerful introduction to nonlinear dynamics. The material is suitable for graduate students and undergraduates with a background in classical mechanics and differential equations.

A Linear Theory for Inflatable Plates of Arbitrary Shape

NASA Technical Reports Server (NTRS)

McComb, Harvey G., Jr.

1961-01-01

A linear small-deflection theory is developed for the elastic behavior of inflatable plates of which Airmat is an example. Included in the theory are the effects of a small linear taper in the depth of the plate. Solutions are presented for some simple problems in the lateral deflection and vibration of constant-depth rectangular inflatable plates.

Dynamic characteristics of Non Newtonian fluid Squeeze film damper

NASA Astrophysics Data System (ADS)

Palaksha, C. P.; Shivaprakash, S.; Jagadish, H. P.

2016-09-01

The fluids which do not follow linear relationship between rate of strain and shear stress are termed as non-Newtonian fluid. The non-Newtonian fluids are usually categorized as those in which shear stress depends on the rates of shear only, fluids for which relation between shear stress and rate of shear depends on time and the visco inelastic fluids which possess both elastic and viscous properties. It is quite difficult to provide a single constitutive relation that can be used to define a non-Newtonian fluid due to a great diversity found in its physical structure. Non-Newtonian fluids can present a complex rheological behaviour involving shear-thinning, viscoelastic or thixotropic effects. The rheological characterization of complex fluids is an important issue in many areas. The paper analyses the damping and stiffness characteristics of non-Newtonian fluids (waxy crude oil) used in squeeze film dampers using the available literature for viscosity characterization. Damping and stiffness characteristic will be evaluated as a function of shear strain rate, temperature and percentage wax concentration etc.

Anomolous Fatigue Crack Growth Phenomena in High-Strength Steel

NASA Technical Reports Server (NTRS)

Forth, Scott C.; James, Mark A.; Johnston, William M., Jr.; Newman, James C., Jr.

2004-01-01

The growth of a fatigue crack through a material is the result of a complex interaction between the applied loading, component geometry, three-dimensional constraint, load history, environment, material microstructure and several other factors. Previous studies have developed experimental and computational methods to relate the fatigue crack growth rate to many of the above conditions, with the intent of discovering some fundamental material response, i.e. crack growth rate as a function of something. Currently, the technical community uses the stress intensity factor solution as a simplistic means to relate fatigue crack growth rate to loading, geometry and all other variables. The stress intensity factor solution is a very simple linear-elastic representation of the continuum mechanics portion of crack growth. In this paper, the authors present fatigue crack growth rate data for two different high strength steel alloys generated using standard methods. The steels exhibit behaviour that appears unexplainable, compared to an aluminium alloy presented as a baseline for comparison, using the stress intensity factor solution.

Fracture spacing in tensile brittle layers adhering to a rigid substrate

NASA Astrophysics Data System (ADS)

Lazarus, Véronique

2017-01-01

A natural question arising when observing crack networks in brittle layers such as, e.g., paints, muds, skins, pottery glazes, coatings, ceramics, is what determines the distance between cracks. This apparently simple question received a wealth of more or less complex and appropriate answers, but no consensus has emerged. Here, we show that the cracks interact mutually as soon as the spacing between them is smaller than ten times the thickness of the layer. Then, a simple Griffith-type balance between the elastic deformation energy and the fracture bulk and debonding costs captures a broad number of observations, going from the square-root or linear increase of the spacing with the thickness, to its decrease with loading until saturation. The adhesion strength is identified as playing a key role in these behaviour changes. As illustration, we show how the model can be applied to study the influence of the layer thickness on crack patterns. We believe that the versatility of the approach should permit wide applicability, from geosciences to engineering.

Stiffness Indices and Fractal Dimension relationship in Arterial Pressure and Diameter Time Series in-Vitro

NASA Astrophysics Data System (ADS)

Cymberknop, L.; Legnani, W.; Pessana, F.; Bia, D.; Zócalo, Y.; Armentano, R. L.

2011-12-01

The advent of vascular diseases, such as hypertension and atherosclerosis, is associated to significant alterations in the physical properties of arterial vessels. Evaluation of arterial biomechanical behaviour is related to the assessment of three representative indices: arterial compliance, arterial distensibility and arterial stiffness index. Elasticity is the most important mechanical property of the arterial wall, whose natures is strictly non-linear. Intervention of elastin and collagen fibres, passive constituent elements of the arterial wall, is related to the applied wall stress level. Concerning this, appropriate tools are required to analyse the temporal dynamics of the signals involved, in order to characterize the whole phenomenon. Fractal geometry can be mentioned as one of those techniques. The aim of this study consisted on arterial pressure and diameter signals processing, by means of nonlinear techniques based on fractal geometry. Time series morphology was related to different arterial stiffness states, generated by means of blood flow variations, during experiences performed in vitro.

New microscale constitutive model of human trabecular bone based on depth sensing indentation technique.

PubMed

Pawlikowski, Marek; Jankowski, Krzysztof; Skalski, Konstanty

2018-05-30

A new constitutive model for human trabecular bone is presented in the present study. As the model is based on indentation tests performed on single trabeculae it is formulated in a microscale. The constitutive law takes into account non-linear viscoelasticity of the tissue. The elastic response is described by the hyperelastic Mooney-Rivlin model while the viscoelastic effects are considered by means of the hereditary integral in which stress depends on both time and strain. The material constants in the constitutive equation are identified on the basis of the stress relaxation tests and the indentation tests using curve-fitting procedure. The constitutive model is implemented into finite element package Abaqus ® by means of UMAT subroutine. The curve-fitting error is low and the viscoelastic behaviour of the tissue predicted by the proposed constitutive model corresponds well to the realistic response of the trabecular bone. Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.

Free volume study on the miscibility of PEEK/PEI blend using positron annihilation and dynamic mechanical thermal analysis

NASA Astrophysics Data System (ADS)

Ramani, R.; Alam, S.

2015-06-01

High performance polymer blend of poly(ether ether ketone) (PEEK) and poly(ether imide) (PEI) was examined for their free volume behaviour using positron annihilation lifetime spectroscopy and dynamic mechanical thermal analysis methods. The fractional free volume obtained from PALS shows a negative deviation from linear additivity rule implying good miscibility between PEEK and PEI. The dynamic modulus and loss tangent were obtained for the blends at three different frequencies 1, 10 and 100 Hz at temperatures close to and above their glass transition temperature. Applying Time-Temperature-Superposition (TTS) principle to the DMTA results, master curves were obtained at a reference temperature To and the WLF coefficients c01 and c02 were evaluated. Both the methods give similar results for the dependence of fractional free volume on PEI content in this blend. The results reveal that free volume plays an important role in determining the visco-elastic properties in miscible polymer blends.

A mathematical model to describe the nonlinear elastic properties of the gastrocnemius tendon of chickens.

PubMed

Foutz, T L

1991-03-01

A phenomenological model was developed to describe the nonlinear elastic behavior of the avian gastrocnemius tendon. Quasistatic uniaxial tensile tests were used to apply a deformation and resulting load on the tendon at a deformation rate of 5 mm/min. Plots of deformation versus load indicated a nonlinear loading response. By calculating engineering stress and engineering strain, the experimental data were normalized for tendon shape. The elastic response was determined from stress-strain curves and was found to vary with engineering strain. The response to the applied engineering strain could best be described by a mathematical model that combined a linear function and a nonlinear function. Three parameters in the model were developed to represent the nonlinear elastic behavior of the tendon, thereby allowing analysis of elasticity without prior knowledge of engineering strain. This procedure reduced the amount of data needed for the statistical analysis of nonlinear elasticity.

Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids

NASA Astrophysics Data System (ADS)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2017-05-01

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number AT=1 , the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998), 10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.

Predicting recycling behaviour: Comparison of a linear regression model and a fuzzy logic model.

PubMed

Vesely, Stepan; Klöckner, Christian A; Dohnal, Mirko

2016-03-01

In this paper we demonstrate that fuzzy logic can provide a better tool for predicting recycling behaviour than the customarily used linear regression. To show this, we take a set of empirical data on recycling behaviour (N=664), which we randomly divide into two halves. The first half is used to estimate a linear regression model of recycling behaviour, and to develop a fuzzy logic model of recycling behaviour. As the first comparison, the fit of both models to the data included in estimation of the models (N=332) is evaluated. As the second comparison, predictive accuracy of both models for "new" cases (hold-out data not included in building the models, N=332) is assessed. In both cases, the fuzzy logic model significantly outperforms the regression model in terms of fit. To conclude, when accurate predictions of recycling and possibly other environmental behaviours are needed, fuzzy logic modelling seems to be a promising technique. Copyright © 2015 Elsevier Ltd. All rights reserved.

Contact mechanics for coated spheres that includes the transition from weak to strong adhesion

DOE PAGES

Reedy, Earl David

2007-09-01

Recently published results for a rigid spherical indenter contacting a thin, linear elastic coating on a rigid planar substrate have been extended to include the case of two contacting spheres, where each sphere is rigid and coated with a thin, linear elastic material. This is done by using an appropriately chosen effective radius and coating modulus. Finally, the earlier work has also been extended to provide analytical results that span the transition between the previously derived Derjaguin–Müller–Toporov (DMT)-like (work of adhesion/coating-modulus ratio is small) and Johnson–Kendall–Roberts (JKR)-like (work of adhesion/coating-modulus ratio is large) limits.

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

NASA Technical Reports Server (NTRS)

Buttrill, Carey S.

1989-01-01

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Nonlinear reflection of shock shear waves in soft elastic media.

PubMed

Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

2010-02-01

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

Elastic constants and pressure derivative of elastic constants of Si1-xGex solid solution

NASA Astrophysics Data System (ADS)

Jivani, A. R.; Baria, J. K.; Vyas, P. S.; Jani, A. R.

2013-02-01

Elastic properties of Si1-xGex solid solution with arbitrary (atomic) concentration (x) are studied using the pseudo-alloy atom model based on the pseudopotential theory and on the higher-order perturbation scheme with the application of our own proposed model potential. We have used local-field correction function proposed by Sarkar et al to study Si-Ge system. The Elastic constants and pressure derivatives of elastic constants of the solid solution is investigated with different concentration x of Ge. It is found in the present study that the calculated numerical values of the aforesaid physical properties of Si-Ge system are function of x. The elastic constants (C11, C12 and C44) decrease linearly with increase in concentration x and pressure derivative of elastic constants (C11, C12 and C44) increase with the concentration x of Ge. This study provides better set of theoretical results for such solid solution for further comparison either with theoretical or experimental results.

Anelasticity of olivine single crystals investigated by stress-reduction tests and high-angular resolution electron backscatter diffraction

NASA Astrophysics Data System (ADS)

Wallis, D.; Hansen, L. N.; Kempton, I.; Wilkinson, A. J.

2017-12-01

Geodynamic phenomena, including glacial isostatic adjustment and postseismic deformation, can involve transient deformation in response to changes in differential stress acting on mantle rocks. As such, rheological models of transient deformation are incorporated in predictions of associated processes, including sea-level rise and stress redistribution after earthquakes. However, experimental constraints on rheological models for transient deformation of mantle materials are sparse. In particular, experiments involving stress reductions have been lacking. Moreover, a material's response to a reduction in stress can provide clues to the microphysical processes controlling deformation. To constrain models of transient deformation of mantle rocks we performed stress-reduction tests on single crystals of olivine at 1250-1300°C. Mechanical and piezoelectric actuators controlled constant initial stress during creep. At various strain intervals stress was reduced near-instantaneously using the piezoelectric actuator, inducing both elastic and anelastic (time-dependent) lengthening of the samples. A range of magnitudes of stress reduction were applied, typically unloading 10-90% of the initial stress. High-angular resolution electron backscatter diffraction (HR-EBSD), based on cross-correlation of diffraction patterns, was used to map dislocation density and elastic strain distributions in the recovered samples. Magnitudes of anelastic back-strain increase with increasing magnitudes of stress reduction and show a marked increase when stress reductions exceed 50% of the initial stress, consistent with previous observations in metals and alloys. This observation is inconsistent with the Burgers rheological model commonly used to describe transient behaviour and suggests that the style of rheological behaviour depends on the magnitude of stress change. HR-EBSD maps reveal that the crystal lattices are smoothly curved and generally lack subgrain boundaries and elastic strain heterogeneities. The dependence of the anelastic behaviour on the initial stress, combined with the lack of subgrain boundaries, suggest that the anelastic behaviour is controlled by local interactions between dislocations, rather than resistance imposed by the lattice or subgrain boundaries.

The influence of time dependent flight and maneuver velocities and elastic or viscoelastic flexibilities on aerodynamic and stability derivatives

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

Cochrane, Alexander P.; Merrett, Craig G.; Hilton, Harry H.

2014-12-10

The advent of new structural concepts employing composites in primary load carrying aerospace structures in UAVs, MAVs, Boeing 787s, Airbus A380s, etc., necessitates the inclusion of flexibility as well as viscoelasticity in static structural and aero-viscoelastic analyses. Differences and similarities between aeroelasticity and aero-viscoelasticity have been investigated in [2]. An investigation is undertaken as to the dependence and sensitivity of aerodynamic and stability derivatives to elastic and viscoelastic structural flexibility and as to time dependent flight and maneuver velocities. Longitudinal, lateral and directional stabilities are investigated. It has been a well established fact that elastic lifting surfaces are subject tomore » loss of control effectiveness and control reversal at certain flight speeds, which depend on aerodynamic, structural and material properties [5]. Such elastic analyses are extended to linear viscoelastic materials under quasi-static, dynamic, and sudden and gradual loading conditions. In elastic wings one of the critical static parameters is the velocity at which control reversal takes place (V{sub REV}{sup E}). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V{sub REV<}{sup ≧}V{sub REV}{sup E}, but furthermore does so in time at 0 < t{sub REV} ≤ ∞. The influence of the twin effects of viscoelastic and elastic materials and of variable flight velocities on longitudinal, lateral, directional and spin stabilities are also investigated. It has been a well established fact that elastic lifting surfaces are subject to loss of control effectiveness and control reversal at certain flight speeds, which depend on aerodynamic, structural and material properties [5]. Such elastic analyses are here extended to linear viscoelastic materials under quasi-static, dynamic, and sudden and gradual loading conditions. In elastic wings the critical parameter is the velocity at which control reversal takes place (V{sub REV}{sup E}). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V{sub REV<}{sup ≧}V{sub REV}{sup E}, but furthermore does so in time at 0 < t{sub REV} ≤ ∞. This paper reports on analytical analyses and simulations of the effects of flexibility and time dependent material properties (viscoelasticity) on aerodynamic derivatives and on lateral, longitudinal, directional and spin stability derivatives. Cases of both constant and variable flight and maneuver velocities are considered. Analytical results for maneuvers involving constant and time dependent rolling velocities are analyzed, discussed and evaluated. The relationships between rolling velocity p and aileron angular displacement β as well as control effectiveness are analyzed and discussed in detail for elastic and viscoelastic wings. Such analyses establish the roll effectiveness derivatives (∂[p(t)])/(V{sub ∞}∂β(t)) . Similar studies involving other stability and aerodynamic derivatives are also undertaken. The influence of the twin effects of viscoelastic and elastic materials and of variable flight, rolling, pitching and yawing velocities on longitudinal, lateral and directional are also investigated. Variable flight velocities, encountered during maneuvers, render the usually linear problem at constant velocities into a nonlinear one.« less

Analysis of the compressive behaviour of the three-dimensional printed porous titanium for dental implants using a modified cellular solid model.

PubMed

Gagg, Graham; Ghassemieh, Elaheh; Wiria, Florencia E

2013-09-01

A set of cylindrical porous titanium test samples were produced using the three-dimensional printing and sintering method with samples sintered at 900 °C, 1000 °C, 1100 °C, 1200 °C or 1300 °C. Following compression testing, it was apparent that the stress-strain curves were similar in shape to the curves that represent cellular solids. This is despite a relative density twice as high as what is considered the threshold for defining a cellular solid. As final sintering temperature increased, the compressive behaviour developed from being elastic-brittle to elastic-plastic and while Young's modulus remained fairly constant in the region of 1.5 GPa, there was a corresponding increase in 0.2% proof stress of approximately 40-80 MPa. The cellular solid model consists of two equations that predict Young's modulus and yield or proof stress. By fitting to experimental data and consideration of porous morphology, appropriate changes to the geometry constants allow modification of the current models to predict with better accuracy the behaviour of porous materials with higher relative densities (lower porosity).

Modeling elastic anisotropy in strained heteroepitaxy

NASA Astrophysics Data System (ADS)

Krishna Dixit, Gopal; Ranganathan, Madhav

2017-09-01

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the Ge0.25 Si0.75 on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to < 1 0 5 > facets on the surface.

Modeling elastic anisotropy in strained heteroepitaxy.

PubMed

Dixit, Gopal Krishna; Ranganathan, Madhav

2017-09-20

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.

Rayleigh wave effects in an elastic half-space.

NASA Technical Reports Server (NTRS)

Aggarwal, H. R.

1972-01-01

Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.

Boundary element modelling of dynamic behavior of piecewise homogeneous anisotropic elastic solids

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Litvinchuk, S. Yu

2018-04-01

A traditional direct boundary integral equations method is applied to solve three-dimensional dynamic problems of piecewise homogeneous linear elastic solids. The materials of homogeneous parts are considered to be generally anisotropic. The technique used to solve the boundary integral equations is based on the boundary element method applied together with the Radau IIA convolution quadrature method. A numerical example of suddenly loaded 3D prismatic rod consisting of two subdomains with different anisotropic elastic properties is presented to verify the accuracy of the proposed formulation.

Elasticity of entangled polymer loops: Olympic gels

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

Vilgis, T.A.; Otto, M.

1997-08-01

In this Rapid Communication we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the nonaffine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as F{proportional_to}{lambda}{sup 5/2} where {lambda} is the deformation ratio. Thus a highly non-Hookian stress-strain relation is predicted. {copyright} {ital 1997} {ital The American Physical Society}

Measurement of elastic constants of monoclinic nickel-titanium and validation of first principles calculations

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

Stebner, A. P.; Brown, D. W.; Brinson, L. C.

2013-05-27

Polycrystalline, monoclinic nickel-titanium specimens were subjected to tensile and compressive deformations while neutron diffraction spectra were recorded in situ. Using these data, orientation-specific and macroscopic Young's moduli are determined from analysis of linear-elastic deformation exhibited by 13 unique orientations of monoclinic lattices and their relationships to each macroscopic stress and strain. Five of 13 elastic compliance constants are also identified: s{sub 11} = 1.15, s{sub 15} = -1.10, s{sub 22} = 1.34, s{sub 33} = 1.06, s{sub 35} = -1.54, all Multiplication-Sign 10{sup -2} GPa{sup -1}. Through these results, recent atomistic calculations of monoclinic nickel-titanium elastic constants are validated.

Linear sampling method applied to non destructive testing of an elastic waveguide: theory, numerics and experiments

NASA Astrophysics Data System (ADS)

Baronian, Vahan; Bourgeois, Laurent; Chapuis, Bastien; Recoquillay, Arnaud

2018-07-01

This paper presents an application of the linear sampling method to ultrasonic non destructive testing of an elastic waveguide. In particular, the NDT context implies that both the solicitations and the measurements are located on the surface of the waveguide and are given in the time domain. Our strategy consists in using a modal formulation of the linear sampling method at multiple frequencies, such modal formulation being justified theoretically in Bourgeois et al (2011 Inverse Problems 27 055001) for rigid obstacles and in Bourgeois and Lunéville (2013 Inverse Problems 29 025017) for cracks. Our strategy requires the inversion of some emission and reception matrices which deserve some special attention due to potential ill-conditioning. The feasibility of our method is proved with the help of artificial data as well as real data.

Elastic anomalies and acoustic dissipation associated with spin state transitions in LnCoO3 (Ln=La, Nd, Gd) and Co3O4: analogue behaviour for spin state transitions in minerals

NASA Astrophysics Data System (ADS)

Zhang, Z.; Carpenter, M. A.; Koppensteiner, J.; Schranz, W.

2010-12-01

Iron ions in lower mantle minerals magnesiowüstitue (Mg,Fe)O, perovskite (Mg,Fe)(Si,Al)O3 and post-perovskite phases undergo electronic spin state transitions from high spin (HS) to low spin (LS) or intermediate spin (IS) at high pressures and high temperatures. These spin state transitions give rise to changes in bulk and shear moduli which have significant implications for the physical and chemical properties of the lower mantle. However, the possibility of increased attenuation does not appear to have been considered yet. Co3+ is isoelectronic with Fe2+ and shows analogous HS/LS behaviour at ambient pressure in a temperature range which is easily accessible for in-situ investigations. We have studied spin state transitions in cobalt perovskites LaCoO3, NdCoO3, GdCoO3 and in Co3O4 using resonant ultrasound spectroscopy (RUS) at high frequencies 0.1-1.5 MHz, and dynamic mechanical analysis (DMA) at low frequencies 0.1-50 Hz, in the temperature range 10-1200 K. The specific objectives were to characterize anomalies in the shear moduli and in acoustic attenuation accompanying changes in the spin state of Co3+. Anomalies in shear moduli have been observed at ~110 K and ~590 K for LaCoO3, ~325 K and ~695 K for NdCoO3, ~720 K for GdCoO3, and ~30 K for Co3O4. For LaCoO3, a spin order parameter qspin is expected to couple with volume strain ea as λeaqspin and with shear strain es as λes2qspin. As a consequence of linear/quadratic coupling with es, the shear modulus is expected to vary linearly with qspin. This appears to be approximately the case for LaCoO3. Changes in spin state do not appear to give rise to acoustic attenuation at either DMA frequencies (~1 Hz) or RUS frequencies (~1 MHz), consistent with the expectation that spin/lattice relaxation is rapid in comparison with the time scale of applied stress in each case. On the other hand, for LaCoO3 there is a peak in dissipation near 590 K at low frequencies, which is attributed to freezing of ferroelastic twin walls. At high frequencies, acoustic attenuation increases steeply below ~110 K, and this is attributed to movement of magnetic polarons under stress. Data for thermally activated relaxation processes in LaCoO3 based on different measurements from the literature and our own elasticity data have been combined to give a preliminary anelasticity map. At seismic frequencies, loss mechanisms are likely to be only due to twin wall and magnetic polaron mobility. NdCoO3 and GdCoO3 both have the Pnma structure at room temperature. They also show significant non-linear behaviour in shear modulus as a function of temperature but neither show evidence of significant attenuation which might be attributed to microstructure, spin/lattice coupling or polarons. On the other hand, Co3O4 shows evidence of increasing attenuation above ~800 K and below ~30 K at high frequencies. The origin of the latter is clearly associated with magnetic ordering in this system but the origin of the former is not yet understood, particularly as Co3O4 crystals are not expected to contain any transformation microstructure.

Non-Singular Dislocation Elastic Fields and Linear Elastic Fracture Mechanics

NASA Astrophysics Data System (ADS)

Korsunsky, Alexander M.

2010-03-01

One of the hallmarks of the traditional linear elastic fracture mechanics (LEFM) is the presence of an (integrable) inverse square root singularity of strains and stresses in the vicinity of the crack tip. It is the presence of this singularity that necessitates the introduction of the concepts of stress intensity factor (and its critical value, the fracture toughness) and the energy release rate (and material toughness). This gives rise to the Griffith theory of strength that includes, apart from applied stresses, the considerations of defect size and geometry. A highly successful framework for the solution of crack problems, particularly in the two-dimensional case, due to Muskhelishvili (1953), Bilby and Eshelby (1968) and others, relies on the mathematical concept of dislocation. Special analytical and numerical methods of dealing with the characteristic 1/r (Cauchy) singularity occupy a prominent place within this theory. Recently, in a different context of dislocation dynamics simulations, Cai et al. (2006) proposed a novel means of removing the singularity associated with the dislocation core, by introducing a blunting radius parameter a into the expressions for elastic fields. Here, using the example of two-dimensional elasticity, we demonstrate how the adoption of the similar mathematically expedient tool leads naturally to a non-singular formulation of fracture mechanics problems. This opens an efficient means of treating a variety of crack problems.

Estimating the price elasticity of expenditure for prescription drugs in the presence of non-linear price schedules: an illustration from Quebec, Canada.

PubMed

Contoyannis, Paul; Hurley, Jeremiah; Grootendorst, Paul; Jeon, Sung-Hee; Tamblyn, Robyn

2005-09-01

The price elasticity of demand for prescription drugs is a crucial parameter of interest in designing pharmaceutical benefit plans. Estimating the elasticity using micro-data, however, is challenging because insurance coverage that includes deductibles, co-insurance provisions and maximum expenditure limits create a non-linear price schedule, making price endogenous (a function of drug consumption). In this paper we exploit an exogenous change in cost-sharing within the Quebec (Canada) public Pharmacare program to estimate the price elasticity of expenditure for drugs using IV methods. This approach corrects for the endogeneity of price and incorporates the concept of a 'rational' consumer who factors into consumption decisions the price they expect to face at the margin given their expected needs. The IV method is adapted from an approach developed in the public finance literature used to estimate income responses to changes in tax schedules. The instrument is based on the price an individual would face under the new cost-sharing policy if their consumption remained at the pre-policy level. Our preferred specification leads to expenditure elasticities that are in the low range of previous estimates (between -0.12 and -0.16). Naïve OLS estimates are between 1 and 4 times these magnitudes. (c) 2005 John Wiley & Sons, Ltd.

Stress stiffening and approximate equations in flexible multibody dynamics

NASA Technical Reports Server (NTRS)

Padilla, Carlos E.; Vonflotow, Andreas H.

1993-01-01

A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.

Characterization of the Nonlinear Elastic Properties of Graphite/Epoxy Composites Using Ultrasound

NASA Technical Reports Server (NTRS)

Prosser, William H.; Green, Robert E., Jr.

1990-01-01

The normalized change in ultrasonic "natural" velocity as a function of stress and temperature was measured in a unidirectional laminate of T300/5208 graphite/epoxy composite using a pulsed phase locked loop ultrasonic interferometer. These measurements were used together with the linear (second order) elastic moduli to calculate some of the nonlinear (third order) moduli of this material.

Forced in-plane vibration of a thick ring on a unilateral elastic foundation

NASA Astrophysics Data System (ADS)

Wang, Chunjian; Ayalew, Beshah; Rhyne, Timothy; Cron, Steve; Dailliez, Benoit

2016-10-01

Most existing studies of a deformable ring on elastic foundation rely on the assumption of a linear foundation. These assumptions are insufficient in cases where the foundation may have a unilateral stiffness that vanishes in compression or tension such as in non-pneumatic tires and bushing bearings. This paper analyzes the in-plane dynamics of such a thick ring on a unilateral elastic foundation, specifically, on a two-parameter unilateral elastic foundation, where the stiffness of the foundation is treated as linear in the circumferential direction but unilateral (i.e. collapsible or tensionless) in the radial direction. The thick ring is modeled as an orthotropic and extensible circular Timoshenko beam. An arbitrarily distributed time-varying in-plane force is considered as the excitation. The Equations of Motion are explicitly derived and a solution method is proposed that uses an implicit Newmark scheme for the time domain solution and an iterative compensation approach to determine the unilateral zone of the foundation at each time step. The dynamic axle force transmission is also analyzed. Illustrative forced vibration responses obtained from the proposed model and solution method are compared with those obtained from a finite element model.

Effects of Initial Geometric Imperfections On the Non-Linear Response of the Space Shuttle Superlightweight Liquid-Oxygen Tank

NASA Technical Reports Server (NTRS)

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

2002-01-01

The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.

Nonlinear damage detection in composite structures using bispectral analysis

NASA Astrophysics Data System (ADS)

Ciampa, Francesco; Pickering, Simon; Scarselli, Gennaro; Meo, Michele

2014-03-01

Literature offers a quantitative number of diagnostic methods that can continuously provide detailed information of the material defects and damages in aerospace and civil engineering applications. Indeed, low velocity impact damages can considerably degrade the integrity of structural components and, if not detected, they can result in catastrophic failure conditions. This paper presents a nonlinear Structural Health Monitoring (SHM) method, based on ultrasonic guided waves (GW), for the detection of the nonlinear signature in a damaged composite structure. The proposed technique, based on a bispectral analysis of ultrasonic input waveforms, allows for the evaluation of the nonlinear response due to the presence of cracks and delaminations. Indeed, such a methodology was used to characterize the nonlinear behaviour of the structure, by exploiting the frequency mixing of the original waveform acquired from a sparse array of sensors. The robustness of bispectral analysis was experimentally demonstrated on a damaged carbon fibre reinforce plastic (CFRP) composite panel, and the nonlinear source was retrieved with a high level of accuracy. Unlike other linear and nonlinear ultrasonic methods for damage detection, this methodology does not require any baseline with the undamaged structure for the evaluation of the nonlinear source, nor a priori knowledge of the mechanical properties of the specimen. Moreover, bispectral analysis can be considered as a nonlinear elastic wave spectroscopy (NEWS) technique for materials showing either classical or non-classical nonlinear behaviour.

Experimental and Numerical Analysis of the Effects of Curing Time on Tensile Mechanical Properties of Thin Spray-on Liners

NASA Astrophysics Data System (ADS)

Guner, D.; Ozturk, H.

2016-08-01

The effects of curing time on tensile elastic material properties of thin spray-on liners (TSLs) were investigated in this study. Two different TSL products supplied by two manufacturers were tested comparatively. The "dogbone" tensile test samples that were prepared in laboratory conditions with different curing times (1, 7, 14, 21, and 28 days) were tested based on ASTM standards. It was concluded that longer curing times improves the tensile strength and the Young's Modulus of the TSLs but decreases their elongation at break. Moreover, as an additional conclusion of the testing procedure, it was observed that during the tensile tests, the common malpractice of measuring sample displacement from the grips of the loading machine with a linear variable displacement transducer versus the sample's gauge length had a major impact on modulus and deformation determination of TSLs. To our knowledge, true stress-strain curves were generated for the first time in TSL literature within this study. Numerical analyses of the laboratory tests were also conducted using Particle Flow Code in 2 Dimensions (PFC2D) in an attempt to guide TSL researchers throughout the rigorous PFC simulation process to model support behaviour of TSLs. A scaling coefficient between macro- and micro-properties of PFC was calculated which will help future TSL PFC modellers mimic their TSL behaviours for various tensile loading support scenarios.

Wave excited motion of a body floating on water confined between two semi-infinite ice sheets

NASA Astrophysics Data System (ADS)

Ren, K.; Wu, G. X.; Thomas, G. A.

2016-12-01

The wave excited motion of a body floating on water confined between two semi-infinite ice sheets is investigated. The ice sheet is treated as an elastic thin plate and water is treated as an ideal and incompressible fluid. The linearized velocity potential theory is adopted in the frequency domain and problems are solved by the method of matched eigenfunctions expansion. The fluid domain is divided into sub-regions and in each sub-region the velocity potential is expanded into a series of eigenfunctions satisfying the governing equation and the boundary conditions on horizontal planes including the free surface and ice sheets. Matching is conducted at the interfaces of two neighbouring regions to ensure the continuity of the pressure and velocity, and the unknown coefficients in the expressions are obtained as a result. The behaviour of the added mass and damping coefficients of the floating body with the effect of the ice sheets and the excitation force are analysed. They are found to vary oscillatorily with the wave number, which is different from that for a floating body in the open sea. The motion of the body confined between ice sheets is investigated, in particular its resonant behaviour with extremely large motion found to be possible under certain conditions. Standing waves within the polynya are also observed.

Static and dynamic strain coupling behaviour of ferroic and multiferroic perovskites from resonant ultrasound spectroscopy.

PubMed

Carpenter, M A

2015-07-08

Resonant ultrasound spectroscopy (RUS) provides a window on the pervasive influence of strain coupling at phase transitions in perovskites through determination of elastic and anelastic relaxations across wide temperature intervals and with the application of external fields. In particular, large variations of elastic constants occur at structural, ferroelectric and electronic transitions and, because of the relatively long interaction length provided by strain fields in a crystal, Landau theory provides an effective formal framework for characterizing their form and magnitude. At the same time, the Debye equations provide a robust description of dynamic relaxational processes involving the mobility of defects which are coupled with strain. Improper ferroelastic transitions driven by octahedral tilting in KMnF3, LaAlO3, (Ca,Sr)TiO3, Sr(Ti,Zr)O3 and BaCeO3 are accompanied by elastic softening of tens of % and characteristic patterns of acoustic loss due to the mobility of twin walls. RUS data for ferroelectrics and ferroelectric relaxors, including BaTiO3, (K,Na)NbO3,Pb(Mg1/3Nb2/3)O3 (PMN), Pb(Sc1/2Ta1/2)O3 (PST), (Pb(Zn1/3Nb2/3)O3)0.955(PbTiO3)0.045 (PZN-PT) and (Pb(In1/2Nb1/2)O3)0.26(Pb(Mg1/3Nb2/3)O3)0.44(PbTiO3)0.30 (PIN-PMN-PT) show similar patterns of softening and attenuation but also have precursor softening associated with the development of polar nano regions. Defect-induced ferroelectricity occurs in KTaO3, without the development of long range ordering. By way of contrast, spin-lattice coupling is much more variable in strength, as reflected in a greater range of softening behaviour for Pr0.48Ca0.52MnO3 and Sm0.6Y0.4MnO3 as well as for the multiferroic perovskites EuTiO3,BiFeO3, Bi0.9Sm0.1FeO3, Bi0.9Nd0.1FeO3, (BiFeO3)0.64(CaFeO2.5)0.36, (Pb(Fe0.5Ti0.5)O3)0.4(Pb(Zr0.53Ti0.47)O3)0.6. A characteristic feature of transitions in which there is a significant Jahn-Teller component is softening as the transition point is approached from above, as illustrated by PrAlO3, and this is suppressed by application of an external magnetic field in the colossal magnetoresistive manganite Pr0.48Ca0.52MnO3 or by reducing grain size in La0.5Ca0.5MnO3. Spin state transitions for Co(3+) in LaCoO3, NdCoO3 and GdCoO3 produce changes in the shear modulus that scale with a spin state order parameter, which is itself coupled with the order parameter(s) for octahedral tilting in a linear-quadratic manner. A new class of phase transitions in perovskites, due to orientational or conformational ordering of organic molecules on the crystallographic A-site of metal organic frameworks, is illustrated for [(CH3)2NH2]Co(HCOO)3 and [(CH2)3NH2]Mn(HCOO)3 which also display elastic and anelastic anomalies due to the influence of intrinsic and extrinsic strain relaxation behaviour.

Evolution of flexural rigidity according to the cross-sectional dimension of a superelastic nickel titanium orthodontic wire.

PubMed

Garrec, Pascal; Tavernier, Bruno; Jordan, Laurence

2005-08-01

The choice of the most suitable orthodontic wire for each stage of treatment requires estimation of the forces generated. In theory, the selection of wire sequences should initially utilize a lower flexural rigidity; thus clinicians use smaller round cross-sectional dimension wires to generate lighter forces during the preliminary alignment stage. This assessment is true for conventional alloys, but not necessarily for superelastic nickel titanium (NiTi). In this case, the flexural rigidity dependence on cross-sectional dimension differs from the linear elasticity prediction because of the martensitic transformation process. It decreases with increasing deflection and this phenomenon is accentuated in the unloading process. This behaviour should lead us to consider differently the biomechanical approach to orthodontic treatment. The present study compared bending in 10 archwires made from NiTi orthodontics alloy of two cross-sectional dimensions. The results were based on microstructural and mechanical investigations. With conventional alloys, the flexural rigidity was constant for each wire and increased largely with the cross-sectional dimension for the same strain. With NiTi alloys, the flexural rigidity is not constant and the influence of size was not as important as it should be. This result can be explained by the non-constant elastic modulus during the martensite transformation process. Thus, in some cases, treatment can begin with full-size (rectangular) wires that nearly fill the bracket slot with a force application deemed to be physiologically desirable for tooth movement and compatible with patient comfort.

Multiscale biomechanics of brain tumours favours cancer invasion by cell softening and tissue stiffening

NASA Astrophysics Data System (ADS)

Kas, Josef; Fritsch, Anatol; Grosser, Steffen; Friebe, Sabrina; Reiss-Zimmermann, Martin; Müller, Wolf; Hoffmann, Karl-Titus; Sack, Ingolf

Cancer progression needs two contradictory mechanical prerequisites. For metastasis individual cancer cells or small clusters have to flow through the microenvironment by overcoming the yield stress exerted by the surrounding. On the other hand a tumour has to behave as a solid to permit cell proliferation and spreading of the tumour mass against its surrounding. We determine that the high mechanical adaptability of cancer cells and the scale controlled viscoelastic properties of tissues reconcile both conflicting properties, fluid and solid, simultaneously in brain tumours. We resolve why different techniques that assess cell and tissue mechanics have produced apparently conflicting results by our finding that tumours generate different viscoelastic behaviours on different length scales, which are in concert optimal for tumour spreading and metastasis. Single cancer cells become very soft in their elastic behavior which promotes cell unjamming. On the level of direct cell-to-cell interactions cells feel their micro-environment as rigid elastic substrate that stimulates cancer on the molecular level. All over a tumour has predominately a stiff elastic character in terms of viscoelastic behaviour caused by a solid backbone. Simultaneously, the tumour mass is characterized by a large local variability in the storage and loss modulus that is caused by areas of a more fluid nature.

Characterizing the Elastic Behaviour of a Press Table through Topology Optimization

NASA Astrophysics Data System (ADS)

Pilthammar, J.; Sigvant, M.; Hansson, M.; Pálsson, E.; Rutgersson, W.

2017-09-01

Sheet metal forming in the car industry is a highly competitive area. The use of digital techniques and numerical methods are therefore of high interest for reduced costs and lead times. One method for reducing the try-out phase is virtual rework of die surfaces. The virtual rework is based on Finite Element (FE) simulations and can reduce and support manual rework. The elastic behaviour of dies and presses must be represented in a reliable way in FE-models to be able to perform virtual rework. CAD-models exists for nearly all dies today, but not for press lines. A full geometrical representation of presses will also yield very large FE- models. This paper will discuss and demonstrate a strategy for measuring and characterizing a press table for inclusion in FE-models. The measurements of the elastic press deformations is carried out with force transducers and an ARAMIS 3D optical measurement system. The press table is then inverse modelled by topology optimization using the recorded results as boundary conditions. Finally, the press table is coupled with a FE-model of a die to demonstrate its influence on the deformations. This indicates the importance of having a reliable representation of the press deformations during virtual rework.

Negative stiffness honeycombs as tunable elastic metamaterials

NASA Astrophysics Data System (ADS)

Goldsberry, Benjamin M.; Haberman, Michael R.

2018-03-01

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.

Complex double-mass dynamic model of rotor on thrust foil gas dynamic bearings

NASA Astrophysics Data System (ADS)

Sytin, A.; Babin, A.; Vasin, S.

2017-08-01

The present paper considers simulation of a rotor’s dynamics behaviour on thrust foil gas dynamic bearings based on simultaneous solution of gas dynamics differential equations, equations of theory of elasticity, motion equations and some additional equations. A double-mass dynamic system was considered during the rotor’s motion simulation which allows not only evaluation of rotor’s dynamic behaviour, but also to evaluate the influence of operational and load parameters on the dynamics of the rotor-bearing system.

Reflection and transmission of elastic waves through a couple-stress elastic slab sandwiched between two half-spaces

NASA Astrophysics Data System (ADS)

Wang, Changda; Chen, Xuejun; Wei, Peijun; Li, Yueqiu

2017-12-01

The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves.

Behavioural and neurobiological implications of linear and non-linear features in larynx phonations of horseshoe bats

PubMed Central

Kobayasi, Kohta I.; Hage, Steffen R.; Berquist, Sean; Feng, Jiang; Zhang, Shuyi; Metzner, Walter

2012-01-01

Mammalian vocalizations exhibit large variations in their spectrotemporal features, although it is still largely unknown which result from intrinsic biomechanical properties of the larynx and which are under direct neuromuscular control. Here we show that mere changes in laryngeal air flow yield several non-linear effects on sound production, in an isolated larynx preparation from horseshoe bats. Most notably, there are sudden jumps between two frequency bands used for either echolocation or communication in natural vocalizations. These jumps resemble changes in “registers” as in yodelling. In contrast, simulated contractions of the main larynx muscle produce linear frequency changes, but are limited to echolocation or communication frequencies. Only by combining non-linear and linear properties can this larynx therefore produce sounds covering the entire frequency range of natural calls. This may give behavioural meaning to yodelling-like vocal behaviour and reshape our thinking about how the brain controls the multitude of spectral vocal features in mammals. PMID:23149729

The Effect of Freezing on the Dynamics of Dike Propagation

NASA Astrophysics Data System (ADS)

Tait, S.; Taisne, B.

2007-12-01

When magma-filled cracks propagate close to the Earth's surface, host rock temperature is well below the magma solidus. Solidification and substantial increase in magma viscosity can occur, are most pronounced near the propagating tip and can slow or arrest the progress of the dike. Quantitative analysis is required to predict whether a given dike will reach the surface to erupt and the duration of the precursor sequence. This challenging physical problem mixes elasticity, fracture mechanics, heat transfer and fluid flow with strong rheologic gradients due to cooling. We describe the propagation behaviour of such a hydraulic fracture using a laboratory experimental system of a crack fed by a constant flux of paraffin wax from a source reservoir propagating through gelatin below the solidus of the wax. The most novel behaviour is an intermittent regime in which cracks periodically stop advancing due to solidification, then swell at constant length while enhancing the elastic deformation in the surrounding solid before propagation resumes. We present a physical model of this system, based on different balances between driving and resistive forces: the former are elastic stress and liquid buoyancy, the latter are fracture resistance at the tip and viscous resistance. The fracture is represented as a head, behind the propagating tip, connected to the source by a narrow tail. Freezing of liquid close to the tip is assumed to enhance fracture resistance according to a cooling law, and propagation is assumed to occur only when the stress exerted by the liquid is enough to overcome fracture resistance. Our theoretical model reproduces intermittent propagation with precise behaviour depending on the controlling stress balances, and provides a tool to analyse natural systems.

A virtual surgical training system that simulates cutting of soft tissue using a modified pre-computed elastic model.

PubMed

Toe, Kyaw Kyar; Huang, Weimin; Yang, Tao; Duan, Yuping; Zhou, Jiayin; Su, Yi; Teo, Soo-Kng; Kumar, Selvaraj Senthil; Lim, Calvin Chi-Wan; Chui, Chee Kong; Chang, Stephen

2015-08-01

This work presents a surgical training system that incorporates cutting operation of soft tissue simulated based on a modified pre-computed linear elastic model in the Simulation Open Framework Architecture (SOFA) environment. A precomputed linear elastic model used for the simulation of soft tissue deformation involves computing the compliance matrix a priori based on the topological information of the mesh. While this process may require a few minutes to several hours, based on the number of vertices in the mesh, it needs only to be computed once and allows real-time computation of the subsequent soft tissue deformation. However, as the compliance matrix is based on the initial topology of the mesh, it does not allow any topological changes during simulation, such as cutting or tearing of the mesh. This work proposes a way to modify the pre-computed data by correcting the topological connectivity in the compliance matrix, without re-computing the compliance matrix which is computationally expensive.

ELASTIC NET FOR COX’S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM

PubMed Central

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox’s proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox’s proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems. PMID:23226932

Quasistatic elastoplasticity via Peridynamics: existence and localization

NASA Astrophysics Data System (ADS)

Kružík, Martin; Mora-Corral, Carlos; Stefanelli, Ulisse

2018-04-01

Peridynamics is a nonlocal continuum mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences of displacement fields over a suitable positive interaction range. The advantage of such perspective is that of directly including nonregular situations, in which discontinuities in the displacement field may occur. In the linearized elastic setting, the mechanical foundation of the theory and its mathematical amenability have been thoroughly analyzed in the last years. We present here the extension of Peridynamics to linearized elastoplasticity. This calls for considering the time evolution of elastic and plastic variables, as the effect of a combination of elastic energy storage and plastic energy dissipation mechanisms. The quasistatic evolution problem is variationally reformulated and solved by time discretization. In addition, by a rigorous evolutive Γ -convergence argument we prove that the nonlocal peridynamic model converges to classic local elastoplasticity as the interaction range goes to zero.

Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

NASA Astrophysics Data System (ADS)

Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

2017-11-01

Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

Compressible Fluids Interacting with a Linear-Elastic Shell

NASA Astrophysics Data System (ADS)

Breit, Dominic; Schwarzacher, Sebastian

2018-05-01

We study the Navier-Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical domain. Its deformation is modeled by a linearized version of Koiter's elastic energy. We show the existence of weak solutions to the corresponding system of PDEs provided the adiabatic exponent satisfies {γ > 12/7} ({γ >1 } in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in Lengeler and Růžičkaka (Arch Ration Mech Anal 211(1):205-255, 2014) on incompressible Navier-Stokes equations.

The elastic theory of shells using geometric algebra

PubMed Central

Lasenby, J.; Agarwal, A.

2017-01-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible. PMID:28405404

The elastic theory of shells using geometric algebra.

PubMed

Gregory, A L; Lasenby, J; Agarwal, A

2017-03-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.

Study of Graphite/Epoxy Composites for Material Flaw Criticality.

DTIC Science & Technology

1980-11-01

criticality of disbonds with two-dimensional planforms located in laminated graphite/epoxy composites has been examined. Linear elastic fracture...mechanics approach, semi-empirical growth laws and methods of stress analysis based on a modified laminated plate theory have been studied for assessing...growth rates of disbonds in a transverse shear environ- ment. Elastic stability analysis has been utilized for laminates with disbonds subjected to in

Computational Overlap Coupling Between Micropolar Linear Elastic Continuum Finite Elements and Nonlinear Elastic Spherical Discrete Elements in One Dimension

DTIC Science & Technology

2013-01-01

Cracking in asphalt pavement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Figure 2. 2D...metallic binder, figure 1(b)), particulate energetic materials (explosive crystalline grains with polymeric binder, figure 1(c)), asphalt pavement (stone...explosive HMX grains and at grain-matrix interfaces (2). (d) Cracking in asphalt pavement . 2 (i) it is limited by current computing power (even

High elastic modulus polymer electrolytes suitable for preventing thermal runaway in lithium batteries

DOEpatents

Mullin, Scott; Panday, Ashoutosh; Balsara, Nitash Pervez; Singh, Mohit; Eitouni, Hany Basam; Gomez, Enrique Daniel

2014-04-22

A polymer that combines high ionic conductivity with the structural properties required for Li electrode stability is useful as a solid phase electrolyte for high energy density, high cycle life batteries that do not suffer from failures due to side reactions and dendrite growth on the Li electrodes, and other potential applications. The polymer electrolyte includes a linear block copolymer having a conductive linear polymer block with a molecular weight of at least 5000 Daltons, a structural linear polymer block with an elastic modulus in excess of 1.times.10.sup.7 Pa and an ionic conductivity of at least 1.times.10.sup.-5 Scm.sup.-1. The electrolyte is made under dry conditions to achieve the noted characteristics. In another aspect, the electrolyte exhibits a conductivity drop when the temperature of electrolyte increases over a threshold temperature, thereby providing a shutoff mechanism for preventing thermal runaway in lithium battery cells.

Non-linear heterogeneous FE approach for FRP strengthened masonry arches

NASA Astrophysics Data System (ADS)

Bertolesi, Elisa; Milani, Gabriele; Fedele, Roberto

2015-12-01

A fast and reliable non-linear heterogeneous FE approach specifically conceived for the analysis of FRP-reinforced masonry arches is presented. The approach proposed relies into the reduction of mortar joints to interfaces exhibiting a non-linear holonomic behavior, with a discretization of bricks by means of four-noded elastic elements. The FRP reinforcement is modeled by means of truss elements with elastic-brittle behavior, where the peak tensile strength is estimated by means of a consolidated approach provided by the Italian guidelines CNR-DT200 on masonry strengthening with fiber materials, where the delamination of the strip from the support is taken into account. The model is validated against some recent experimental results relying into circular masonry arches reinforced at both the intrados and the extrados. Some sensitivity analyses are conducted varying the peak tensile strength of the trusses representing the FRP reinforcement.

Elastic properties and optical absorption studies of mixed alkali borogermanate glasses

NASA Astrophysics Data System (ADS)

Taqiullah, S. M.; Ahmmad, Shaik Kareem; Samee, M. A.; Rahman, Syed

2018-05-01

First time the mixed alkali effect (MAE) has been investigated in the glass system xNa2O-(30-x)Li2O-40B2O3- 30GeO2 (0≤x≤30 mol%) through density and optical absorption studies. The present glasses were prepared by melt quench technique. The density of the present glasses varies non-linearly exhibiting mixed alkali effect. Using the density data, the elastic moduli namely Young's modulus, bulk and shear modulus show strong linear dependence as a function of compositional parameter. From the absorption edge studies, the values of optical band gap energies for all transitions have been evaluated. It was established that the type of electronic transition in the present glass system is indirect allowed. The indirect optical band gap exhibit non-linear behavior with compositional parameter showing the mixed alkali effect.

Theoretical study of strength of elastic-plastic water-saturated interface under constrained shear

NASA Astrophysics Data System (ADS)

Dimaki, Andrey V.; Shilko, Evgeny V.; Psakhie, Sergey G.

2016-11-01

This paper presents a theoretical study of shear strength of an elastic-plastic water-filled interface between elastic permeable blocks under compression. The medium is described within the discrete element method. The relationship between the stress-strain state of the solid skeleton and pore pressure of a liquid is described in the framework of the Biot's model of poroelasticity. The simulation demonstrates that shear strength of an elastic-plastic interface depends non-linearly on the values of permeability and loading to a great extent. We have proposed an empirical relation that approximates the obtained results of the numerical simulation in assumption of the interplay of dilation of the material and mass transfer of the liquid.

The effect of topography of upper-mantle discontinuities on SS precursors

NASA Astrophysics Data System (ADS)

Koroni, Maria; Trampert, Jeannot

2016-01-01

Using the spectral-element method, we explored the effect of topography of upper-mantle discontinuities on the traveltimes of SS precursors recorded on transverse component seismograms. The latter are routinely used to infer the topography of mantle transition zone discontinuities. The step from precursory traveltimes to topographic changes is mainly done using linearised ray theory, or sometimes using finite-frequency kernels. We simulated exact seismograms in 1-D and 3-D elastic models of the mantle. In a second simulation, we added topography to the discontinuities. We compared the waveforms obtained with and without topography by cross correlation of the SS precursors. Since we did not add noise, the precursors are visible in individual seismograms without the need of stacking. The resulting time anomalies were then converted into topographic variations and compared to the original topographic models. Based on the correlation between initial and inferred models, and provided that ray coverage is good, we found that linearised ray theory gives a relatively good idea on the location of the uplifts and depressions of the discontinuities. It seriously underestimates the amplitude of the topographic variations by a factor ranging between 2 and 7. Real data depend on the 3-D elastic structure and the topography. All studies to date correct for the 3-D elastic effects assuming that the traveltimes can be linearly decomposed into a structure and a discontinuity part. We found a strong non-linearity in this decomposition which cannot be modelled without a fully non-linear inversion for elastic structure and discontinuities simultaneously.

Linear and nonlinear stiffness and friction in biological rhythmic movements.

PubMed

Beek, P J; Schmidt, R C; Morris, A W; Sim, M Y; Turvey, M T

1995-11-01

Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as theta3) and van der Pol (involving terms such as theta2theta), and the nonlinear elastic functions identified by Duffing (involving terms such as theta3), constitute elementary nonlinear components for the assembling of self-sustained oscillators, Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as theta2theta3 and thetatheta2, and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.

Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process

NASA Astrophysics Data System (ADS)

Natário, José; Queimada, Leonel; Vicente, Rodrigo

2018-04-01

We rederive the equations of motion for relativistic strings, that is, one-dimensional elastic bodies whose internal energy depends only on their stretching, and use them to study circular string loops rotating in the equatorial plane of flat and black hole spacetimes. We start by obtaining the conditions for equilibrium, and find that: (i) if the string’s longitudinal speed of sound does not exceed the speed of light then its radius when rotating in Minkowski’s spacetime is always larger than its radius when at rest; (ii) in Minkowski’s spacetime, equilibria are linearly stable for rotation speeds below a certain threshold, higher than the string’s longitudinal speed of sound, and linearly unstable for some rotation speeds above it; (iii) equilibria are always linearly unstable in Schwarzschild’s spacetime. Moreover, we study interactions of a rotating string loop with a Kerr black hole, namely in the context of the weak cosmic censorship conjecture and the Penrose process. We find that: (i) elastic string loops that satisfy the null energy condition cannot overspin extremal black holes; (ii) elastic string loops that satisfy the dominant energy condition cannot increase the maximum efficiency of the usual particle Penrose process; (iii) if the dominant energy condition (but not the weak energy condition) is violated then the efficiency can be increased. This last result hints at the interesting possibility that the dominant energy condition may underlie the well known upper bounds for the efficiencies of energy extraction processes (including, for example, superradiance).

Equations for normal-mode statistics of sound scattering by a rough elastic boundary in an underwater waveguide, including backscattering.

PubMed

Morozov, Andrey K; Colosi, John A

2017-09-01

Underwater sound scattering by a rough sea surface, ice, or a rough elastic bottom is studied. The study includes both the scattering from the rough boundary and the elastic effects in the solid layer. A coupled mode matrix is approximated by a linear function of one random perturbation parameter such as the ice-thickness or a perturbation of the surface position. A full two-way coupled mode solution is used to derive the stochastic differential equation for the second order statistics in a Markov approximation.

Cointegration of output, capital, labor, and energy

NASA Astrophysics Data System (ADS)

Stresing, R.; Lindenberger, D.; Kã¼mmel, R.

2008-11-01

Cointegration analysis is applied to the linear combinations of the time series of (the logarithms of) output, capital, labor, and energy for Germany, Japan, and the USA since 1960. The computed cointegration vectors represent the output elasticities of the aggregate energy-dependent Cobb-Douglas function. The output elasticities give the economic weights of the production factors capital, labor, and energy. We find that they are for labor much smaller and for energy much larger than the cost shares of these factors. In standard economic theory output elasticities equal cost shares. Our heterodox findings support results obtained with LINEX production functions.

Radiation-damage-induced transitions in zircon: Percolation theory applied to hardness and elastic moduli as a function of density

NASA Astrophysics Data System (ADS)

Beirau, Tobias; Nix, William D.; Ewing, Rodney C.; Pöllmann, Herbert; Salje, Ekhard K. H.

2018-05-01

Two in literature predicted percolation transitions in radiation-damaged zircon (ZrSiO4) were observed experimentally by measurement of the indentation hardness as a function of density and their correlation with the elastic moduli. Percolations occur near 30% and 70% amorphous fractions, where hardness deviates from its linear correlation with the elastic modulus (E), the shear modulus (G) and the bulk modulus (K). The first percolation point pc1 generates a cusp in the hardness versus density evolution, while the second percolation point is seen as a change of slope.

Nanoscale characterization of the biomechanical properties of collagen fibrils in the sclera

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

Papi, M.; Paoletti, P.; Geraghty, B.

We apply the PeakForce Quantitative Nanomechanical Property Mapping (PFQNM) atomic force microscopy mode for the investigation of regional variations in the nanomechanical properties of porcine sclera. We examine variations in the collagen fibril diameter, adhesion, elastic modulus and dissipation in the posterior, equatorial and anterior regions of the sclera. The mean fibril diameter, elastic modulus and dissipation increased from the posterior to the anterior region. Collagen fibril diameter correlated linearly with elastic modulus. Our data matches the known macroscopic mechanical behavior of the sclera. We propose that PFQNM has significant potential in ocular biomechanics and biophysics research.

Metamodel-based inverse method for parameter identification: elastic-plastic damage model

NASA Astrophysics Data System (ADS)

Huang, Changwu; El Hami, Abdelkhalak; Radi, Bouchaïb

2017-04-01

This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic-plastic damage model parameter identification. An elastic-plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic-plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.

Cones of localized shear strain in incompressible elasticity with prestress: Green's function and integral representations

PubMed Central

Argani, L. P.; Bigoni, D.; Capuani, D.; Movchan, N. V.

2014-01-01

The infinite-body three-dimensional Green's function set (for incremental displacement and mean stress) is derived for the incremental deformation of a uniformly strained incompressible, nonlinear elastic body. Particular cases of the developed formulation are the Mooney–Rivlin elasticity and the J2-deformation theory of plasticity. These Green's functions are used to develop a boundary integral equation framework, by introducing an ad hoc potential, which paves the way for a boundary element formulation of three-dimensional problems of incremental elasticity. Results are used to investigate the behaviour of a material deformed near the limit of ellipticity and to reveal patterns of shear failure. In fact, within the investigated three-dimensional framework, localized deformations emanating from a perturbation are shown to be organized in conical geometries rather than in planar bands, so that failure is predicted to develop through curved and thin surfaces of intense shearing, as can for instance be observed in the cup–cone rupture of ductile metal bars. PMID:25197258

Towards an Aero-Propulso-Servo-Elasticity Analysis of a Commercial Supersonic Transport

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George; Chwalowski, Pawel; Sanetrik, Mark D.; Carlson, Jan-Renee; Silva, Walt A.; McNamara, Jack

2016-01-01

This paper covers the development of an aero-propulso-servo-elastic (APSE) model using computational fluid dynamics (CFD) and linear structural deformations. The APSE model provides the integration of the following two previously developed nonlinear dynamic simulations: a variable cycle turbofan engine and an elastic supersonic commercial transport vehicle. The primary focus of this study is to provide a means to include relevant dynamics of a turbomachinery propulsion system into the aeroelastic studies conducted during a vehicle design, which have historically neglected propulsion effects. A high fidelity CFD tool is used here for the integration platform. The elastic vehicle neglecting the propulsion system serves as a comparison of traditional approaches to the APSE results. An overview of the methodology is presented for integrating the propulsion system and elastic vehicle. Static aeroelastic analysis comparisons between the traditional and developed APSE models for a wing tip detection indicate that the propulsion system impact on the vehicle elastic response could increase the detection by approximately ten percent.

Behaviour of Masonry Walls under Horizontal Shear in Mining Areas

NASA Astrophysics Data System (ADS)

Kadela, Marta; Bartoszek, Marek; Fedorowicz, Jan

2017-12-01

The paper discusses behaviour of masonry walls constructed with small-sized elements under the effects of mining activity. It presents some mechanisms of damage occurring in such structures, its forms in real life and the behaviour of large fragments of masonry walls subjected to specific loads in FEM computational models. It offers a constitutive material model, which enables numerical analyses and monitoring of the behaviour of numerical models as regards elastic-plastic performance of the material, with consideration of its degradation. Results from the numerical analyses are discussed for isolated fragments of the wall subjected to horizontal shear, with consideration of degradation, impact of imposed vertical load as well as the effect of weakening of the wall, which was achieved by introducing openings in it, on the performance and deformation of the wall.

A novel method to determine the elastic modulus of extremely soft materials.

PubMed

Stirling, Tamás; Zrínyi, Miklós

2015-06-07

Determination of the elastic moduli of extremely soft materials that may deform under their own weight is a rather difficult experimental task. A new method has been elaborated by means of which the elastic modulus of such materials can be determined. This method is generally applicable to all soft materials with purely neo-Hookean elastic deformation behaviour with elastic moduli lower than 1 kPa. Our novel method utilises the self-deformation of pendent gel cylinders under gravity. When suspended, the material at the very top bears the weight of the entire gel cylinder, but that at the bottom carries no load at all. Due to the non-uniform stress distribution along the gel sample both the stress and the resulting strain show position dependence. The cross-sectional area of the material is lowest at the top of the sample and gradually increases towards its bottom. The equilibrium geometry of the pendant gel is used to evaluate the elastic modulus. Experimental data obtained by the proposed new method were compared to the results obtained from underwater measurements. The parameters affecting the measurement uncertainty were studied by a Pareto analysis of a series of adaptive Monte Carlo simulations. It has been shown that our method provides an easily achievable method to provide an accurate determination of the elastic modulus of extremely soft matter typically applicable for moduli below 1 kPa.

AnisoVis: a MATLAB™ toolbox for the visualisation of elastic anisotropy

NASA Astrophysics Data System (ADS)

Healy, D.; Timms, N.; Pearce, M. A.

2016-12-01

The elastic properties of rocks and minerals vary with direction, and this has significant consequences for their physical response to acoustic waves and natural or imposed stresses. This anisotropy of elasticity is well described mathematically by 4th rank tensors of stiffness or compliance. These tensors are not easy to visualise in a single diagram or graphic, and visualising Poisson's ratio and shear modulus presents a further challenge in that their anisotropy depends on two principal directions. Students and researchers can easily underestimate the importance of elastic anisotropy. This presentation describes an open source toolbox of MATLAB scripts that aims to visualise elastic anisotropy in rocks and minerals. The code produces linked 2-D and 3-D representations of the standard elastic constants, such as Young's modulus, Poisson's ratio and shear modulus, all from a simple GUI. The 3-D plots can be manipulated by the user (rotated, panned, zoomed), to encourage investigation and a deeper understanding of directional variations in the fundamental properties. Examples are presented of common rock forming minerals, including those with negative Poisson's ratio (auxetic behaviour). We hope that an open source code base will encourage further enhancements from the rock physics and wider geoscience communities. Eventually, we hope to generate 3-D prints of these complex and beautiful natural surfaces to provide a tactile link to the underlying physics of elastic anisotropy.

Low temperature internal friction spectrum of YBa 2Cu 3O x

NASA Astrophysics Data System (ADS)

Mi, Y.; Schaller, R.; Berger, H.; Benoit, W.; Sathish, S.

1991-01-01

The elastic and anelastic behaviours of polycrystalline YBa 2Cu 3O x specimens have been studied between 80 and 300 K, by means of a resonant bar technique. Three damping peaks have been observed at 90, 115 and 220 K. The stability of these peaks during annealing in vacuum has been carefully examined. The 90 K peak is not related to the superconducting transition because it is still observed after thermal treatments leading to the disappearance of superconductivity. The 115 K is due to a relaxation mechanism. The activation energy is ∼0.17 eV and the frequency factor is ∼10 12s -1. Also this peak is certainly correlated with the excess oxygen atoms, because it disappears with annealing in vacuum. The 220 K maximum, which was also observed by ultrasonic measurements, seems to be affected by the sample preparation, i.e. by the sintering conditions. Finally, a frequency hysteresis has been observed in every superconducting sample, which accounts for an anomalous behaviour of the elastic modulus.

Modelling of photodegradation effect on elastic-viscoplastic behaviour of amorphous polylactic acid films

NASA Astrophysics Data System (ADS)

Belbachir, S.; Zaïri, F.; Ayoub, G.; Maschke, U.; Naït-Abdelaziz, M.; Gloaguen, J. M.; Benguediab, M.; Lefebvre, J. M.

2010-02-01

Polylactic acid (PLA) films were subjected to accelerated ultra-violet (UV) ageing. The UV irradiation leads to the alteration of the chemical structure which influences directly the mechanical response of the polymer. The chemical modification of the polymer was followed by gel permeation chromatography. Uniaxial tension tests were conducted at 50 °C and for different strain rates in order to characterize the large deformation response of PLA. The influence of UV irradiation on the alteration of the large deformation response of PLA was examined. A physically based elastic-viscoplastic model was used to describe the mechanical response of virgin PLA. The photodegradation effect was incorporated into the constitutive model to capture the stress-strain behaviour up to failure of aged PLA. To that end, the measured molecular weight was used as a direct input into the model. The model is shown to be in good agreement with experimental results over a wide range of UV irradiation doses.

Preparation and Elastic Moduli of Germanate Glass Containing Lead and Bismuth

PubMed Central

Sidek, Hj A. A.; Bahari, Hamid R.; Halimah, Mohamed K.; Yunus, Wan M. M.

2012-01-01

This paper reports the rapid melt quenching technique preparation for the new family of bismuth-lead germanate glass (BPG) systems in the form of (GeO2)60–(PbO)40−x–(½Bi2O3)x where x = 0 to 40 mol%. Their densities with respect of Bi2O3 concentration were determined using Archimedes’ method with acetone as a floatation medium. The current experimental data are compared with those of bismuth lead borate (B2O3)20–(PbO)80−x–(Bi2O3)x. The elastic properties of BPG were studied using the ultrasonic pulse-echo technique where both longitudinal and transverse sound wave velocities have been measured in each glass samples at a frequency of 15 MHz and at room temperature. Experimental data shows that all the physical parameters of BPG including density and molar volume, both longitudinal and transverse velocities increase linearly with increasing of Bi2O3 content in the germanate glass network. Their elastic moduli such as longitudinal, shear and Young’s also increase linearly with addition of Bi2O3 but the bulk modulus did not. The Poisson’s ratio and fractal dimensionality are also found to vary linearly with the Bi2O3 concentration. PMID:22606000

Preparation and elastic moduli of germanate glass containing lead and bismuth.

PubMed

Sidek, Hj A A; Bahari, Hamid R; Halimah, Mohamed K; Yunus, Wan M M

2012-01-01

This paper reports the rapid melt quenching technique preparation for the new family of bismuth-lead germanate glass (BPG) systems in the form of (GeO(2))(60)-(PbO)(40-) (x)-(½Bi(2)O(3))(x) where x = 0 to 40 mol%. Their densities with respect of Bi(2)O(3) concentration were determined using Archimedes' method with acetone as a floatation medium. The current experimental data are compared with those of bismuth lead borate (B(2)O(3))(20)-(PbO)(80-) (x)-(Bi(2)O(3))(x). The elastic properties of BPG were studied using the ultrasonic pulse-echo technique where both longitudinal and transverse sound wave velocities have been measured in each glass samples at a frequency of 15 MHz and at room temperature. Experimental data shows that all the physical parameters of BPG including density and molar volume, both longitudinal and transverse velocities increase linearly with increasing of Bi(2)O(3) content in the germanate glass network. Their elastic moduli such as longitudinal, shear and Young's also increase linearly with addition of Bi(2)O(3) but the bulk modulus did not. The Poisson's ratio and fractal dimensionality are also found to vary linearly with the Bi(2)O(3) concentration.

The effect of stent graft oversizing on radial forces considering nitinol wire behavior and vessel characteristics.

PubMed

Senf, B; von Sachsen, S; Neugebauer, R; Drossel, W-G; Florek, H-J; Mohr, F W; Etz, C D

2014-11-01

Stent graft fixation in the vessel affects the success of endovascular aneurysm repair. Thereby the radial forces of the stent, which are dependent on several factors, play a significant role. In the presented work, a finite element sensitivity study was performed. The radial forces are 29% lower when using the hyperelastic approach for the vessel compared with linear elastic assumptions. Without the linear elastic modeled plaque, the difference increases to 35%. Modeling plaque with linear elastic material approach results in 8% higher forces than with a hyperelastic characteristic. The significant differences resulting from the investigated simplifications of the material lead to the conclusion that it is important to apply an anisotropic nonlinear approach for the vessel. The oversizing study shows that radial forces increase by 64% (0.54 N) when raising the oversize from 10 to 22%, and no further increase in force can be observed beyond these values (vessel diameter D=12 mm). Starting from an oversize of 24%, the radial force steadily decreases. The findings of the investigation show that besides the oversizing the material properties, the ring design and the vessel characteristics have an influence on radial forces. Copyright © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.

The Elementary Operations of Human Vision Are Not Reducible to Template-Matching

PubMed Central

Neri, Peter

2015-01-01

It is generally acknowledged that biological vision presents nonlinear characteristics, yet linear filtering accounts of visual processing are ubiquitous. The template-matching operation implemented by the linear-nonlinear cascade (linear filter followed by static nonlinearity) is the most widely adopted computational tool in systems neuroscience. This simple model achieves remarkable explanatory power while retaining analytical tractability, potentially extending its reach to a wide range of systems and levels in sensory processing. The extent of its applicability to human behaviour, however, remains unclear. Because sensory stimuli possess multiple attributes (e.g. position, orientation, size), the issue of applicability may be asked by considering each attribute one at a time in relation to a family of linear-nonlinear models, or by considering all attributes collectively in relation to a specified implementation of the linear-nonlinear cascade. We demonstrate that human visual processing can operate under conditions that are indistinguishable from linear-nonlinear transduction with respect to substantially different stimulus attributes of a uniquely specified target signal with associated behavioural task. However, no specific implementation of a linear-nonlinear cascade is able to account for the entire collection of results across attributes; a satisfactory account at this level requires the introduction of a small gain-control circuit, resulting in a model that no longer belongs to the linear-nonlinear family. Our results inform and constrain efforts at obtaining and interpreting comprehensive characterizations of the human sensory process by demonstrating its inescapably nonlinear nature, even under conditions that have been painstakingly fine-tuned to facilitate template-matching behaviour and to produce results that, at some level of inspection, do conform to linear filtering predictions. They also suggest that compliance with linear transduction may be the targeted outcome of carefully crafted nonlinear circuits, rather than default behaviour exhibited by basic components. PMID:26556758

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

NASA Astrophysics Data System (ADS)

Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.

2018-04-01

Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.

Thermophoretically induced large-scale deformations around microscopic heat centers

NASA Astrophysics Data System (ADS)

Puljiz, Mate; Orlishausen, Michael; Köhler, Werner; Menzel, Andreas M.

2016-05-01

Selectively heating a microscopic colloidal particle embedded in a soft elastic matrix is a situation of high practical relevance. For instance, during hyperthermic cancer treatment, cell tissue surrounding heated magnetic colloidal particles is destroyed. Experiments on soft elastic polymeric matrices suggest a very long-ranged, non-decaying radial component of the thermophoretically induced displacement fields around the microscopic heat centers. We theoretically confirm this conjecture using a macroscopic hydrodynamic two-fluid description. Both thermophoretic and elastic effects are included in this theory. Indeed, we find that the elasticity of the environment can cause the experimentally observed large-scale radial displacements in the embedding matrix. Additional experiments confirm the central role of elasticity. Finally, a linearly decaying radial component of the displacement field in the experiments is attributed to the finite size of the experimental sample. Similar results are obtained from our theoretical analysis under modified boundary conditions.

Fluid-structure interaction in Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Kempf, Martin Horst Willi

1998-10-01

The linear stability of a viscous fluid between two concentric, rotating cylinders is considered. The inner cylinder is a rigid boundary and the outer cylinder has an elastic layer exposed to the fluid. The subject is motivated by flow between two adjoining rollers in a printing press. The governing equations of the fluid layer are the incompressible Navier-Stokes equations, and the governing equations of the elastic layer are Navier's equations. A narrow gap, neutral stability, and axisymmetric disturbances are assumed. The solution involves a novel technique for treating two layer stability problems, where an exact solution in the elastic layer is used to isolate the problem in the fluid layer. The results show that the presence of the elastic layer has only a slight effect on the critical Taylor numbers for the elastic parameters of modern printing presses. However, there are parameter values where the critical Taylor number is dramatically different than the classical Taylor-Couette problem.

Measurement of Shear Elastic Moduli in Quasi-Incompressible Soft Solids

NASA Astrophysics Data System (ADS)

Rénier, Mathieu; Gennisson, Jean-Luc; Barrière, Christophe; Catheline, Stefan; Tanter, Mickaël; Royer, Daniel; Fink, Mathias

2008-06-01

Recently a nonlinear equation describing the plane shear wave propagation in isotropic quasi-incompressible media has been developed using a new expression of the strain energy density, as a function of the second, third and fourth order shear elastic constants (respectively μ, A, D) [1]. In such a case, the shear nonlinearity parameter βs depends only from these last coefficients. To date, no measurement of the parameter D have been carried out in soft solids. Using a set of two experiments, acoustoelasticity and finite amplitude shear waves, the shear elastic moduli up to the fourth order of soft solids are measured. Firstly, this theoretical background is applied to the acoustoelasticity theory, giving the variations of the shear wave speed as a function of the stress applied to the medium. From such variations, both linear (μ) and third order shear modulus (A) are deduced in agar-gelatin phantoms. Experimentally the radiation force induced by a focused ultrasound beam is used to generate quasi-plane linear shear waves within the medium. Then the shear wave propagation is imaged with an ultrafast ultrasound scanner. Secondly, in order to give rise to finite amplitude plane shear waves, the radiation force generation technique is replaced by a vibrating plate applied at the surface of the phantoms. The propagation is also imaged using the same ultrafast scanner. From the assessment of the third harmonic amplitude, the nonlinearity parameter βS is deduced. Finally, combining these results with the acoustoelasticity experiment, the fourth order modulus (D) is deduced. This set of experiments provides the characterization, up to the fourth order, of the nonlinear shear elastic moduli in quasi-incompressible soft media. Measurements of the A moduli reveal that while the behaviors of both soft solids are close from a linear point of view, the corresponding nonlinear moduli A are quite different. In a 5% agar-gelatin phantom, the fourth order elastic constant D is found to be 30±10 kPa.

Dependence of elastic hadron collisions on impact parameter

NASA Astrophysics Data System (ADS)

Procházka, Jiří; Lokajíček, Miloš V.; Kundrát, Vojtěch

2016-05-01

Elastic proton-proton collisions represent probably the greatest ensemble of available measured data, the analysis of which may provide a large amount of new physical results concerning fundamental particles. It is, however, necessary to analyze first some conclusions concerning pp collisions and their interpretations differing fundamentally from our common macroscopic experience. It has been argued, e.g., that elastic hadron collisions have been more central than inelastic ones, even if any explanation of the existence of so different processes, i.e., elastic and inelastic (with hundreds of secondary particles) collisions, under the same conditions has not been given until now. The given conclusion has been based on a greater number of simplifying mathematical assumptions (already done in earlier calculations), without their influence on physical interpretation being analyzed and entitled; the corresponding influence has started to be studied in the approach based on the eikonal model. The possibility of a peripheral interpretation of elastic collisions will be demonstrated and the corresponding results summarized. The arguments will be given on why no preference may be given to the mentioned centrality against the standard peripheral behaviour. The corresponding discussion on the contemporary description of elastic hadronic collision in dependence on the impact parameter will be summarized and the justification of some important assumptions will be considered.

Quantitative micro-elastography: imaging of tissue elasticity using compression optical coherence elastography

PubMed Central

Kennedy, Kelsey M.; Chin, Lixin; McLaughlin, Robert A.; Latham, Bruce; Saunders, Christobel M.; Sampson, David D.; Kennedy, Brendan F.

2015-01-01

Probing the mechanical properties of tissue on the microscale could aid in the identification of diseased tissues that are inadequately detected using palpation or current clinical imaging modalities, with potential to guide medical procedures such as the excision of breast tumours. Compression optical coherence elastography (OCE) maps tissue strain with microscale spatial resolution and can delineate microstructural features within breast tissues. However, without a measure of the locally applied stress, strain provides only a qualitative indication of mechanical properties. To overcome this limitation, we present quantitative micro-elastography, which combines compression OCE with a compliant stress sensor to image tissue elasticity. The sensor consists of a layer of translucent silicone with well-characterized stress-strain behaviour. The measured strain in the sensor is used to estimate the two-dimensional stress distribution applied to the sample surface. Elasticity is determined by dividing the stress by the strain in the sample. We show that quantification of elasticity can improve the ability of compression OCE to distinguish between tissues, thereby extending the potential for inter-sample comparison and longitudinal studies of tissue elasticity. We validate the technique using tissue-mimicking phantoms and demonstrate the ability to map elasticity of freshly excised malignant and benign human breast tissues. PMID:26503225

Wrinkle-to-fold transition in soft layers under equi-biaxial strain: A weakly nonlinear analysis

NASA Astrophysics Data System (ADS)

Ciarletta, P.

2014-12-01

Soft materials can experience a mechanical instability when subjected to a finite compression, developing wrinkles which may eventually evolve into folds or creases. The possibility to control the wrinkling network morphology has recently found several applications in many developing fields, such as scaffolds for biomaterials, stretchable electronics and surface micro-fabrication. Albeit much is known of the pattern initiation at the linear stability order, the nonlinear effects driving the pattern selection in soft materials are still unknown. This work aims at investigating the nature of the elastic bifurcation undertaken by a growing soft layer subjected to a equi-biaxial strain. Considering a skin effect at the free surface, the instability thresholds are found to be controlled by a characteristic length, defined by the ratio between capillary energy and bulk elasticity. For the first time, a weakly nonlinear analysis of the wrinkling instability is performed here using the multiple-scale perturbation method applied to the incremental theory in finite elasticity. The Ginzburg-Landau equations are derived for different superposing linear modes. This study proves that a subcritical pitchfork bifurcation drives the observed wrinkle-to-fold transition in swelling gels experiments, favoring the emergence of hexagonal creased patterns, albeit quasi-hexagonal patterns might later emerge because of an expected symmetry break. Moreover, if the surface energy is somewhat comparable to the bulk elastic energy, it has the same stabilizing effect as for fluid instabilities, driving the formation of stable wrinkles, as observed in elastic bi-layered materials.

Moored offshore structures - evaluation of forces in elastic mooring lines

NASA Astrophysics Data System (ADS)

Crudu, L.; Obreja, D. C.; Marcu, O.

2016-08-01

In most situations, the high frequency motions of the floating structure induce important effects in the mooring lines which affect also the motions of the structure. The experience accumulated during systematic experimental tests and calculations, carried out for different moored floating structures, showed a complex influence of various parameters on the dynamic effects. Therefore, it was considered that a systematic investigation is necessary. Due to the complexity of hydrodynamics aspects of offshore structures behaviour, experimental tests are practically compulsory in order to be able to properly evaluate and then to validate their behaviour in real sea. Moreover the necessity to carry out hydrodynamic tests is often required by customers, classification societies and other regulatory bodies. Consequently, the correct simulation of physical properties of the complex scaled models becomes a very important issue. The paper is investigating such kind of problems identifying the possible simplification, generating different approaches. One of the bases of the evaluation has been found consideringtheresults of systematic experimental tests on the dynamic behaviour of a mooring chain reproduced at five different scales. Dynamic effects as well as the influences of the elasticity simulation for 5 different scales are evaluated together. The paper presents systematic diagrams and practical results for a typical moored floating structure operating as pipe layer based on motion evaluations and accelerations in waves.

Flexural edge waves generated by steady-state propagation of a loaded rectilinear crack in an elastically supported thin plate

NASA Astrophysics Data System (ADS)

Nobili, Andrea; Radi, Enrico; Lanzoni, Luca

2017-08-01

The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The full-field solution is obtained and the spotlight is set on flexural edge wave generation. Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist. These waves are characterized by a novel dispersion relation and fade off from the crack line in an oscillatory manner, whence they play an important role in the far field behaviour. Dynamic stress intensity factors are obtained and, for speed close to the critical speed, they show a resonant behaviour which expresses the most efficient way to channel external work into the crack. Indeed, this behaviour is justified through energy considerations regarding the work of the applied load and the energy release rate. Results might be useful in a wide array of applications, ranging from fracturing and machining to acoustic emission and defect detection.

Flexural edge waves generated by steady-state propagation of a loaded rectilinear crack in an elastically supported thin plate.

PubMed

Nobili, Andrea; Radi, Enrico; Lanzoni, Luca

2017-08-01

The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The full-field solution is obtained and the spotlight is set on flexural edge wave generation. Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist. These waves are characterized by a novel dispersion relation and fade off from the crack line in an oscillatory manner, whence they play an important role in the far field behaviour. Dynamic stress intensity factors are obtained and, for speed close to the critical speed, they show a resonant behaviour which expresses the most efficient way to channel external work into the crack. Indeed, this behaviour is justified through energy considerations regarding the work of the applied load and the energy release rate. Results might be useful in a wide array of applications, ranging from fracturing and machining to acoustic emission and defect detection.

[Evaluation of pendulum testing of spasticity].

PubMed

Le Cavorzin, P; Hernot, X; Bartier, O; Carrault, G; Chagneau, F; Gallien, P; Allain, H; Rochcongar, P

2002-11-01

To identify valid measurements of spasticity derived from the pendulum test of the leg in a representative population of spastic patients. Pendulum testing was performed in 15 spastic and 10 matched healthy subjects. The reflex-mediated torque evoked in quadriceps femoris, as well as muscle mechanical parameters (viscosity and elasticity), were calculated using mathematical modelling. Correlation with the two main measures derived from the pendulum test reported in the literature (the Relaxation Index and the area under the curve) was calculated in order to select the most valid. Among mechanical parameters, only viscosity was found to be significantly higher in the spastic group. As expected, the computed integral of the reflex-mediated torque was found to be larger in spastics than in healthy subjects. A significant non-linear (logarithmic) correlation was found between the clinically-assessed muscle spasticity (Ashworth grading) and the computed reflex-mediated torque, emphasising the non-linear behaviour of this scale. Among measurements derived from the pendulum test which are proposed in the literature for routine estimation of spasticity, the Relaxation Index exhibited an unsuitable U-shaped pattern of variation with increasing reflex-mediated torque. On the opposite, the area under the curve revealed a linear regression, which is more convenient for routine estimation of spasticity. The pendulum test of the leg is a simple technique for the assessment of spastic hypertonia. However, the measurement generally used in the literature (the Relaxation Index) exhibits serious limitations, and would benefit to be replaced by more valid measures, such as the area under the goniometric curve, especially for the assessment of therapeutics.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

Crack Initiation and Propagation Properties of HY 130 Steel Weldments Following Temper Embrittlement.

DTIC Science & Technology

1982-09-01

mechanics ( EPFM ) may be applied to engineering problems to determine material properties related to crack initiation and propagation. Specifically, these...Introduction The application of linear elastic fracture mechanics (LEFM) to engineering fracture analyses has become increasingly widespread and the use...structures to which the particular material was to be applied. The advent of elastic-plastic fracture mechanics ( EPFM ) has proven valuable because a

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

The influence of closed brine pockets and permeable brine channels on the thermo-elastic properties of saline ice

PubMed Central

Lishman, Ben

2017-01-01

A model of the thermo-elastic behaviour of saline ice is formulated, and model solutions describing thermo-elastic waves (TEW) propagating into a half-space of the ice are investigated. The model is based on a proposal that saline ice is a matrix, which encompasses both closed brine pockets and permeable channels filled with brine. Experiments on the thermal expansion of saline ice samples, and on TEW in saline ice, have been performed in the cold laboratories of the University Centre in Svalbard and in University College London. The experimental data are compared with theoretical conclusions. The experimental data support our hypothesis that the brine in saline ice is divided between closed pockets and open, permeable channels. This article is part of the themed issue ‘Microdynamics of ice’. PMID:28025299

Real-space Wigner-Seitz Cells Imaging of Potassium on Graphite via Elastic Atomic Manipulation

PubMed Central

Yin, Feng; Koskinen, Pekka; Kulju, Sampo; Akola, Jaakko; Palmer, Richard E.

2015-01-01

Atomic manipulation in the scanning tunnelling microscopy, conventionally a tool to build nanostructures one atom at a time, is here employed to enable the atomic-scale imaging of a model low-dimensional system. Specifically, we use low-temperature STM to investigate an ultra thin film (4 atomic layers) of potassium created by epitaxial growth on a graphite substrate. The STM images display an unexpected honeycomb feature, which corresponds to a real-space visualization of the Wigner-Seitz cells of the close-packed surface K atoms. Density functional simulations indicate that this behaviour arises from the elastic, tip-induced vertical manipulation of potassium atoms during imaging, i.e. elastic atomic manipulation, and reflects the ultrasoft properties of the surface under strain. The method may be generally applicable to other soft e.g. molecular or biomolecular systems. PMID:25651973

Extrapolation of bulk rock elastic moduli of different rock types to high pressure conditions and comparison with texture-derived elastic moduli

NASA Astrophysics Data System (ADS)

Ullemeyer, Klaus; Lokajíček, Tomás; Vasin, Roman N.; Keppler, Ruth; Behrmann, Jan H.

2018-02-01

In this study elastic moduli of three different rock types of simple (calcite marble) and more complex (amphibolite, micaschist) mineralogical compositions were determined by modeling of elastic moduli using texture (crystallographic preferred orientation; CPO) data, experimental investigation and extrapolation. 3D models were calculated using single crystal elastic moduli, and CPO measured using time-of-flight neutron diffraction at the SKAT diffractometer in Dubna (Russia) and subsequently analyzed using Rietveld Texture Analysis. To define extrinsic factors influencing elastic behaviour, P-wave and S-wave velocity anisotropies were experimentally determined at 200, 400 and 600 MPa confining pressure. Functions describing variations of the elastic moduli with confining pressure were then used to predict elastic properties at 1000 MPa, revealing anisotropies in a supposedly crack-free medium. In the calcite marble elastic anisotropy is dominated by the CPO. Velocities continuously increase, while anisotropies decrease from measured, over extrapolated to CPO derived data. Differences in velocity patterns with sample orientation suggest that the foliation forms an important mechanical anisotropy. The amphibolite sample shows similar magnitudes of extrapolated and CPO derived velocities, however the pattern of CPO derived velocity is closer to that measured at 200 MPa. Anisotropy decreases from the extrapolated to the CPO derived data. In the micaschist, velocities are higher and anisotropies are lower in the extrapolated data, in comparison to the data from measurements at lower pressures. Generally our results show that predictions for the elastic behavior of rocks at great depths are possible based on experimental data and those computed from CPO. The elastic properties of the lower crust can, thus, be characterized with an improved degree of confidence using extrapolations. Anisotropically distributed spherical micro-pores are likely to be preserved, affecting seismic velocity distributions. Compositional variations in the polyphase rock samples do not significantly change the velocity patterns, allowing the use of RTA-derived volume percentages for the modeling of elastic moduli.

Computational Modeling of Micro-Crack Induced Attenuation in CFRP Composites

NASA Technical Reports Server (NTRS)

Roberts, R. A.; Leckey, C. A. C.

2012-01-01

A computational study is performed to determine the contribution to ultrasound attenuation in carbon fiber reinforced polymer composite laminates of linear elastic scattering by matrix micro-cracking. Multiple scattering approximations are benchmarked against exact computational approaches. Results support linear scattering as the source of observed increased attenuation in the presence of micro-cracking.

Constitutive error based parameter estimation technique for plate structures using free vibration signatures

NASA Astrophysics Data System (ADS)

Guchhait, Shyamal; Banerjee, Biswanath

2018-04-01

In this paper, a variant of constitutive equation error based material parameter estimation procedure for linear elastic plates is developed from partially measured free vibration sig-natures. It has been reported in many research articles that the mode shape curvatures are much more sensitive compared to mode shape themselves to localize inhomogeneity. Complying with this idea, an identification procedure is framed as an optimization problem where the proposed cost function measures the error in constitutive relation due to incompatible curvature/strain and moment/stress fields. Unlike standard constitutive equation error based procedure wherein a solution of a couple system is unavoidable in each iteration, we generate these incompatible fields via two linear solves. A simple, yet effective, penalty based approach is followed to incorporate measured data. The penalization parameter not only helps in incorporating corrupted measurement data weakly but also acts as a regularizer against the ill-posedness of the inverse problem. Explicit linear update formulas are then developed for anisotropic linear elastic material. Numerical examples are provided to show the applicability of the proposed technique. Finally, an experimental validation is also provided.

Mechanical factors direct mouse aortic remodelling during early maturation

PubMed Central

Le, Victoria P.; Cheng, Jeffrey K.; Kim, Jungsil; Staiculescu, Marius C.; Ficker, Shawn W.; Sheth, Saahil C.; Bhayani, Siddharth A.; Mecham, Robert P.; Yanagisawa, Hiromi; Wagenseil, Jessica E.

2015-01-01

Numerous diseases have been linked to genetic mutations that lead to reduced amounts or disorganization of arterial elastic fibres. Previous work has shown that mice with reduced amounts of elastin (Eln+/−) are able to live a normal lifespan through cardiovascular adaptations, including changes in haemodynamic stresses, arterial geometry and arterial wall mechanics. It is not known if the timeline and presence of these adaptations are consistent in other mouse models of elastic fibre disease, such as those caused by the absence of fibulin-5 expression (Fbln5−/−). Adult Fbln5−/− mice have disorganized elastic fibres, decreased arterial compliance and high blood pressure. We examined mechanical behaviour of the aorta in Fbln5−/− mice through early maturation when the elastic fibres are being assembled. We found that the physiologic circumferential stretch, stress and modulus of Fbln5−/− aorta are maintained near wild-type levels. Constitutive modelling suggests that elastin contributions to the total stress are decreased, whereas collagen contributions are increased. Understanding how collagen fibre structure and mechanics compensate for defective elastic fibres to meet the mechanical requirements of the maturing aorta may help to better understand arterial remodelling in human elastinopathies. PMID:25652465

Hunting for ghosts in elastic snap-through

NASA Astrophysics Data System (ADS)

Gomez, Michael; Moulton, Derek E.; Vella, Dominic

Elastic `snap-through' is a striking instability often seen when an elastic system loses bistability, e.g. due to a change in geometry or external loading. The switch from one state to another is generally rapid and hence is used to generate fast motions in biology and engineering. While the onset of instability has been well studied, the dynamics of the transition itself remain much less well understood. For example, the dynamics exhibited by children's jumping popper toys, or the leaves of the Venus flytrap plant, are much slower than would be expected based on a naive estimate of the elastic timescales. To explain this discrepancy, the natural conclusion has been drawn that some other effect, such as viscoelasticity, must play a role. We demonstrate here that purely elastic systems may show similar `slow' dynamics during snap-through. This behaviour is due to a remnant (or `ghost') of the snap-through bifurcation underlying the instability, analogously to bottleneck phenomena in 1-D dynamical systems. This slowness is a generic consequence of being close to bifurcation -- it does not require dissipation. We obtain scaling laws for the length of the delay and compare these to numerical simulations and experiments on real samples.

The Dispersion of the Axisymmetric Longitudinal Waves in the Pre-Strained Bi-Material Hollow Cylinder with the Imperfect Interface Conditions

NASA Astrophysics Data System (ADS)

Akbarov, S. D.; Ipek, C.

This work studies the influence of the imperfectness of the interface conditions on the dispersion of the axisymmetric longitudinal waves in the pre-strained bi-material hollow cylinder. The investigations are made within the 3D linearized theory of elastic waves in elastic bodies with initial stresses. It is assumed that the materials of the layers of the hollow cylinder are made from hyper elastic compressible materials and the elasticity relations of those are given through the harmonic potential. The shear spring type imperfectness of the interface conditions is considered and the degree of this imperfectness is estimated by the shear-spring parameter. Numerical results on the influence of this parameter on the behavior of the dispersion curves are presented and discussed.

Discontinuous Galerkin method for coupled problems of compressible flow and elastic structures

NASA Astrophysics Data System (ADS)

Kosík, A.; Feistauer, M.; Hadrava, M.; Horáček, J.

2013-10-01

This paper is concerned with the numerical simulation of the interaction of 2D compressible viscous flow and an elastic structure. We consider the model of dynamical linear elasticity. Each individual problem is discretized in space by the discontinuous Galerkin method (DGM). For the time discretization we can use either the BDF (backward difference formula) method or also the DGM. The time dependence of the domain occupied by the fluid is given by the deformation of the elastic structure adjacent to the flow domain. It is treated with the aid of the Arbitrary Lagrangian-Eulerian (ALE) method. The fluid-structure interaction, given by transient conditions, is realized by an iterative process. The developed method is applied to the simulation of the biomechanical problem containing the onset of the voice production.

First principles predictions of electronic and elastic properties of BaPb2As2 in the ThCr2Si2-type structure

NASA Astrophysics Data System (ADS)

Bourourou, Y.; Amari, S.; Yahiaoui, I. E.; Bouhafs, B.

2018-01-01

A first-principles approach is used to predicts the electronic and elastic properties of BaPb2As2 superconductor compound, using full-potential linearized augmented plane wave plus local orbitals (FP-L/APW+lo) scheme within the local density approximation LDA. The calculated equilibrium structural parameter a agree well with the experiment while the c/a ratio is far away from the experimental result. The band structure, density of states, together with the charge density and chemical bonding are discussed. The calculated elastic constants for our compound indicate that it is mechanically stable at ambient pressure. Polycrystalline elastic moduli (Young's, Bulk, shear Modulus and the Poisson's ratio) were calculated according to the Voigte-Reusse-Hill (VRH) average.

Structural, elastic and electronic properties of transition metal carbides ZnC, NbC and their ternary alloys ZnxNb1-xC

NASA Astrophysics Data System (ADS)

Zidi, Y.; Méçabih, S.; Abbar, B.; Amari, S.

2018-02-01

We have investigated the structural, electronic and elastic properties of transition-metal carbides ZnxNb1-xC alloys in the range of 0 ≤ x ≤ 1 using the density functional theory (DFT). The full potential linearized augmented plane wave (FP-LAPW) method within a framework of the generalized gradient approximation (GGA) and GGA + U (where U is the Hubbard correlation terms) approach is used to perform the calculations presented here. The lattice parameters, the bulk modulus, its pressure derivative and the elastic constants were determined. We have obtained Young's modulus, shear modulus, Poisson's ratio, anisotropy factor by the aid of the calculated elastic constants. We discuss the total and partial densities of states and charge densities.

3D Modeling Effect of Spherical Inclusions on the Magnetostriction of Bulk Superconductors

NASA Astrophysics Data System (ADS)

Zhao, Yufeng; Pan, Baocai

2018-02-01

In this paper, the dependence of the effective magnetostriction of bulk superconductors on the elastic parameters including the volume fraction and elastic modulus ratio is studied by a three-dimensional model consisting of a spherical inclusion-superconducting matrix system. The effect of the elastic modulus and volume fraction on the magnetostriction is also obtained through the magnetostriction loop. The results indicate that the elastic modulus and volume fraction have obvious effects on the effective magnetostriction of the superconducting composite, which gives an explanation about the differences between the experimental and the theoretical results. Furthermore, it is worth pointing out that the linear field dependence of magnetostriction is unique to the Bean model by comparing the curve shapes of the magnetostriction loop with and without inclusion.

An Auxetic structure configured as oesophageal stent with potential to be used for palliative treatment of oesophageal cancer; development and in vitro mechanical analysis.

PubMed

Ali, Murtaza N; Rehman, Ihtesham Ur

2011-11-01

Oesophageal cancer is the ninth leading cause of malignant cancer death and its prognosis remains poor. Dysphagia which is an inability to swallow is a presenting symptom of oesophageal cancer and is indicative of incurability. The goal of this study was to design and manufacture an Auxetic structure film and to configure this film as an Auxetic stent for the palliative treatment of oesophageal cancer, and for the prevention of dysphagia. Polypropylene was used as a material for its flexibility and non-toxicity. The Auxetic (rotating-square geometry) structure was made by laser cutting the polypropylene film. This flat structure was welded together to form a tubular form (stent), by an adjustable temperature control soldering iron station: following this, an annealing process was also carried out to ease any material stresses. Poisson's ratio was estimated and elastic and plastic deformation of the Auxetic structure was evaluated. The elastic and plastic deformation behaviours of the Auxetic polypropylene film were evaluated by applying repetitive uniaxial tensile loads. Observation of the structure showed that it was initially elastically deformed, thereafter plastic deformation occurred. This research discusses a novel way of fabricating an Auxetic structure (rotating-squares connected together through hinges) on Polypropylene films, by estimating the Poisson's ratio and evaluating the plastic deformation relevant to the expansion behaviour of an Auxetic stent within the oesophageal lumen.

Biomechanical properties of the tomato (Solanum lycopersicum) fruit cuticle during development are modulated by changes in the relative amounts of its components.

PubMed

España, Laura; Heredia-Guerrero, José A; Segado, Patricia; Benítez, José J; Heredia, Antonio; Domínguez, Eva

2014-05-01

In this study, growth-dependent changes in the mechanical properties of the tomato (Solanum lycopersicum) cuticle during fruit development were investigated in two cultivars with different patterns of cuticle growth and accumulation. The mechanical properties were determined in uniaxial tensile tests using strips of isolated cuticles. Changes in the functional groups of the cuticle chemical components were analysed by attenuated total reflectance-Fourier transform infrared (ATR-FTIR). The early stages of fruit growth are characterized by an elastic cuticle, and viscoelastic behaviour only appeared at the beginning of cell enlargement. Changes in the cutin:polysaccharide ratio during development affected the strength required to achieve viscoelastic deformation. The increase in stiffness and decrease in extensibility during ripening, related to flavonoid accumulation, were accompanied by an increase in cutin depolymerization as a result of a reduction in the overall number of ester bonds. Quantitative changes in cuticle components influence the elastic/viscoelastic behaviour of the cuticle. The cutin:polysaccharide ratio modulates the stress required to permanently deform the cuticle and allow cell enlargement. Flavonoids stiffen the elastic phase and reduce permanent viscoelastic deformation. Ripening is accompanied by a chemical cleavage of cutin ester bonds. An infrared (IR) band related to phenolic accumulation can be used to monitor changes in the cutin esterification index. © 2014 The Authors. New Phytologist © 2014 New Phytologist Trust.

The influence of geometric imperfections on the stability of three-layer beams with foam core

NASA Astrophysics Data System (ADS)

Wstawska, Iwona

2017-01-01

The main objective of this work is the numerical analysis (FE analysis) of stability of three-layer beams with metal foam core (alumina foam core). The beams were subjected to pure bending. The analysis of the local buckling was performed. Furthermore, the influence of geometric parameters of the beam and material properties of the core (linear and non-linear model) on critical loads values and buckling shape were also investigated. The calculations were made on a family of beams with different mechanical properties of the core (elastic and elastic-plastic material). In addition, the influence of geometric imperfections on deflection and normal stress values of the core and the faces has been evaluated.

Simulative design in macroscale for prospective application to micro-catheters.

PubMed

Ha, Cheol Woo

2018-02-09

In this paper, a motion-transforming element is applied to the development of a new catheter device. The motion-transforming element structure allows a reduction of linear movement and converts linear movement to rotational movement. The simulative design of micro-catheters is based on a proposed structure called the Operating Mini Station (OMS). OMS is operated by movement of a motion-transforming element. A new motion-transforming element is designed using multiple links that are connected by hinged joints based on an elastic design. The design of the links and the hinges are optimized for precise and reliable movement of the motion-transforming element. Because of the elastic design, it is possible to realize a catheter that allows various movements in small spaces like capillaries.

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

NASA Astrophysics Data System (ADS)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

Modelling of the mechanical behavior of a polyurethane finger interphalangeal joint endoprosthesis after surface modification by ion implantation

NASA Astrophysics Data System (ADS)

Beliaev, A.; Svistkov, A.; Iziumov, R.; Osorgina, I.; Kondyurin, A.; Bilek, M.; McKenzie, D.

2016-04-01

Production of biocompatible implants made of polyurethane treated with plasma is very perspective. During plasma treatment the surface of polyurethane acquires unique physic-chemical properties. However such treatment may change the mechanical properties of polyurethane which may adversely affect the deformation behaviour of the real implant. Therefore careful study of the mechanical properties of the plasma-modified polyurethane is needed. In this paper, experimental observations of the elastic characteristics of plasma treated polyurethane and modelling of the deformation behaviour of polyurethane bio-implants are reported.

CFD analysis of linear compressors considering load conditions

NASA Astrophysics Data System (ADS)

Bae, Sanghyun; Oh, Wonsik

2017-08-01

This paper is a study on computational fluid dynamics (CFD) analysis of linear compressor considering load conditions. In the conventional CFD analysis of the linear compressor, the load condition was not considered in the behaviour of the piston. In some papers, behaviour of piston is assumed as sinusoidal motion provided by user defined function (UDF). In the reciprocating type compressor, the stroke of the piston is restrained by the rod, while the stroke of the linear compressor is not restrained, and the stroke changes depending on the load condition. The greater the pressure difference between the discharge refrigerant and the suction refrigerant, the more the centre point of the stroke is pushed backward. And the behaviour of the piston is not a complete sine wave. For this reason, when the load condition changes in the CFD analysis of the linear compressor, it may happen that the ANSYS code is changed or unfortunately the modelling is changed. In addition, a separate analysis or calculation is required to find a stroke that meets the load condition, which may contain errors. In this study, the coupled mechanical equations and electrical equations are solved using the UDF, and the behaviour of the piston is solved considering the pressure difference across the piston. Using the above method, the stroke of the piston with respect to the motor specification of the analytical model can be calculated according to the input voltage, and the piston behaviour can be realized considering the thrust amount due to the pressure difference.

Effects of non-structural components and soil-structure interaction on the seismic response of framed structures

NASA Astrophysics Data System (ADS)

Ditommaso, Rocco; Auletta, Gianluca; Iacovino, Chiara; Nigro, Antonella; Carlo Ponzo, Felice

2017-04-01

In this paper, several nonlinear numerical models of reinforced concrete framed structures have been defined in order to evaluate the effects of non-structural elements and soil-structure interaction on the elastic dynamic behaviour of buildings. In the last few years, many and various studies have highlighted the significant effects derived from the interaction between structural and non-structural components on the main dynamic characteristics of a building. Usually, structural and non-structural elements act together, adding both masses and stiffness. The presence of infill panels is generally neglected in the design process of structural elements, although these elements can significantly increase the lateral stiffness of a structure leading to a modification in the dynamic properties. Particularly, at the Damage Limit State (where an elastic behaviour is expected), soil-structure interaction effects and non-structural elements may further affect the elastic natural period of buildings, changing the spectral accelerations compared with those provided by seismic codes in case of static analyses. In this work, a parametric study has been performed in order to evaluate the elastic fundamental period of vibration of buildings as a function of structural morphology (height, plan area, ratio between plan dimensions), infills presence and distribution and soil characteristics. Acknowledgements This study was partially funded by the Italian Department of Civil Protection within the project DPC-RELUIS 2016 - RS4 ''Seismic observatory of structures and health monitoring'' and by the "Centre of Integrated Geomorphology for the Mediterranean Area - CGIAM" within the Framework Agreement with the University of Basilicata "Study, Research and Experimentation in the Field of Analysis and Monitoring of Seismic Vulnerability of Strategic and Relevant Buildings for the purposes of Civil Protection and Development of Innovative Strategies of Seismic Reinforcement".

The anisotropic nature of the human vocal fold: an ex vivo study.

PubMed

Rohlfs, Anna-Katharina; Goodyer, Eric; Clauditz, Till; Hess, Markus; Kob, Malte; Koops, Susan; Püschel, Klaus; Roemer, Frank W; Müller, Frank

2013-05-01

The purpose of this study was to measure the relationship between the shear elastic properties of vocal fold with respect to the direction of applied stress. There is extensive published material that quantifies the shear viscoelastic properties of the vocal fold, but as much of these data were obtained using rotating parallel plate rheometers, which are unable to resolve out difference of the shear elastic behaviour with respect to direction, there is very little data that indicates anisotropic behaviour. To overcome this gap in knowledge, the team devised an apparatus that is capable of applying a shear stress in a known direction. A series of measurements were taken at the mid-membranous position, in the transverse and longitudinal directions. Point-specific measurements were performed using fourteen human cadaver excised larynges, which were hemi-sectioned to expose the vocal fold. An extremely low sinusoidal shear force of 1 g was applied tangentially to the membrane surface in both the longitudinal and transverse direction, and the resultant shear strain was measured. With the probe applied to the intact vocal fold, the average ratio of the elasticity in the transverse with respect to the longitudinal direction was 0.55. Further investigation using histological staining of collagens in the lamina propria indicates that there is a visible difference in the general alignment of collagen fibres when comparing the coronal and the sagittal sections. Our conclusion is that there is a quantifiable difference between the shear elastic response of the lamina propria in the longitudinal and transverse directions, and that this could be explained by the difference in alignment of collagen fibres within the lamina propria.

Structural, electronic and elastic properties of heavy fermion YbRh2 Laves phase compound

NASA Astrophysics Data System (ADS)

Pawar, Harsha; Shugani, Mani; Aynyas, Mahendra; Sanyal, Sankar P.

2018-05-01

The structural, electronic and elastic properties of YbRh2 Laves phase intermetallic compound which crystallize in cubic (MgCu2-type) structure have been investigated using ab-initio full potential linearized augmented plane wave (FP- LAPW) method with LDA and LDA+U approximation. The calculated ground state properties such as lattice parameter (a0), bulk modulus (B) and its pressure derivative (B') are in good agreement with available experimental and theoretical data. The electronic properties are analyzed from band structures and density of states. Elastic constants are predicted first time for this compound which obeys the stability criteria for cubic system.

Identification and control of structures in space

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Quinn, R. D.; Norris, M. A.

1984-01-01

The derivation of the equations of motion for the Spacecraft Control Laboratory Experiment (SCOLE) is reported and the equations of motion of a similar structure orbiting the earth are also derived. The structure is assumed to undergo large rigid-body maneuvers and small elastic deformations. A perturbation approach is proposed whereby the quantities defining the rigid-body maneuver are assumed to be relatively large, with the elastic deformations and deviations from the rigid-body maneuver being relatively small. The perturbation equations have the form of linear equations with time-dependent coefficients. An active control technique can then be formulated to permit maneuvering of the spacecraft and simultaneously suppressing the elastic vibration.

The effect of carbon concentration and plastic deformation on ultrasonic higher order elastic properties of steel

NASA Technical Reports Server (NTRS)

Heyman, J. S.; Allison, S. G.; Salama, K.

1985-01-01

The behavior of higher order elastic properties, which are much more sensitive to material state than are second order properties, has been studied for steel alloys AISI 1016, 1045, 1095, and 8620 by measuring the stress derivative of the acoustic natural velocity to determine the stress acoustic constants (SAC's). Results of these tests show a 20 percent linear variation of SAC's with carbon content as well as even larger variations with prestrain (plastic deformation). The use of higher order elastic characterization permits quantitative evaluation of solids and may prove useful in studies of fatigue and fracture.

Hands-on Force Spectroscopy: Weird Springs and Protein Folding

ERIC Educational Resources Information Center

Euler, Manfred

2008-01-01

A force spectroscopy model experiment is presented using a low-cost tensile apparatus described earlier. Force-extension measurements of twisted rubber bands are obtained. They exhibit a complex nonlinear elastic behaviour that resembles atomic force spectroscopy investigations of molecules of titin, a muscle protein. The model experiments open up…

Euler Teaches a Class in Structural Steel Design

ERIC Educational Resources Information Center

Boyajian, David M.

2009-01-01

Even before steel was a topic of formal study for structural engineers, the brilliant eighteenth century Swiss mathematician and physicist, Leonhard Euler (1707-1783), investigated the theory governing the elastic behaviour of columns, the results of which are incorporated into the American Institute of Steel Construction's (AISC's) Bible: the…

Pre-melting Behaviour in fcc Metals

NASA Astrophysics Data System (ADS)

Pamato, M. G.; Wood, I. G.; Dobson, D. P.; Hunt, S.; Vocadlo, L.

2016-12-01

Although the Earth's core is accepted to be made of an iron-nickel alloy with a few percent of light elements, its exact structure and composition are still unknown. Seismological and mineralogical models in the Earth's inner core do not agree, with mineralogical models derived from ab initiocalculations predicting shear-wave velocities up to 30% greater than seismically observed values. Recent computer simulations revealed that such difference may be explained by a dramatic, non-linear, softening of the elastic constants of Fe prior to melting. Up to date, computer calculations are the only result on pre-melting of direct applicability to the Earth's core and it is essential to systematically investigate such phenomena at inner core pressures and temperatures. Measuring the pressure dependence of pre-melting effects at such conditions and to the required precision is however extremely challenging. Also, pre-melting effects have been observed or suggested to occur in other materials, particularly noble metals, which exhibit large departures from linearity (modulus defects) at elevated temperatures. The aim of this study is to investigate to what extent pre-melting behaviour occurs in the physical properties of other metals at more experimentally tractable conditions. In particular, we report measurements of density and thermal expansion coefficients of both pure and alloyed gold (Au) up to their melting points. Au is an ideal test material since it crystallises in a simple monatomic face-centred structure and has a relatively low melting temperature. Precise measurements of unit cell lattice parameters were performed using a PANalytical X'Pert Pro powder diffractometer, equipped with an incident beam monochromator (giving very high resolution diffraction patterns) and with environmental stages covering the range from 40 K to 1373 K, with a readily achievable temperature resolution of 1K. We will discuss the circumstances under which pre-melting occurs, its mechanism(s), the effect of impurities and defects in the solid, and the consequences of pre-melting in the Earth's core.

Effect of large deformation and surface stiffening on the transmission of a line load on a neo-Hookean half space.

PubMed

Wu, Haibin; Liu, Zezhou; Jagota, Anand; Hui, Chung-Yuen

2018-03-07

A line force acting on a soft elastic solid, say due to the surface tension of a liquid drop, can cause significant deformation and the formation of a kink close to the point of force application. Analysis based on linearized elasticity theory shows that sufficiently close to its point of application, the force is borne entirely by the surface stress, not by the elasticity of the substrate; this local balance of three forces is called Neumann's triangle. However, it is not difficult to imagine realistic properties for which this force balance cannot be satisfied. For example, if the line force corresponds to surface tension of water, the numerical values of (unstretched) solid-vapor and solid-liquid surface stresses can easily be such that their sum is insufficient to balance the applied force. In such cases conventional (or naïve) Neumann's triangle of surface forces must break down. Here we study how force balance is rescued from the breakdown of naïve Neumann's triangle by a combination of (a) large hyperelastic deformations of the underlying bulk solid, and (b) increase in surface stress due to surface elasticity (surface stiffening). For a surface with constant surface stress (no surface stiffening), we show that the linearized theory remains accurate if the applied force is less than about 1.3 times the solid surface stress. For a surface in which the surface stress increases linearly with the surface stretch, we find that the Neumann's triangle construction works well as long as we replace the constant surface stress in the naïve Neumann triangle by the actual surface stress underneath the line load.

Biomechanical properties of low back myofascial tissue in younger adult ankylosing spondylitis patients and matched healthy control subjects.

PubMed

White, Allison; Abbott, Hannah; Masi, Alfonse T; Henderson, Jacqueline; Nair, Kalyani

2018-06-06

Ankylosing spondylitis is a degenerative and inflammatory rheumatologic disorder that primarily affects the spine. Delayed diagnosis leads to debilitating spinal damage. This study examines biomechanical properties of non-contracting (resting) human lower lumbar myofascia in ankylosing spondylitis patients and matched healthy control subjects. Biomechanical properties of stiffness, frequency, decrement, stress relaxation time, and creep were quantified from 24 ankylosing spondylitis patients (19 male, 5 female) and 24 age- and sex-matched control subjects in prone position on both sides initially and after 10 min rest. Concurrent surface electromyography measurements were performed to ensure resting state. Statistical analyses were conducted, and significance was set at p < 0.05. Decreased lumbar muscle elasticity (inverse of decrement) was primarily correlated with disease duration in ankylosing spondylitis subjects, whereas BMI was the primary correlate in control subjects. In ankylosing spondylitis and control groups, significant positive correlations were observed between the linear elastic properties of stiffness and frequency as well as between the viscoelastic parameters of stress relaxation time and creep. The preceding groups also showed significant negative correlations between the linear elastic and viscoelastic properties. Findings indicate that increased disease duration is associated with decreased tissue elasticity or myofascial degradation. Both ankylosing spondylitis and healthy subjects revealed similar correlations between the linear and viscoelastic properties which suggest that the disease does not directly alter their inherent interrelations. The novel results that stiffness is greater in AS than normal subjects, whereas decrement is significantly correlated with AS disease duration deserves further investigation of the biomechanical properties and their underlying mechanisms. Copyright © 2018 Elsevier Ltd. All rights reserved.

We should be using nonlinear indices when relating heart-rate dynamics to cognition and mood

PubMed Central

Young, Hayley; Benton, David

2015-01-01

Both heart rate (HR) and brain functioning involve the integrated output of a multitude of regulatory mechanisms, that are not quantified adequately by linear approximations such as means and standard deviations. It was therefore considered whether non-linear measures of HR complexity are more strongly associated with cognition and mood. Whilst resting, the inter-beat (R-R) time series of twenty-one males and twenty-four females were measured for five minutes. The data were summarised using time, frequency and nonlinear complexity measures. Attention, memory, reaction times, mood and cortisol levels were assessed. Nonlinear HR indices captured additional information, enabling a greater percentage of the variance in behaviour to be explained. On occasions non-linear indices were related to aspects for behaviour, for example focused attention and cortisol production, when time or frequency indices were not. These effects were sexually dimorphic with HR complexity being more strongly associated with the behaviour of females. It was concluded that nonlinear rather than linear methods of summarizing the HR times series offers a novel way of relating brain functioning and behaviour. It should be considered whether non-linear measures of HR complexity can be used as a biomarker of the integrated functioning of the brain. PMID:26565560

Simulation of Blast Loading on an Ultrastructurally-based Computational Model of the Ocular Lens

DTIC Science & Technology

2016-12-01

organelles. Additionally, the cell membranes demonstrated the classic ball-and-socket loops . For the SEM images, they were placed in two fixatives and mounted...considered (fibrous network and matrix), both components are modelled using a hyper - elastic framework, and the resulting constitutive model is embedded in a...within the framework of hyper - elasticity). Full details on the linearization procedures that were adopted in these previous models or the convergence

Asymptotic analysis of hierarchical martensitic microstructure

NASA Astrophysics Data System (ADS)

Cesana, Pierluigi; Porta, Marcel; Lookman, Turab

2014-12-01

We consider a hierarchical nested microstructure, which also contains a point of singularity (disclination) at the origin, observed in lead orthovanadate. We show how to exactly compute the energy cost and associated displacement field within linearized elasticity by enforcing geometric compatibility of strains across interfaces of the three-phase mixture of distortions (variants) in the microstructure. We prove that the mechanical deformation is purely elastic and discuss the behavior of the system close to the origin.

Finite-element modeling of magma chamber-host rock interactions prior to caldera collapse

NASA Astrophysics Data System (ADS)

Kabele, Petr; Žák, Jiří; Somr, Michael

2017-06-01

Gravity-driven failure of shallow magma chamber roofs and formation of collapse calderas are commonly accompanied by ejection of large volumes of pyroclastic material to the Earth's atmosphere and thus represent severe volcanic hazards. In this respect, numerical analysis has proven as a key tool in understanding the mechanical conditions of caldera collapse. The main objective of this paper is to find a suitable approach to finite-element simulation of roof fracturing and caldera collapse during inflation and subsequent deflation of shallow magma chambers. Such a model should capture the dominant mechanical phenomena, for example, interaction of the host rock with magma and progressive deformation of the chamber roof. To this end, a comparative study, which involves various representations of magma (inviscid fluid, nearly incompressible elastic, or plastic solid) and constitutive models of the host rock (fracture and plasticity), was carried out. In particular, the quasi-brittle fracture model of host rock reproduced well the formation of tension-induced radial and circumferential fractures during magma injection into the chamber (inflation stage), especially at shallow crustal levels. Conversely, the Mohr-Coulomb shear criterion has shown to be more appropriate for greater depths. Subsequent magma withdrawal from the chamber (deflation stage) results in further damage or even collapse of the chamber roof. While most of the previous studies of caldera collapse rely on the elastic stress analysis, the proposed approach advances modeling of the process by incorporating non-linear failure phenomena and nearly incompressible behaviour of magma. This leads to a perhaps more realistic representation of the fracture processes preceding roof collapse and caldera formation.

Lapse-time-dependent coda-wave depth sensitivity to local velocity perturbations in 3-D heterogeneous elastic media

NASA Astrophysics Data System (ADS)

Obermann, Anne; Planès, Thomas; Hadziioannou, Céline; Campillo, Michel

2016-10-01

In the context of seismic monitoring, recent studies made successful use of seismic coda waves to locate medium changes on the horizontal plane. Locating the depth of the changes, however, remains a challenge. In this paper, we use 3-D wavefield simulations to address two problems: first, we evaluate the contribution of surface- and body-wave sensitivity to a change at depth. We introduce a thin layer with a perturbed velocity at different depths and measure the apparent relative velocity changes due to this layer at different times in the coda and for different degrees of heterogeneity of the model. We show that the depth sensitivity can be modelled as a linear combination of body- and surface-wave sensitivity. The lapse-time-dependent sensitivity ratio of body waves and surface waves can be used to build 3-D sensitivity kernels for imaging purposes. Second, we compare the lapse-time behaviour in the presence of a perturbation in horizontal and vertical slabs to address, for instance, the origin of the velocity changes detected after large earthquakes.

Investigation of aquifer-system compaction in the Hueco basin, El Paso, Texas, USA

USGS Publications Warehouse

Heywood, Charles

1995-01-01

The Pleistocene geologic history of the Rio Grande valley in the Hueco basin included a cycle of sediment erosion and re-aggradation, resulting in unconformable stratification of sediment of contrasting compressibility and stress history. Since the 1950s large groundwater withdrawals have resulted in significant water-level declines and associated land subsidence. Knowledge of the magnitude and variation of specific storage is needed for developing predictive models of subsidence and groundwater flow simulations. Analyses of piezometric and extensometric data in the form of stress-strain diagrams from a 16 month period yield in situ measurements of aquifer-system compressibility across two discrete aquifer intervals. The linear elastic behaviour of the deeper interval indicates over-consolidation of basin deposits, probably resulting from deeper burial depth before the middle Pleistocene. By contrast, the shallow aquifer system displays an inelastic component, suggesting pre-consolidation stress not significantly greater than current effective stress levels for a sequence of late Pleistocene clay. Harmonic analyses of the piezometric response to earth tides in two water-level piezometers provide an independent estimate of specific storage of aquifer sands.

Realistic Features in Analysing the Effect of the Seismic Motion upon Localized Structures Considering Base Isolation Influence on Their Dynamic Behaviour

NASA Astrophysics Data System (ADS)

Apostol, Bogdan Felix; Florin Balan, Stefan; Ionescu, Constantin

2017-12-01

The effects of the earthquakes on buildings and the concept of seismic base isolation are investigated by using the model of the vibrating bar embedded at one end. The normal modes and the eigenfrequencies of the bar are highlighted and the amplification of the response due to the excitation of the normal modes (eigenmodes) is computed. The effect is much enhanced at resonance, for oscillating shocks which contain eigenfrequencies of the bar. Also, the response of two linearly joined bars with one end embedded is calculated. It is shown that for very different elastic properties the eigenfrequencies are due mainly to the “softer” bar. The effect of the base isolation in seismic structural engineering is assessed by formulating the model of coupled harmonic oscillators, as a simplified model for the structure building-foundation viewed as two coupled vibrating bars. The coupling decreases the lower eigenfrequencies of the structure and increases the higher ones. Similar amplification factors are derived for coupled oscillators at resonance with an oscillating shock.

Muscle-driven finite element simulation of human foot movements.

PubMed

Spyrou, L A; Aravas, N

2012-01-01

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.

Using the Seismic Amplitude Decay of Low-Frequency Events to Constrain Magma Properties.

NASA Astrophysics Data System (ADS)

Smith, P. J.; Neuberg, J. W.

2007-12-01

Low-frequency events are considered a key part of volcanic monitoring, as they are one of the few tools available that can link surface observations directly to internal volcanic processes and properties. Our model for their generation on the Soufrière Hills Volcano, Montserrat, is brittle fracturing of the magma at the conduit walls, providing the seismic trigger mechanism, followed by conduit resonance. The attenuation of seismic waves in a viscous magma is highly dependent on the properties of the attenuating material, in particular the viscous friction, controlled by the melt viscosity, gas content and diffusivity. Therefore we can use the seismicity to gain information on these magma properties. This research uses a two-dimensional viscoelastic finite-difference model, with the attenuative behaviour of the magma parameterised by an array of Standard Linear Solids. By examining the relationship between the amplitude decay of the synthetic low-frequency events, the intrinsic attenuation and the elastic parameter contrast, this research aims to link observables such as amplitude decay of the coda directly to properties such as the magma viscosity.

Analysis of Foundation of Tall R/C Chimney Incorporating Flexibility of Soil

NASA Astrophysics Data System (ADS)

Jayalekshmi, B. R.; Jisha, S. V.; Shivashankar, R.

2017-09-01

Three dimensional Finite Element (FE) analysis was carried out for 100 and 400 m high R/C chimneys having piled annular raft and annular raft foundations considering the flexibility of soil subjected to across-wind load. Stiffness of supporting soil and foundation were varied to evaluate the significance of Soil-Structure Interaction (SSI). The integrated chimney-foundation-soil system was analysed by finite element software ANSYS based on direct method of SSI assuming linear elastic material behaviour. FE analyses were carried out for two cases of SSI namely, (1) chimney with annular raft foundation and (2) chimney with piled annular raft foundation. The responses in raft such as bending moments and settlements were evaluated for both the cases and compared to those obtained from the conventional method of analysis of annular raft foundation. It is found that the responses in raft vary considerably depending on the stiffness of the underlying soil and the stiffness of foundation. Piled raft foundations are better suited for tall chimneys to be constructed in loose or medium sand.

Critical and post-critical behaviour of two-degree-of-freedom flutter-based generators

NASA Astrophysics Data System (ADS)

Pigolotti, Luca; Mannini, Claudio; Bartoli, Gianni; Thiele, Klaus

2017-09-01

Energy harvesting from flow-induced vibrations is a recent research field, which considers a diverse range of systems, among which two-degree-of-freedom flutter-based solutions were individuated as good candidates to obtain high energy performance. In the present work, numerical linear analyses and wind-tunnel tests were conducted on a flat-plate sectional model. The aim is to identify some design guidelines for generators exploiting the classical-flutter instability, through the investigation of the critical condition and the response during the post-critical regime. Many sets of governing parameters of interest from the energy-harvesting point of view were considered, including high levels of heaving damping to simulate the operation of a conversion apparatus. In particular, eccentricity of the elastic centre and small downstream mass unbalance can be introduced as solutions aiming at optimal operative ranges. The collected results suggest the high potentiality of flutter-based generators, and a significant enhancement of performance can be envisaged. Moreover, they contribute to improve the knowledge of the flutter excitation mechanism and to widen the dataset of measurements in the post-critical regime.

A new method for the visualization and quantification of internal skin elasticity by ultrasound imaging.

PubMed

Osanai, Osamu; Ohtsuka, Mayumi; Hotta, Mitsuyuki; Kitaharai, Takashi; Takema, Yoshinori

2011-08-01

Skin elasticity has been assessed previously only in the surface layer. We developed a new method that uses tissue strain imaging (TSI) technology, and the aim of this study was to test this new method to assess internal skin elasticity. Using a pressure device with a 12 MHz ultrasound transducer, constant and linear compressions were applied to the cheek skin of 35 volunteers (aged: 20-60 years). The elasticity of each layer (dermis, subcutaneous and muscle) was measured and analyzed using the TSI application software incorporated into the Toshiba Aplio(™) XV ultrasound system. A skin tissue-equivalent phantom, which is a block of material with the acoustic velocity (1530 m/s) of human skin, was collaboratively developed by OST Inc. This phantom was placed between the skin and the transducer as a reference material. Skin elasticity was clearly visualized and quantified in each layer of the skin. Age-dependent decreases in elasticity were determined in all layers of the skin. Among the three internal skin layers, the highest elasticity was determined in the subcutaneous layer followed by the muscle layer. These findings support the validity and sensitivity of the TSI method to assess the elasticity of various layers of skin. © 2011 John Wiley & Sons A/S.

Inverse finite element methods for extracting elastic-poroviscoelastic properties of cartilage and other soft tissues from indentation

NASA Astrophysics Data System (ADS)

Namani, Ravi

Mechanical properties are essential for understanding diseases that afflict various soft tissues, such as osteoarthritic cartilage and hypertension which alters cardiovascular arteries. Although the linear elastic modulus is routinely measured for hard materials, standard methods are not available for extracting the nonlinear elastic, linear elastic and time-dependent properties of soft tissues. Consequently, the focus of this work is to develop indentation methods for soft biological tissues; since analytical solutions are not available for the general context, finite element simulations are used. First, parametric studies of finite indentation of hyperelastic layers are performed to examine if indentation has the potential to identify nonlinear elastic behavior. To answer this, spherical, flat-ended conical and cylindrical tips are examined and the influence of thickness is exploited. Also the influence of the specimen/substrate boundary condition (slip or non-slip) is clarified. Second, a new inverse method---the hyperelastic extraction algorithm (HPE)---was developed to extract two nonlinear elastic parameters from the indentation force-depth data, which is the basic measurement in an indentation test. The accuracy of the extracted parameters and the influence of noise in measurements on this accuracy were obtained. This showed that the standard Berkovitch tip could only extract one parameter with sufficient accuracy, since the indentation force-depth curve has limited sensitivity to both nonlinear elastic parameters. Third, indentation methods for testing tissues from small animals were explored. New methods for flat-ended conical tips are derived. These account for practical test issues like the difficulty in locating the surface or soft specimens. Also, finite element simulations are explored to elucidate the influence of specimen curvature on the indentation force-depth curve. Fourth, the influence of inhomogeneity and material anisotropy on the extracted "average" linear elastic modulus was studied. The focus here is on murine tibial cartilage, since recent experiments have shown that the modulus measured by a 15 mum tip is considerably larger than that obtained from a 90 mum tip. It is shown that a depth-dependent modulus could give rise to such a size effect. Lastly, parametric studies were performed within the small strain setting to understand the influence of permeability and viscoelastic properties on the indentation stress-relaxation response. The focus here is on cartilage, and specific test protocols (single-step vs. multi-step stress relaxation) are explored. An inverse algorithm was developed to extract the poroviscoelastic parameters. A sensitivity study using this algorithm shows that the instantaneous elastic modulus (which is a measure of the viscous relaxation) can be extracted with very good accuracy, but the permeability and long-time relaxation constant cannot be extracted with good accuracy. The thesis concludes with implications of these studies. The potential and limitations of indentation tests for studying cartilage and other soft tissues is discussed.

Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1986-01-01

The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.

A novel pressure variation study on electronic structure, mechanical stability and thermodynamic properties of potassium based fluoroperovskite

NASA Astrophysics Data System (ADS)

Erum, Nazia; Azhar Iqbal, Muhammad

2017-09-01

The effect of pressure variation on stability, structural parameters, elastic constants, mechanical, electronic and thermodynamic properties of cubic SrKF3 fluoroperovskite have been investigated by using the full-potential linearized augmented plane wave (FP-LAPW) method combined with Quasi-harmonic Debye model in which the phonon effects are considered. The calculated lattice parameters show a prominent decrease in lattice constant and bonds length with the increase in pressure. The application of pressure from 0 to 25 GPa reveals a predominant characteristic associated with widening of bandgap with GGA and GGA plus Tran-Blaha modified Becke-Johnson (TB-mBJ) potential. The influence of pressure on elastic constants and their related mechanical parameters have been discussed in detail. Apart of linear dependence of elastic coefficients, transition from brittle to ductile behavior is also observed at elevated pressure ranges. We have successfully computed variation of lattice constant, volume expansion, bulk modulus, Debye temperature and specific heat capacities at pressure and temperature in the range of 0-25 GPa and 0-600 K.

On the Opening of Thick Walled Elastic Tubes: A Fluid-Structure Model for Acid Reflux

NASA Astrophysics Data System (ADS)

Ghosh, Sudip; Kahrilas, Peter

2005-11-01

A coupled fluid-structure mathematical model was developed to quantify rapid opening of thick-walled elastic tubes, a phenomenon underlying biological flows such as gastroesophageal reflux disease (GERD). The wall was modeled using non-linear finite deformation theory to predict space-time radial distention of an axisymmetric tube with luminal fluid flow. Anisotropic azimuthal and longitudinal muscle-induced stresses were incorporated, and interstitial material properties were assumed isotropic and linearly elastic. Fluid flow was modeled using lubrication theory with inertial correction. Opening and flow were driven by a specified inflow pressure and zero pressure gradient was specified at outflow. No-slip and surface force balance were applied at the fluid-wall interface. Viscoelasticity was modeled with ad hoc damping and the evolution of the tube geometry was predicted at mid-layer. A potentially important discovery was made when applied to studies of initiation of opening with GERD: while material stiffness is of minor consequence, small changes in resting lumen distension (˜2 mm diameter) may be a sensitive distinguishing feature of the disease.

Process Modelling of Curing Process-Induced Internal Stress and Deformation of Composite Laminate Structure with Elastic and Viscoelastic Models

NASA Astrophysics Data System (ADS)

Li, Dongna; Li, Xudong; Dai, Jianfeng

2018-06-01

In this paper, two kinds of transient models, the viscoelastic model and the linear elastic model, are established to analyze the curing deformation of the thermosetting resin composites, and are calculated by COMSOL Multiphysics software. The two models consider the complicated coupling between physical and chemical changes during curing process of the composites and the time-variant characteristic of material performance parameters. Subsequently, the two proposed models are implemented respectively in a three-dimensional composite laminate structure, and a simple and convenient method of local coordinate system is used to calculate the development of residual stresses, curing shrinkage and curing deformation for the composite laminate. Researches show that the temperature, degree of curing (DOC) and residual stresses during curing process are consistent with the study in literature, so the curing shrinkage and curing deformation obtained on these basis have a certain referential value. Compared the differences between the two numerical results, it indicates that the residual stress and deformation calculated by the viscoelastic model are more close to the reference value than the linear elastic model.

Lattice dynamic properties of Rh2XAl (X=Fe and Y) alloys

NASA Astrophysics Data System (ADS)

Al, Selgin; Arikan, Nihat; Demir, Süleyman; Iyigör, Ahmet

2018-02-01

The electronic band structure, elastic and vibrational spectra of Rh2FeAl and Rh2YAl alloys were computed in detail by employing an ab-initio pseudopotential method and a linear-response technique based on the density-functional theory (DFT) scheme within a generalized gradient approximation (GGA). Computed lattice constants, bulk modulus and elastic constants were compared. Rh2YAl exhibited higher ability to resist volume change than Rh2FeAl. The elastic constants, shear modulus, Young modulus, Poisson's ratio, B/G ratio electronic band structure, total and partial density of states, and total magnetic moment of alloys were also presented. Rh2FeAl showed spin up and spin down states whereas Rh2YAl showed none due to being non-magnetic. The calculated total densities of states for both materials suggest that both alloys are metallic in nature. Full phonon spectra of Rh2FeAl and Rh2YA1 alloys in the L21 phase were collected using the ab-initio linear response method. The obtained phonon frequencies were in the positive region indicating that both alloys are dynamically stable.

Exploring the remarkable limits of continuum elastic theory to understand the nanomechanics of viruses

NASA Astrophysics Data System (ADS)

Roos, Wouter; Gibbons, Melissa; Klug, William; Wuite, Gijs

2009-03-01

We report nanoindentation experiments by atomic force microscopy on capsids of the Hepatitis B Virus (HBV). HBV is investigated because its capsids can form in either a smaller T=3 or a bigger T=4 configuration, making it an ideal system to test the predictive power of continuum elastic theory to describe nanometre-sized objects. It is shown that for small, consecutive indentations the particles behave reversibly linear and no material fatigue occurs. For larger indentations the particles start to deform non-linearly. The experimental force response fits very well with finite element simulations on coarse grained models of HBV capsids. Furthermore, this also fits with thin shell simulations guided by the F"oppl- von K'arm'an (FvK) number (the dimensionless ratio of stretching and bending stiffness of a thin shell). Both the T=3 and T=4 morphology are very well described by the simulations and the capsid material turns out to have the same Young's modulus, as expected. The presented results demonstrate the surprising strength of continuum elastic theory to describe indentation of viral capsids.

Buckling delamination of the circular sandwich plate with piezoelectric face and elastic core layers under rotationally symmetric external pressure

NASA Astrophysics Data System (ADS)

Akbarov, Surkay D.; Cafarova, Fazile I.; Yahnioglu, Nazmiye

2017-02-01

The axisymmetric buckling delamination of the piezoelectric circular sandwich plate with piezoelectric face and elastic (metal) core layers around the interface penny-shaped cracks is investigated. The case is considered where short-circuit conditions with respect to the electrical potential on the upper and lower and also lateral surfaces of face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. Solution to the considered nonlinear problem is reduced to solution of the series boundary value problems derived by applying the linearization procedure with respect to small imperfection of the sought values. Numerical results reveal the effect of piezoelectricity as well as geometrical and material parameters on the critical values are determined numerically by employing finite element method (FEM).

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

NASA Astrophysics Data System (ADS)

Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.

2017-07-01

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

Significance of third-order elasticity for determination of the pressure coefficient of the light emission in strained quantum wells

NASA Astrophysics Data System (ADS)

Łepkowski, S. P.

2008-10-01

We investigate the contribution arising from third-order elasticity to the pressure coefficient of the light emission (dEE/dP) in strained zinc-blende InGaAs/GaAs and InGaN/GaN quantum wells (QWs) grown in a (001) direction. In the framework of the third-order elasticity theory, we develop a model of pressure tuning of strains in these structures, which is then used to determine the coefficient dEE/dP . In the calculations of dEE/dP , we use a consistent set of the second- and third-order elastic constants which has been obtained from ab initio calculations. Our results indicate that the usage of third-order elasticity leads to significant reduction in dEE/dP in strained (001)-oriented InGaAs/GaAs and InGaN/GaN QWs, in comparison to the values of dEE/dP obtained by using the linear theory of elasticity. In the case of InGaAs/GaAs QWs, the values of dEE/dP calculated using third-order elasticity are in reasonable agreement with experimental data. For InGaN/GaN QWs, better agreement between theoretical and experimental values of dEE/dP is obtained when instead of third-order elasticity, pressure dependence of the second-order elastic constants is taken into account.

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

Design, Optimization and Evaluation of Integrally Stiffened Al 7050 Panel with Curved Stiffeners

NASA Technical Reports Server (NTRS)

Slemp, Wesley C. H.; Bird, R. Keith; Kapania, Rakesh K.; Havens, David; Norris, Ashley; Olliffe, Robert

2011-01-01

A curvilinear stiffened panel was designed, manufactured, and tested in the Combined Load Test Fixture at NASA Langley Research Center. The panel was optimized for minimum mass subjected to constraints on buckling load, yielding, and crippling or local stiffener failure using a new analysis tool named EBF3PanelOpt. The panel was designed for a combined compression-shear loading configuration that is a realistic load case for a typical aircraft wing panel. The panel was loaded beyond buckling and strains and out-of-plane displacements were measured. The experimental data were compared with the strains and out-of-plane deflections from a high fidelity nonlinear finite element analysis and linear elastic finite element analysis of the panel/test-fixture assembly. The numerical results indicated that the panel buckled at the linearly elastic buckling eigenvalue predicted for the panel/test-fixture assembly. The experimental strains prior to buckling compared well with both the linear and nonlinear finite element model.

Identification of internal properties of fibers and micro-swimmers

NASA Astrophysics Data System (ADS)

Plouraboue, Franck; Thiam, Ibrahima; Delmotte, Blaise; Climent, Eric; PSC Collaboration

2016-11-01

In this presentation we discuss the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibers or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibers, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalised velocities from computing contact forces. This linear formulation then permits to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for elastic parameters as well as active ones in the presence of Langevin-like forcing with Gaussian noise using normal linear regression models and maximum likelihood method. These theoretical results are illustrated in various configurations of relaxed or actuated passives fibers, and active filament of known passive properties, showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.

Inelastic strain analogy for piecewise linear computation of creep residues in built-up structures

NASA Technical Reports Server (NTRS)

Jenkins, Jerald M.

1987-01-01

An analogy between inelastic strains caused by temperature and those caused by creep is presented in terms of isotropic elasticity. It is shown how the theoretical aspects can be blended with existing finite-element computer programs to exact a piecewise linear solution. The creep effect is determined by using the thermal stress computational approach, if appropriate alterations are made to the thermal expansion of the individual elements. The overall transient solution is achieved by consecutive piecewise linear iterations. The total residue caused by creep is obtained by accumulating creep residues for each iteration and then resubmitting the total residues for each element as an equivalent input. A typical creep law is tested for incremental time convergence. The results indicate that the approach is practical, with a valid indication of the extent of creep after approximately 20 hr of incremental time. The general analogy between body forces and inelastic strain gradients is discussed with respect to how an inelastic problem can be worked as an elastic problem.

Experimental and Computational Investigation of Viscoelasticity of Native and Engineered Ligament and Tendon

NASA Astrophysics Data System (ADS)

Ma, J.; Narayanan, H.; Garikipati, K.; Grosh, K.; Arruda, E. M.

The important mechanisms by which soft collagenous tissues such as ligament and tendon respond to mechanical deformation include non-linear elasticity, viscoelasticity and poroelasticity. These contributions to the mechanical response are modulated by the content and morphology of structural proteins such as type I collagen and elastin, other molecules such as glycosaminoglycans, and fluid. Our ligament and tendon constructs, engineered from either primary cells or bone marrow stromal cells and their autogenous matricies, exhibit histological and mechanical characteristics of native tissues of different levels of maturity. In order to establish whether the constructs have optimal mechanical function for implantation and utility for regenerative medicine, constitutive relationships for the constructs and native tissues at different developmental levels must be established. A micromechanical model incorporating viscoelastic collagen and non-linear elastic elastin is used to describe the non-linear viscoelastic response of our homogeneous engineered constructs in vitro. This model is incorporated within a finite element framework to examine the heterogeneity of the mechanical responses of native ligament and tendon.

Viscoelastic behaviour of cold recycled asphalt mixes

NASA Astrophysics Data System (ADS)

Cizkova, Zuzana; Suda, Jan

2017-09-01

Behaviour of cold recycled mixes depends strongly on both the bituminous binder content (bituminous emulsion or foamed bitumen) and the hydraulic binder content (usually cement). In the case of cold recycled mixes rich in bitumen and with low hydraulic binder content, behaviour is close to the viscoelastic behaviour of traditional hot mix asphalt. With decreasing bituminous binder content together with increasing hydraulic binder content, mixes are characteristic with brittle behaviour, typical for concrete pavements or hydraulically bound layers. The behaviour of cold recycled mixes with low content of both types of binders is similar to behaviour of unbound materials. This paper is dedicated to analysing of the viscoelastic behaviour of the cold recycled mixes. Therefore, the tested mixes contained higher amount of the bituminous binder (both foamed bitumen and bituminous emulsion). The best way to characterize any viscoelastic material in a wide range of temperatures and frequencies is through the master curves. This paper includes interesting findings concerning the dependency of both parts of the complex modulus (elastic and viscous) on the testing frequency (which simulates the speed of heavy traffic passing) and on the testing temperature (which simulates the changing climate conditions a real pavement is subjected to).

Functional similarities in the mechanical design of the aorta in lower vertebrates and mammals.

PubMed

Gibbons, C A; Shadwick, R E

1989-12-01

The mechanical properties of the aorta from the toad Bufo marinus, the lizard Gekko gecko and the garter snake Thamnophis radix were compared to those of the rat, by inflation of vessel segments in vitro. The arteries of the lower vertebrates, like those of mammals, were compliant, highly resilient, and non-linearly elastic. The elastic modulus of the artery wall was similar in the lower vertebrates and mammals, at their respective mean physiological pressures. We conclude that the aorta in each of these animals is suitably designed to function effectively as an elastic pulse smoothing component in the circulation; differences in the pressure wave transmission characteristics of lower vertebrates and mammals do not result from dissimilarities in arterial elastic properties, but from substantial differences in heart rate of these two groups.

Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

NASA Technical Reports Server (NTRS)

Wu, R. W.; Witmer, E. A.

1972-01-01

Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

Mathematical modeling of aeroelastic systems

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.

2017-12-01

In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at a subsonic flow and the mathematical models of protective surface at a supersonic flow are considered. Models are described by the related systems of the partial differential equations. An analytic investigation of stability is carried out on the basis of the construction of Lyapunov-type functionals, a numerical investigation is carried out on the basis of the Galerkin method. The various models of the gas-liquid environment (compressed, incompressible) and the various models of a deformable body (elastic linear and elastic nonlinear) are considered.

Buckling of a stiff thin film on an elastic graded compliant substrate.

PubMed

Chen, Zhou; Chen, Weiqiu; Song, Jizhou

2017-12-01

The buckling of a stiff film on a compliant substrate has attracted much attention due to its wide applications such as thin-film metrology, surface patterning and stretchable electronics. An analytical model is established for the buckling of a stiff thin film on a semi-infinite elastic graded compliant substrate subjected to in-plane compression. The critical compressive strain and buckling wavelength for the sinusoidal mode are obtained analytically for the case with the substrate modulus decaying exponentially. The rigorous finite element analysis (FEA) is performed to validate the analytical model and investigate the postbuckling behaviour of the system. The critical buckling strain for the period-doubling mode is obtained numerically. The influences of various material parameters on the results are investigated. These results are helpful to provide physical insights on the buckling of elastic graded substrate-supported thin film.

Hexadecapolar Colloids

DOE PAGES

Senyuk, Bohdan; Puls, Owen; Tovkach, Oleh M.; ...

2016-02-11

Outermost occupied electron shells of chemical elements can have symmetries resembling that of monopoles, dipoles, quadrupoles and octupoles corresponding to filled s-, p-, d- and forbitals. Theoretically, elements with hexadecapolar outer shells could also exist, but none of the known elements have filled g-orbitals. On the other hand, the research paradigm of ‘colloidal atoms’ displays complexity of particle behaviour exceeding that of atomic counterparts, which is driven by DNA functionalization, geometric shape and topology and weak external stimuli. We describe elastic hexadecapoles formed by polymer microspheres dispersed in a liquid crystal, a nematic fluid of orientationally ordered molecular rods. Becausemore » of conically degenerate boundary conditions, the solid microspheres locally perturb the alignment of the nematic host, inducing hexadecapolar distortions that drive anisotropic colloidal interactions. We uncover physical underpinnings of formation of colloidal elastic hexadecapoles and report the ensuing bonding inaccessible to elastic dipoles, quadrupoles and other nematic colloids studied previously.« less

Experimental study of turbulent structures over hairy poro-elastic surfaces

NASA Astrophysics Data System (ADS)

Couliou, Marie; Hansson, Jonas; van der Wijngaart, Wouter; Lundell, Fredrik; Bagheri, Shervin

2016-11-01

Flows over slender, deformable and dense structures are ubiquitous in both nature and technological applications, ranging from the atmospheric flow over trees to the flow over the over the skin of organisms. In order to create a fundamental understanding of how poro-elatic surface can be used for flow control purposes, our work focuses on the behaviour of wall-bounded turbulent flows over fibrous poro-elastic surfaces. We fabricate the coatings using Off-Stoichiometry-Thiolene-Epoxy (OSTE+) polymers and multidirectional UV-lithography which enables us to design arrays of flexible pillars with various geometrical parameters (aspect ratio, pitch, inclinaison, etc.). We assess the effects of these coatings on an overlying low-Reynolds number turbulent flow using a water-table facility and PIV measurements. In particular, we focus on the modification of near wall turbulent structures in both space and time due to the presence of the poro-elastic coatings.

Buckling of a stiff thin film on an elastic graded compliant substrate

NASA Astrophysics Data System (ADS)

Chen, Zhou; Chen, Weiqiu; Song, Jizhou

2017-12-01

The buckling of a stiff film on a compliant substrate has attracted much attention due to its wide applications such as thin-film metrology, surface patterning and stretchable electronics. An analytical model is established for the buckling of a stiff thin film on a semi-infinite elastic graded compliant substrate subjected to in-plane compression. The critical compressive strain and buckling wavelength for the sinusoidal mode are obtained analytically for the case with the substrate modulus decaying exponentially. The rigorous finite element analysis (FEA) is performed to validate the analytical model and investigate the postbuckling behaviour of the system. The critical buckling strain for the period-doubling mode is obtained numerically. The influences of various material parameters on the results are investigated. These results are helpful to provide physical insights on the buckling of elastic graded substrate-supported thin film.

Structure-property relations of orthorhombic [(CH3)3NCH2COO]2(CuCl2)3 · 2H2 O

NASA Astrophysics Data System (ADS)

Haussühl, Eiken; Schreuer, Jürgen; Wiehl, Leonore; Paulsen, Natalia

2014-04-01

Large single crystals of orthorhombic [(CH3)3NCH2COO]2(CuCl2)3 · 2H2 O with dimensions up to 40×40×30 mm3 were grown from aqueous solutions. The elastic and piezoelastic coefficients were derived from ultrasonic resonance frequencies and their shifts upon variation of pressure, respectively, using the plate-resonance technique. Additionally, the coefficients of thermal expansion were determined between 95 K and 305 K by dilatometry. The elastic behaviour at ambient conditions is dominated by the 2-dimensional network of strong hydrogen bonds within the (001) plane leading to a corresponding pseudo-tetragonal anisotropy of the longitudinal elastic stiffness. The variation of elastic properties with pressure, however, as well as the thermal expansion shows strong deviations from the pseudo-tetragonal symmetry. These deviations are probably correlated with tilts of the elongated tri-nuclear betaine-CuCl2-water complexes. Neither the thermal expansion nor the specific heat capacity gives any hint on a phase transition in the investigated temperature range.

Stress transmission through a model system of cohesionless elastic grains

NASA Astrophysics Data System (ADS)

Da Silva, Miguel; Rajchenbach, Jean

2000-08-01

Understanding the mechanical properties of granular materials is important for applications in civil and chemical engineering, geophysical sciences and the food industry, as well as for the control or prevention of avalanches and landslides. Unlike continuous media, granular materials lack cohesion, and cannot resist tensile stresses. Current descriptions of the mechanical properties of collections of cohesionless grains have relied either on elasto-plastic models classically used in civil engineering, or on a recent model involving hyperbolic equations. The former models suggest that collections of elastic grains submitted to a compressive load will behave elastically. Here we present the results of an experiment on a two-dimensional model system-made of discrete square cells submitted to a point load-in which the region in which the stress is confined is photoelastically visualized as a parabola. These results, which can be interpreted within a statistical framework, demonstrate that the collective response of the pile contradicts the standard elastic predictions and supports a diffusive description of stress transmission. We expect that these findings will be applicable to problems in soil mechanics, such as the behaviour of cohesionless soils or sand piles.

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.

1996-01-01

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

Closed-form solution for Eshelby's elliptic inclusion in antiplane elasticity using complex variable

NASA Astrophysics Data System (ADS)

Chen, Y. Z.

2013-12-01

This paper provides a closed-form solution for the Eshelby's elliptic inclusion in antiplane elasticity. In the formulation, the prescribed eigenstarins are not only for the uniform distribution, but also for the linear form. After using the complex variable and the conformal mapping, the continuation condition for the traction and displacement along the interface in the physical plane can be reduced to a condition along the unit circle. The relevant complex potentials defined in the inclusion and the matrix can be separated from the continuation conditions of the traction and displacement along the interface. The expressions of the real strains and stresses in the inclusion from the assumed eigenstrains are presented. Results for the case of linear distribution of eigenstrain are first obtained in the paper.

Sensitivity of inelastic response to numerical integration of strain energy. [for cantilever beam

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1976-01-01

The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.

Observing (non)linear lattice dynamics in graphite by ultrafast Kikuchi diffraction

PubMed Central

Liang, Wenxi; Vanacore, Giovanni M.; Zewail, Ahmed H.

2014-01-01

In materials, the nature of the strain–stress relationship, which is fundamental to their properties, is determined by both the linear and nonlinear elastic responses. Whereas the linear response can be measured by various techniques, the nonlinear behavior is nontrivial to probe and to reveal its nature. Here, we report the methodology of time-resolved Kikuchi diffraction for mapping the (non)linear elastic response of nanoscale graphite following an ultrafast, impulsive strain excitation. It is found that the longitudinal wave propagating along the c-axis exhibits echoes with a frequency of 9.1 GHz, which indicates the reflections of strain between the two surfaces of the material with a speed of ∼4 km/s. Because Kikuchi diffraction enables the probing of strain in the transverse direction, we also observed a higher-frequency mode at 75.5 GHz, which has a relatively long lifetime, on the order of milliseconds. The fluence dependence and the polarization properties of this nonlinear mode are entirely different from those of the linear, longitudinal mode, and here we suggest a localized breather motion in the a-b plane as the origin of the nonlinear shear dynamics. The approach presented in this contribution has the potential for a wide range of applications because most crystalline materials exhibit Kikuchi diffraction. PMID:24706785

A Focused Fundamental Study of Predicting Materials Degradation & Fatigue. Volume 1

DTIC Science & Technology

1997-05-31

physical properties are: bulk modulus, shear strength, coefficient of friction, modulus of elasticity/ rigidity and Poisson’s ratio. Each of these physical...acting on a subsurface crack when abrasive motion occurs on the surface using linear elastic fracture mechanics theory. Both mechanisms involve a...The body of the scattering 5 cell was a 4-way Swagelok*(Crawford Fitting Co., Solon, OH) connector with a 1.5 mm hole drilled in the top for

Dependence of laser radiation intensity on the elastic deformation of a revolving optical disk with a reflective coating

NASA Astrophysics Data System (ADS)

Gladyshev, V. O.; Portnov, D. I.

2016-12-01

The physical mechanism of alteration of intensity of linearly polarized monochromatic electromagnetic radiation with λ = 630 nm in a revolving dielectric disk with a mirror coating is examined. The effect is induced by elastic deformation due to the revolution and by thermoelastic deformation of the optically transparent disk. These deformations result in birefringence, the polarization plane rotation, and a 30-40% change in the intensity of reflected radiation.

Density and mechanical properties of calcium aluminate cement

NASA Astrophysics Data System (ADS)

Ahmed, Syed Taqi Uddin; Ahmmad, Shaik Kareem

2018-04-01

Calcium aluminate cements are a special type of cements which have their composition mainly dominated by the presence of Monocalcium Aluminates. In the present paper for the first time we have shown theoretical density and elastic constants for various calcium aluminate cements. The density of the present CAS decrease with aluminates presents in the cement. Using the density data, the elastic moduli namely Young's modulus, bulk and shear modulus show strong linear dependence as a function of compositional parameter.

Effect of Emplacement Material Properties on Chemical Explosion Spectra - Preliminary Analysis Using Synthetic Waveforms Near Elastic Radii

NASA Astrophysics Data System (ADS)

Saikia, C. K.; Ezzedine, S. M.; Vorobiev, O.; Antoun, T.; Woods, M. T.

2017-12-01

The focus of this study is to investigate the effect of the non-linear material properties on synthetic waveforms at receivers located within the elastic region near the non-linear zone around energetic chemical explosions. The primary goal is to characterize the effect of porosity and joint properties. The joint sizes are typically small compared with the wavelength represented by the computational grid, so the calculations become time consuming to properly represent the fidelity of the calculations. In this study, we use GEODYN-L Lagrangian code, where the joints are included explicitly. We simulate a suite of synthetics for chemical explosions in granite, and varying the porosity and joint orientation. Using the generated synthetic waveforms in the elastic region, we calculate displacement spectra and compare them with homogenous medium solutions (i.e., free of porosity and joints). We are attempting to develop a set of correction factors necessary to apply in various field (emplacement) conditions so that the spectral characteristics can be compared to those predicted by the Mueller-Murphy (MM, 1971; Saikia, 2017) and other source functions (Denny and Johnson, 1991; Ford and Walter, 2013) near the elastic radii. Future investigations will include similar analysis for the nuclear explosions. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Passive and active ventricular elastances of the left ventricle

PubMed Central

Zhong, Liang; Ghista, Dhanjoo N; Ng, Eddie YK; Lim, Soo T

2005-01-01

Background Description of the heart as a pump has been dominated by models based on elastance and compliance. Here, we are presenting a somewhat new concept of time-varying passive and active elastance. The mathematical basis of time-varying elastance of the ventricle is presented. We have defined elastance in terms of the relationship between ventricular pressure and volume, as: dP = EdV + VdE, where E includes passive (Ep) and active (Ea) elastance. By incorporating this concept in left ventricular (LV) models to simulate filling and systolic phases, we have obtained the time-varying expression for Ea and the LV-volume dependent expression for Ep. Methods and Results Using the patient's catheterization-ventriculogram data, the values of passive and active elastance are computed. Ea is expressed as: ; Epis represented as: . Ea is deemed to represent a measure of LV contractility. Hence, Peak dP/dt and ejection fraction (EF) are computed from the monitored data and used as the traditional measures of LV contractility. When our computed peak active elastance (Ea,max) is compared against these traditional indices by linear regression, a high degree of correlation is obtained. As regards Ep, it constitutes a volume-dependent stiffness property of the LV, and is deemed to represent resistance-to-filling. Conclusions Passive and active ventricular elastance formulae can be evaluated from a single-beat P-V data by means of a simple-to-apply LV model. The active elastance (Ea) can be used to characterize the ventricle's contractile state, while passive elastance (Ep) can represent a measure of resistance-to-filling. PMID:15707494

Effects of guided breath exercise on complex behaviour of heart rate dynamics.

PubMed

Tavares, Bruna S; de Paula Vidigal, Giovanna; Garner, David M; Raimundo, Rodrigo D; de Abreu, Luiz Carlos; Valenti, Vitor E

2017-11-01

Cardiac autonomic regulation is influenced by changes in respiratory rate, which has been demonstrated by linear analysis of heart rate variability (HRV). Conversely, the complex behaviour is not well defined for HRV during this physiological state. In this sense, Higuchi Fractal Dimension is applied directly to the time series. It analyses the fractal dimension of discrete time sequences and is simpler and faster than correlation dimension and many other classical measures derived from chaos theory. We investigated chaotic behaviour of heart rate dynamics during guided breath exercises. We investigated 21 healthy male volunteers aged between 18 and 30 years. HRV was analysed 10 min before and 10 min during guided breath exercises. HRV was analysed in the time and frequency domain for linear analysis and through HFD for non-linear analysis. Linear analysis indicated that SDNN, pNN50, RMSSD, LF, HF and LF/HF increased during guided breath exercises. HFD analysis illustrated that between K max 20 to K max 120 intervals, was enhanced during guided breath exercises. Guided breath exercises acutely increased chaotic behaviour of HRV measured by HFD. © 2016 Scandinavian Society of Clinical Physiology and Nuclear Medicine. Published by John Wiley & Sons Ltd.

A mechanical characterisation on multiple timescales of electroconductive magnetorheological elastomers

NASA Astrophysics Data System (ADS)

Schümann, M.; Morich, J.; Kaufhold, T.; Böhm, V.; Zimmermann, K.; Odenbach, S.

2018-05-01

Magnetorheological elastomers are a type of smart hybrid material which combines elastic properties of a soft elastomer matrix with magnetic properties of magnetic micro particles. This leads to a material with magnetically controllable mechanical properties of which the magnetorheological effect is the best known. The addition of electroconductive particles to the polymer mix adds electrical properties to the material behaviour. The resulting electrical resistance of the sample can be manipulated by external magnetic fields and mechanical loads. This results in a distinct interplay of mechanical, electrical and magnetic effects with a highly complex time behaviour. In this paper a mechanical characterisation on multiple time scales was conducted to get an insight on the short and long-term electrical and mechanical behaviour of this novel material. The results show a complex resistivity behaviour on several timescales, sensitive to magnetic fields and strain velocity. The observed material exhibits fatigue and relaxation behaviour, whereas the magnetorheological effect appears not to interfere with the piezoresistive properties.

Effects on behaviour and rein tension on horses ridden with or without martingales and rein inserts.

PubMed

Heleski, C R; McGreevy, P D; Kaiser, L J; Lavagnino, M; Tans, E; Bello, N; Clayton, H M

2009-07-01

Unsteady hand position can cause discomfort to the horse, potentially leading to conflict behaviours (CB) such as head tossing or tail lashing. Some instructors feel that martingales or elastic rein inserts can reduce discomfort caused by inexperienced and unsteady hands. Others consider these devices to be inappropriate 'crutches'. Four horses and nine riders were tested under three conditions in random order: plain reins, adjustable training martingales (TM), and elasticised rein inserts (RI). Rein-tension data (7s) and behavioural data (30s) were collected in each direction. Rein-tension data were collected via strain-gauge transducers. Behavioural data were assessed using an ethogram of defined behaviours. No differences in the number of CB were observed. Mean rein tension for TM was higher than that of RI or controls. Relative to the withers, the head was lower for horses ridden with martingales. Carefully fitted martingales may have a place in riding schools that teach novices.

Evaluation of the confusion matrix method in the validation of an automated system for measuring feeding behaviour of cattle.

PubMed

Ruuska, Salla; Hämäläinen, Wilhelmiina; Kajava, Sari; Mughal, Mikaela; Matilainen, Pekka; Mononen, Jaakko

2018-03-01

The aim of the present study was to evaluate empirically confusion matrices in device validation. We compared the confusion matrix method to linear regression and error indices in the validation of a device measuring feeding behaviour of dairy cattle. In addition, we studied how to extract additional information on classification errors with confusion probabilities. The data consisted of 12 h behaviour measurements from five dairy cows; feeding and other behaviour were detected simultaneously with a device and from video recordings. The resulting 216 000 pairs of classifications were used to construct confusion matrices and calculate performance measures. In addition, hourly durations of each behaviour were calculated and the accuracy of measurements was evaluated with linear regression and error indices. All three validation methods agreed when the behaviour was detected very accurately or inaccurately. Otherwise, in the intermediate cases, the confusion matrix method and error indices produced relatively concordant results, but the linear regression method often disagreed with them. Our study supports the use of confusion matrix analysis in validation since it is robust to any data distribution and type of relationship, it makes a stringent evaluation of validity, and it offers extra information on the type and sources of errors. Copyright © 2018 Elsevier B.V. All rights reserved.

Comparison between layering NbSe2 and rod characteristic of MgB2 by investigation of elastic constants

NASA Astrophysics Data System (ADS)

Shokri, Asiye; Yazdani, Ahmad; Barakati, Behrad

2018-03-01

The delicate balancing of strong anisotropy on strength of hybridisation resulted to CDW- order “TCDW=33K” and finally emerging superconductivity at “Tc = 7.2K” are the most intriguing question in characteristic behaviour of NbSe2. On other hand, the original mechanism of MgB2 old superconductor, which has unlike the cuprates a lower anisotropy on strength hybridisation is still unknown. We believe this could result to bond exchange and larger coherence length of the grain boundary to current. Since the cause and the mechanism of band strengths of two original layering and rod structures are consequence of bond- rupturing-atomic displacement, here the stability of crystalline structure of inter atomic potential through the elasticity-compressibility is investigated. Consequently, in order to clear out the strong difference between the layering NbSe2 and domination of rod-character of MgB2 the stability of both crystal structures through the cohesive energy c/a, czz and c33 are investigated. The proposed investigations are more evident on different characteristic behaviour of calculated parameters.

Closed-form solutions in stress-driven two-phase integral elasticity for bending of functionally graded nano-beams

NASA Astrophysics Data System (ADS)

Barretta, Raffaele; Fabbrocino, Francesco; Luciano, Raimondo; Sciarra, Francesco Marotti de

2018-03-01

Strain-driven and stress-driven integral elasticity models are formulated for the analysis of the structural behaviour of fuctionally graded nano-beams. An innovative stress-driven two-phases constitutive mixture defined by a convex combination of local and nonlocal phases is presented. The analysis reveals that the Eringen strain-driven fully nonlocal model cannot be used in Structural Mechanics since it is ill-posed and the local-nonlocal mixtures based on the Eringen integral model partially resolve the ill-posedeness of the model. In fact, a singular behaviour of continuous nano-structures appears if the local fraction tends to vanish so that the ill-posedness of the Eringen integral model is not eliminated. On the contrary, local-nonlocal mixtures based on the stress-driven theory are mathematically and mechanically appropriate for nanosystems. Exact solutions of inflected functionally graded nanobeams of technical interest are established by adopting the new local-nonlocal mixture stress-driven integral relation. Effectiveness of the new nonlocal approach is tested by comparing the contributed results with the ones corresponding to the mixture Eringen theory.

Elastic-Plastic Behaviour of Ultrasonic Assisted Compression of Polyvinyl Chloride (PVC) Foam

NASA Astrophysics Data System (ADS)

Muhalim, N. A. D.; Hassan, M. Z.; Daud, Y.

2018-04-01

The present study aims to investigate the elastic-plastic behaviour of ultrasonic assisted compression of PVC closed-cell foam. A series of static and ultrasonic compression test of PVC closed-cell foam were conducted at a constant cross head speed of 30 mm/min on dry surface condition. For quasi-static test, specimen was compressed between two rigid platens using universal testing machine. In order to evaluate the specimen behavior under ultrasonic condition, specimen was placed between a specifically design double-slotted block horn and rigid platen. The horn was designed and fabricated prior to the test as a medium to transmit the ultrasonic vibration from the ultrasonic transducer to the working specimen. It was tuned to a frequency of 19.89 kHz in longitudinal mode and provided an average oscillation amplitude at 6 µm on the uppermost surface. Following, the characteristics of stress-strain curves for quasi-static and ultrasonic compression tests were analyzed. It was found that the compressive stress was significantly reduced at the onset of superimposed ultrasonic vibration during plastic deformation.

Elastodynamic metasurface: Depolarization of mechanical waves and time effects

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

Boutin, Claude, E-mail: claude.boutin@entpe.fr; Schwan, Logan; Dietz, Matthew S.

2015-02-14

We report the concept of microstructured surfaces with inner resonance in the field of elastodynamics, so-called elastodynamic metasurfaces. Such metasurfaces allow for wavefield manipulation of mechanical waves by tuning the boundary conditions at specific frequencies. In particular, they can be used to depolarize elastic waves without introducing heterogeneities in the medium itself; the physical means to do so in homogeneous elastic media used to remain, surprisingly, an open question while depolarization is commonplace in electromagnetism. The principle relies on the anisotropic behaviour of a subwavelength array of resonators: Their subwavelength configuration confines the Bragg interferences scattered by resonators into amore » boundary layer. The effective behaviour of the resonating array is expressed with homogenization as an unconventional impedance, the frequency-dependence, and anisotropy of which lead to depolarization and time effects. The concept of the elastodynamic metasurface is tested experimentally and results bear testament to its efficacy and robustness. Elastodynamic metasurfaces are easily realized and analytically predictable, opening new possibilities in tomography techniques, ultrasonics, geophysics, vibration control, materials and structure design.« less

Structural, Electronic and Elastic Properties of Heavy Fermion YbTM2 (TM= Ir and Pt) Laves Phase Compounds

NASA Astrophysics Data System (ADS)

Pawar, H.; Shugani, M.; Aynyas, M.; Sanyal, S. P.

2018-02-01

The structural, electronic and elastic properties of YbTM2 (TM = Ir and Pt) Laves phase intermetallic compounds which crystallize in cubic (MgCu2-type) structure, have been investigated using ab-initio full potential linearized augmented plane wave (FP-LAPW) method with LDA and LDA+U approximation. The calculated ground state properties such as lattice parameter (a0), bulk modulus (B) and its pressure derivative (B‧) are in good agreement with available experimental and theoretical data. The electronic properties are analyzed from band structures and density of states. Elastic constants are predicted first time for these compounds which obey the stability criteria for cubic system.

Ab-initio thermodynamic and elastic properties of AlNi and AlNi3 intermetallic compounds

NASA Astrophysics Data System (ADS)

Yalameha, Shahram; Vaez, Aminollah

2018-04-01

In this paper, thermodynamic and elastic properties of the AlNi and AlNi3 were investigated using density functional theory (DFT). The full-potential linearized augmented plane-wave (APW) in the framework of the generalized gradient approximation as used as implemented in the Wien2k package. The temperature dependence of thermal expansion coefficient, bulk modulus and heat capacity in a wide range of temperature (0-1600 K) were investigated. The calculated elastic properties of the compounds show that both intermetallic compounds of AlNi and AlNi3 have surprisingly negative Poisson’s ratio (NPR). The results were compared with other experimental and computational data.

Hypo-Elastic Model for Lung Parenchyma

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

Freed, Alan D.; Einstein, Daniel R.

2012-03-01

A simple elastic isotropic constitutive model for the spongy tissue in lung is derived from the theory of hypoelasticity. The model is shown to exhibit a pressure dependent behavior that has been interpreted by some as indicating extensional anisotropy. In contrast, we show that this behavior arises natural from an analysis of isotropic hypoelastic invariants, and is a likely result of non-linearity, not anisotropy. The response of the model is determined analytically for several boundary value problems used for material characterization. These responses give insight into both the material behavior as well as admissible bounds on parameters. The model ismore » characterized against published experimental data for dog lung. Future work includes non-elastic model behavior.« less

Behaviour study of thick laminated composites: Experimentation and finite element analyses

NASA Astrophysics Data System (ADS)

Duchaine, Francois

In today's industries, it is common practice to utilize composite materials in very large and thick structures like bridge decks, high pressure vessels, wind turbine blades and aircraft parts to mention a few. Composite materials are highly favoured due to their physical characteristics: low weight, low cost, adaptable mechanical properties, high specific strength and stiffness. The use of composite materials for large structures has however raised several concerns in the prediction of the behaviour of thick laminated composite parts. A lack of knowledge and experience in the use of composite materials during the design, sizing and manufacturing of thick composite parts can lead to catastrophic events. In this thesis, it was supposed that the elastic material properties may vary with the laminate thickness. In order to measure the influence of the thickness on nine orthotropic elastic material properties (E1, E2, E3, nu12, nu 13, nu23, G12, G13 and G23), three categories of thickness have been defined using a comparison between the classical lamination theory (CLT), different beam theories and a numerical 3D solid finite element analysis (FEA) model. The defined categories are: thin laminates for thicknesses below 6 mm (0.236"), moderately thick laminates for thicknesses up to 16 mm (0.630") and thick laminates for thicknesses above 16 mm (0.630"). For three different thicknesses (thin -- 1.5 mm, moderately thick -- 10 mm and thick -- 20 mm), the influence of the thickness on the orthotropic elastic material properties of unidirectional (UD) fibreglass/epoxy laminates has been measured. A torsion test on rectangular bar is also proposed to measure the influence of the thickness on G13 and G23. The nine elastic material properties, in function of the thickness, have been used in CLT and 3D solid FEA model in order to predict the axial Young's modulus and Poisson's ratios of cross-ply and quasi-isotropic laminates. Experimental results have also been obtained for those laminates. The analysis of test results with CLT and FEA showed that the variation of elastic material properties with the thickness is not significant for in-plane problems. On the other hand, a substantial influence has been highlighted on UD elastic material properties driven by the matrix like E 2, E3, nu13 and G12. .

Price elasticity of tobacco products among economic classes in India, 2011–2012

PubMed Central

Selvaraj, Sakthivel; Srivastava, Swati; Karan, Anup

2015-01-01

Objectives The objectives of this study are to: (1) examine the pattern of price elasticity of three major tobacco products (bidi, cigarette and leaf tobacco) by economic groups of population based on household monthly per capita consumption expenditure in India and (2) assess the effect of tax increases on tobacco consumption and revenue across expenditure groups. Setting Data from the 2011–2012 nationally representative Consumer Expenditure Survey from 101 662 Indian households were used. Participants Households which consumed any tobacco or alcohol product were retained in final models. Primary outcome measures The study draws theoretical frameworks from a model using the augmented utility function of consumer behaviour, with a two-stage two-equation system of unit values and budget shares. Primary outcome measures were price elasticity of demand for different tobacco products for three hierarchical economic groups of population and change in tax revenue due to changes in tax structure. We finally estimated price elasticity of demand for bidi, cigarette and leaf tobacco and effects of changes in their tax rates on demand for these tobacco products and tax revenue. Results Own price elasticities for bidi were highest in the poorest group (−0.4328) and lowest in the richest group (−0.0815). Cigarette own price elasticities were −0.832 in the poorest group and −0.2645 in the richest group. Leaf tobacco elasticities were highest in the poorest (−0.557) and middle (−0.4537) groups. Conclusions Poorer group elasticities were the highest, indicating that poorer consumers are more price responsive. Elasticity estimates show positive distributional effects of uniform bidi and cigarette taxation on the poorest consumers, as their consumption is affected the most due to increases in taxation. Leaf tobacco also displayed moderate elasticities in poor and middle tertiles, suggesting that tax increases may result in a trade-off between consumption decline and revenue generation. A broad spectrum rise in tax rates across all products is critical for tobacco control. PMID:26656009

The stability of cassette walls in compression

NASA Astrophysics Data System (ADS)

Voutay, Pierre-Arnaud

Much research into the behaviour of cold formed steel columns in the last decade has focused on channel sections undergoing local, distortional and overall buckling. Light gauge steel cassette sections are a particular form of channel section which offers an alternative form of load-bearing wall assembly for use in low-rise steel framed construction. Cassette wall sections possess wide and slender flanges so that, by including intermediate stiffeners in these wide flanges, a significant increase in the ultimate load capacity may be achieved. However, the introduction of intermediate stiffeners also increases the number of buckling modes (stiffener buckling) and, therefore complicates the behaviour and increases the risk of interactive buckling between these modes. The work undertaken in this thesis aims to clarify the behaviour of wide flanges in compression with and without intermediate stiffeners. In this research, the distortional mode of web and narrow flange buckling was inhibited by connecting the narrow flanges of the cassettes together at suitable intervals. "Generalised Beam Theory" (GBT), which allows the individual buckling modes to be considered individually and in predetermined combinations, provides a particularly good tool with which to analyse and understand the buckling behaviour of cassette sections with and without intermediate stiffeners. "Generalised Beam Theory" (GBT) is used throughout this work to determine the elastic buckling stress of the sections studied (simply supported stiffened plates, as well as cassette sections). Since the economic design of cold-formed steel sections requires the consideration of post- buckling behaviour, elastic buckling values are not directly comparable with design code values which are usually based on the concept of effective width. Therefore, finite element analysis with both material and geometric nonlinearity has also been carried out in order to obtain the ultimate strength in the critical mode or mode combination. Firstly the results of experimental test are analysed and their behaviour reproduced numerically. This serves to explain the test results and verify the numerical model. Confidence in modelling non-linear instability phenomena with the finite element method is acquired. Secondly, an initial parametric study was undertaken on the behaviour of cassette sections with and without intermediate stiffeners. This study considers the effect of the length and overall buckling on the behaviour of cassette sections, the effect of load eccentricity and the effect of the rotational restraint given by the web to the stiffened wide flange. A second parametric study including 96 specimens was undertaken next. This study considered the effect of the number (up to three intermediate stiffeners) and sizes of intermediate stiffeners on slender flanges with a slenderness ratio between 150 ≤ w/t ≤ 600. A wide range of geometries was studied covering single and interactive buckling modes. Comparison of the ultimate strength obtained from finite element analysis with the ultimate strength obtained using the effective width approach of modem design codes such as Eurocode 3 part 1.3 (1996) and NAS (North American specification (2001)) was then possible. By integrating the stress distribution over the length of the specimen, the stiffened wide flange can be isolated from the rest of the section (webs and narrow flanges). Design procedures tor plate elements incorporating one or two intermediate stiffeners under compressive load are given in Eurocode 3; Part 1.3. However, cassette sections, which have wider and more slender flanges than typical sheeting and decking, are increasingly being used in practical construction. For such cases, the design procedures in Eurocode 3 are less well founded. An improvement of the Eurocode 3 procedure dealing with intermediate stiffeners is proposed and validated for one, two or three stiffeners. Throughout the work, simple expressions suitable for design calculations are presented. Modern design codes as well as Direct Strength Method are evaluated in the light of findings of this work and wherever possible suggestions for improvements are made.

Cigarette Smoking in Indonesia: Examination of a Myopic Model of Addictive Behaviour

PubMed Central

Hidayat, Budi; Thabrany, Hasbullah

2010-01-01

Using aggregated panel data taken from three waves of the Indonesian Family Life Survey (1993–2000), this article tests the myopic addiction behaviour of cigarette demand. Sensitivity analysis is done by examining a rational addiction behavior of cigarette demand. The results provide support for myopic addiction. The short- and long-run price elasticities of cigarette demand are estimated at −0.28 and −0.73 respectively. Excise taxes are more likely to act as an effective tobacco control in the long-run rather than a major source of government revenue. PMID:20644684

[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.

Mechanical behaviour of cerclage material consisting of silicon rubber.

PubMed

Hinrichsen, G; Eberhardt, A; Springer, H

1979-09-01

Silicon rubber specimens of circular or rectangular cross-section (cross-section area between ca. 2 and 7 mm2) are used as cerclage bands. A series of commercial cerclage elements was investigated for mechanical characteristics, such as stress-strain behaviour and modulus of elasticity, using a tensile-testing machine. Large differences in these properties exist among the various specimens. Moreover, time-dependent effects, such as stress-relaxation, retardation, and creep, were analysed by the present investigations. One has to take into consideration that the initial length and stress of the cerclage band vary significantly with time after the operation.

Linear movement of plywood and flakeboards as related to the longitudinal movement of wood

Treesearch

B. G. Heebink; E. W. Kuenzi; A. C. Maki

1964-01-01

Veneer, plywood, and flakeboard specimens were subjected to various humidity conditions. Physical and elastic properties of the veneer were determined and the influence of these properties on the movement of plywood and flakeboards fabricated of like material was evaluated, The linear movement of the plywood and flakeboards was closely related to the longitudinal-to-...

Mechanisms Inducing Jet Rotation in Shear-Formed Shaped-Charge Liners.

DTIC Science & Technology

1990-03-01

of deviatoric strain, and compressibility affects only the equation of state , not the deviatoric stress /strain relation. An anisotropic formulation is...strains, a more accurate scalar equation of state should simultaneously be employed to account for non-linear compressibility effects . A4 A.3 Elastic... obtainable knowing the previous and present cycles’ average stress . However, many non-linear equations

Polymer concentration and properties of elastic turbulence in a von Karman swirling flow

NASA Astrophysics Data System (ADS)

Jun, Yonggun; Steinberg, Victor

2017-10-01

We report detailed experimental studies of statistical, scaling, and spectral properties of elastic turbulence (ET) in a von Karman swirling flow between rotating and stationary disks of polymer solutions in a wide, from dilute to semidilute entangled, range of polymer concentrations ϕ . The main message of the investigation is that the variation of ϕ just weakly modifies statistical, scaling, and spectral properties of ET in a swirling flow. The qualitative difference between dilute and semidilute unentangled versus semidilute entangled polymer solutions is found in the dependence of the critical Weissenberg number Wic of the elastic instability threshold on ϕ . The control parameter of the problem, the Weissenberg number Wi, is defined as the ratio of the nonlinear elastic stress to dissipation via linear stress relaxation and quantifies the degree of polymer stretching. The power-law scaling of the friction coefficient on Wi/Wic characterizes the ET regime with the exponent independent of ϕ . The torque Γ and pressure p power spectra show power-law decays with well-defined exponents, which has values independent of Wi and ϕ separately at 100 ≤ϕ ≤900 ppm and 1600 ≤ϕ ≤2300 ppm ranges. Another unexpected observation is the presence of two types of the boundary layers, horizontal and vertical, distinguished by their role in the energy pumping and dissipation, which has width dependence on Wi and ϕ differs drastically. In the case of the vertical boundary layer near the driving disk, wvv is independent of Wi/Wic and linearly decreases with ϕ /ϕ * , while in the case of the horizontal boundary layer wvh its width is independent of ϕ /ϕ * , linearly decreases with Wi/Wic , and is about five times smaller than wvv. Moreover, these Wi and ϕ dependencies of the vertical and horizontal boundary layer widths are found in accordance with the inverse turbulent intensity calculated inside the boundary layers Vθh/Vθh rms and Vθv/Vθv rms , respectively. Specifically, the dependence of Vθv/Vθv rms in the vertical boundary layer on Wi and ϕ agrees with a recent theoretical prediction [S. Belan, A. Chernych, and V. Lebedev, Boundary layer of elastic turbulence (unpublished)].

What Do Observations of Postseismic Deformation Tell us About the Rheology of the Lithoshpere?

NASA Astrophysics Data System (ADS)

Fialko, Y.

2006-12-01

Geodetic observations in epicentral areas of large shallow earthquakes reveal transient displacements that typically have the same sense as the coseismic ones, but are about an order of magnitude smaller. A number of different mechanisms has been proposed to explain the observed time-dependent deformation, including afterslip on a deep extension of the seismic rupture, viscous-like response of a substrate below the brittle-ductile transition (e.g., the lower crust or upper mantle), and re-distribution of pore fluids in the upper crust. Distinguishing the relative contributions of these relaxation mechanisms is important before one can make robust inferences about the effective rheology of the upper part of the continental lithosphere. Either the bulk visco-elastic relaxation or afterslip is required to explain large horizontal displacements observed in the aftermath of large strike-slip earthquakes. Both temporal and spatial signatures of postseismic deformation were used to demonstrate that simple linear Maxwell rheologies are not adequate. For non-linear (e.g., powerlaw) rheologies, the surface deformation field may be indistinguishable from that due to afterslip at the early stages of relaxation, when the deformation is localized in high stress areas on the downdip continuation of the earthquake fault. However, at later stages of relaxation visco-elastic models predict appreciable changes in the displacement pattern. In particular, vertical velocities may change sign after viscous flow in the ductile substrate becomes more diffuse. Thus afterslip and non-linear visco-elastic models can be in principle distinguished given a sufficiently long observation period. Fluid flow and poro-elastic effects are incapable of explaining the observed horizontal deformation, but may substantially contribute to vertical postseismic motions, further complicating a discrimination between afterslip and visco-elastic relaxation. I will present space geodetic measurements of postseismic deformation due to several large earthquakes in California and Asia, and discuss implications from these measurements for the crust and upper mantle rheology. The main conclusion is that the deformation patterns are not consistent between different events, suggesting either various contributions from different relaxation mechanisms, or significant variations in crustal rheologies.

Automatic control: the vertebral column of dogfish sharks behaves as a continuously variable transmission with smoothly shifting functions.

PubMed

Porter, Marianne E; Ewoldt, Randy H; Long, John H

2016-09-15

During swimming in dogfish sharks, Squalus acanthias, both the intervertebral joints and the vertebral centra undergo significant strain. To investigate this system, unique among vertebrates, we cyclically bent isolated segments of 10 vertebrae and nine joints. For the first time in the biomechanics of fish vertebral columns, we simultaneously characterized non-linear elasticity and viscosity throughout the bending oscillation, extending recently proposed techniques for large-amplitude oscillatory shear (LAOS) characterization to large-amplitude oscillatory bending (LAOB). The vertebral column segments behave as non-linear viscoelastic springs. Elastic properties dominate for all frequencies and curvatures tested, increasing as either variable increases. Non-linearities within a bending cycle are most in evidence at the highest frequency, 2.0 Hz, and curvature, 5 m -1 Viscous bending properties are greatest at low frequencies and high curvatures, with non-linear effects occurring at all frequencies and curvatures. The range of mechanical behaviors includes that of springs and brakes, with smooth transitions between them that allow for continuously variable power transmission by the vertebral column to assist in the mechanics of undulatory propulsion. © 2016. Published by The Company of Biologists Ltd.

Finite element analysis of the design and manufacture of thin-walled pressure vessels used as aerosol cans

NASA Astrophysics Data System (ADS)

Abdussalam, Ragba Mohamed

Thin-walled cylinders are used extensively in the food packaging and cosmetics industries. The cost of material is a major contributor to the overall cost and so improvements in design and manufacturing processes are always being sought. Shape optimisation provides one method for such improvements. Aluminium aerosol cans are a particular form of thin-walled cylinder with a complex shape consisting of truncated cone top, parallel cylindrical section and inverted dome base. They are manufactured in one piece by a reverse-extrusion process, which produces a vessel with a variable thickness from 0.31 mm in the cylinder up to 1.31 mm in the base for a 53 mm diameter can. During manufacture, packaging and charging, they are subjected to pressure, axial and radial loads and design calculations are generally outside the British and American pressure vessel codes. 'Design-by-test' appears to be the favoured approach. However, a more rigorous approach is needed in order to optimise the designs. Finite element analysis (FEA) is a powerful tool for predicting stress, strain and displacement behaviour of components and structures. FEA is also used extensively to model manufacturing processes. In this study, elastic and elastic-plastic FEA has been used to develop a thorough understanding of the mechanisms of yielding, 'dome reversal' (an inherent safety feature, where the base suffers elastic-plastic buckling at a pressure below the burst pressure) and collapse due to internal pressure loading and how these are affected by geometry. It has also been used to study the buckling behaviour under compressive axial loading. Furthermore, numerical simulations of the extrusion process (in order to investigate the effects of tool geometry, friction coefficient and boundary conditions) have been undertaken. Experimental verification of the buckling and collapse behaviours has also been carried out and there is reasonable agreement between the experimental data and the numerical predictions.

Plastic deformation in nanoscale gold single crystals and open-celled nanoporous gold

NASA Astrophysics Data System (ADS)

Lee, Dongyun; Wei, Xiaoding; Zhao, Manhong; Chen, Xi; Jun, Seong C.; Hone, James; Kysar, Jeffrey W.

2007-01-01

The results of two sets of experiments to measure the elastic-plastic behaviour of gold at the nanometre length scale are reported. One set of experiments was on free-standing nanoscale single crystals of gold, and the other was on free-standing nanoscale specimens of open-celled nanoporous gold. Both types of specimens were fabricated from commercially available leaf which was either pure Au or a Au/Ag alloy following by dealloying of the Ag. Mechanical testing specimens of a 'dog-bone' shape were fabricated from the leaf using standard lithographic procedures after the leaf had been glued onto a silicon wafer. The thickness of the gauge portion of the specimens was about 100 nm, the width between 250 nm and 300 nm and the length 7 µm. The specimens were mechanically loaded with a nanoindenter (MTS) at the approximate midpoint of the gauge length. The resulting force-displacement curve of the single crystal gold was serrated and it was evident that slip localization occurred on individual slip systems; however, the early stages of the plastic deformation occurred in a non-localized manner. The results of detailed finite element analyses of the specimen suggest that the critical resolved shear stress of the gold single crystal was as high as 135 MPa which would lead to a maximum uniaxial stress of about 500 MPa after several per cent strain. The behaviour of the nanoporous gold was substantially different. It exhibited an apparent elastic behaviour until the point where it failed in an apparently brittle manner, although it is assumed that plastic deformation occurred in the ligaments prior to failure. The average elastic stiffness of three specimens was measured to be Enp = 8.8 GPa and the stress at ultimate failure averaged 190 MPa for the three specimens tested. Scaling arguments suggest that the stress in the individual ligaments could approach the theoretical shear strength. Presented at the IUTAM Symposium on Plasticity at the Micron Scale, Technical University of Denmark, Copenhagen, Denmark.

An instrument to measure mechanical up-conversion phenomena in metals in the elastic regime

NASA Astrophysics Data System (ADS)

Vajente, G.; Quintero, E. A.; Ni, X.; Arai, K.; Gustafson, E. K.; Robertson, N. A.; Sanchez, E. J.; Greer, J. R.; Adhikari, R. X.

2016-06-01

Crystalline materials, such as metals, are known to exhibit deviation from a simple linear relation between strain and stress when the latter exceeds the yield stress. In addition, it has been shown that metals respond to varying external stress in a discontinuous way in this regime, exhibiting discrete releases of energy. This crackling noise has been extensively studied both experimentally and theoretically when the metals are operating in the plastic regime. In our study, we focus on the behavior of metals in the elastic regime, where the stresses are well below the yield stress. We describe an instrument that aims to characterize non-linear mechanical noise in metals when stressed in the elastic regime. In macroscopic systems, this phenomenon is expected to manifest as a non-stationary noise modulated by external disturbances applied to the material, a form of mechanical up-conversion of noise. The main motivation for this work is for the case of maraging steel components (cantilevers and wires) in the suspension systems of terrestrial gravitational wave detectors. Such instruments are planned to reach very ambitious displacement sensitivities, and therefore mechanical noise in the cantilevers could prove to be a limiting factor for the detectors' final sensitivities, mainly due to non-linear up-conversion of low frequency residual seismic motion to the frequencies of interest for the gravitational wave observations. We describe here the experimental setup, with a target sensitivity of 10-15 m/ √{ Hz } in the frequency range of 10-1000 Hz, a simple phenomenological model of the non-linear mechanical noise, and the analysis method that is inspired by this model.

Rheological characterisation of gluten from triticale (x Triticosecale Wittmack).

PubMed

Pruska-Kędzior, Anna; Makowska, Agnieszka; Kędzior, Zenon; Salmanowicz, Bolesław P

2017-11-01

Triticale gluten still remains very poorly characterised rheologically. In this study the mechanical spectra of gluten isolated from four triticale cultivars were registered and fitted with Cole-Cole functions yielding the visco-elastic plateau parameters. Master spectra were calculated. A retardation test was performed and used to calculate the composite mechanical spectra and the width of visco-elastic plateau l. Protein fractional composition of triticale flour and gluten was studied using capillary zone electrophoresis. Differentiated HMW-GS/SS compositions were identified in the triticale cultivars studied. The rheological parameters reached the following values: J N 0 1.05·10 -3 to 2.69·10 -3 Pa -1 , G N 0 372 to 956 Pa, ω 0 0.003 to 0.06 rad s -1 , l 169 to 3121, J e 0 1.57·10 -3 to 5.03·10 -3 Pa -1 , G e 0 199 to 637 Pa and η 0 1.06·10 7 to 3.93·10 7 Pa s. Visco-elastic properties of triticale gluten correspond to the lower end of medium visco-elasticity shown by common wheat gluten. Master spectra and the composite mechanical spectra prove that four triticale glutens exhibit practically an identical type of visco-elastic behaviour of a biopolymeric visco-elastic liquid similar to wheat gluten. The visco-elastic plateau parameters G N 0 , J N 0 , ω 0 and l appeared significantly correlated with the contents of prolamins and secaloglutenins in triticale flours and glutens. © 2017 Society of Chemical Industry. © 2017 Society of Chemical Industry.

Why glass elasticity affects the thermodynamics and fragility of supercooled liquids

PubMed Central

Yan, Le; Düring, Gustavo; Wyart, Matthieu

2013-01-01

Supercooled liquids are characterized by their fragility: The slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure controls fragility remains a challenge. Surprisingly, experiments indicate that the linear elasticity of the glass—a purely local property of the free energy landscape—is a good predictor of fragility. In particular, materials presenting a large excess of soft elastic modes, the so-called boson peak, are strong. This is also the case for network liquids near the rigidity percolation, known to affect elasticity. Here we introduce a model of the glass transition based on the assumption that particles can organize locally into distinct configurations that are coupled spatially via elasticity. The model captures the mentioned observations connecting elasticity and fragility. We find that materials presenting an abundance of soft elastic modes have little elastic frustration: Energy is insensitive to most directions in phase space, leading to a small jump of specific heat. In this framework strong liquids turn out to lie the closest to a critical point associated with a rigidity or jamming transition, and their thermodynamic properties are related to the problem of number partitioning and to Hopfield nets in the limit of small memory. PMID:23576746

Why glass elasticity affects the thermodynamics and fragility of supercooled liquids.

PubMed

Yan, Le; Düring, Gustavo; Wyart, Matthieu

2013-04-16

Supercooled liquids are characterized by their fragility: The slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure controls fragility remains a challenge. Surprisingly, experiments indicate that the linear elasticity of the glass--a purely local property of the free energy landscape--is a good predictor of fragility. In particular, materials presenting a large excess of soft elastic modes, the so-called boson peak, are strong. This is also the case for network liquids near the rigidity percolation, known to affect elasticity. Here we introduce a model of the glass transition based on the assumption that particles can organize locally into distinct configurations that are coupled spatially via elasticity. The model captures the mentioned observations connecting elasticity and fragility. We find that materials presenting an abundance of soft elastic modes have little elastic frustration: Energy is insensitive to most directions in phase space, leading to a small jump of specific heat. In this framework strong liquids turn out to lie the closest to a critical point associated with a rigidity or jamming transition, and their thermodynamic properties are related to the problem of number partitioning and to Hopfield nets in the limit of small memory.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Mathematical modeling of spinning elastic bodies for modal analysis.

NASA Technical Reports Server (NTRS)

Likins, P. W.; Barbera, F. J.; Baddeley, V.

1973-01-01

The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

Non-invasive determination of the complete elastic moduli of spider silks

NASA Astrophysics Data System (ADS)

Koski, Kristie J.; Akhenblit, Paul; McKiernan, Keri; Yarger, Jeffery L.

2013-03-01

Spider silks possess nature’s most exceptional mechanical properties, with unrivalled extensibility and high tensile strength. Unfortunately, our understanding of silks is limited because the complete elastic response has never been measured—leaving a stark lack of essential fundamental information. Using non-invasive, non-destructive Brillouin light scattering, we obtain the entire stiffness tensors (revealing negative Poisson’s ratios), refractive indices, and longitudinal and transverse sound velocities for major and minor ampullate spider silks: Argiope aurantia, Latrodectus hesperus, Nephila clavipes, Peucetia viridans. These results completely quantify the linear elastic response for all possible deformation modes, information unobtainable with traditional stress-strain tests. For completeness, we apply the principles of Brillouin imaging to spatially map the elastic stiffnesses on a spider web without deforming or disrupting the web in a non-invasive, non-contact measurement, finding variation among discrete fibres, junctions and glue spots. Finally, we provide the stiffness changes that occur with supercontraction.

Dynamic elasticity measurement for prosthetic socket design.

PubMed

Kim, Yujin; Kim, Junghoon; Son, Hyeryon; Choi, Youngjin

2017-07-01

The paper proposes a novel apparatus to measure the dynamic elasticity of human limb in order to help the design and fabrication of the personalized prosthetic socket. To take measurements of the dynamic elasticity, the desired force generated as an exponential chirp signal in which the frequency increases and amplitude is maintained according to time progress is applied to human limb and then the skin deformation is recorded, ultimately, to obtain the frequency response of its elasticity. It is referred to as a Dynamic Elasticity Measurement Apparatus (DEMA) in the paper. It has three core components such as linear motor to provide the desired force, loadcell to implement the force feedback control, and potentiometer to record the skin deformation. After measuring the force/deformation and calculating the dynamic elasticity of the limb, it is visualized as 3D color map model of the limb so that the entire dynamic elasticity can be shown at a glance according to the locations and frequencies. For the visualization, the dynamic elasticities measured at specific locations and frequencies are embodied using the color map into 3D limb model acquired by using 3D scanner. To demonstrate the effectiveness, the visualized dynamic elasticities are suggested as outcome of the proposed system, although we do not have any opportunity to apply the proposed system to the amputees. Ultimately, it is expected that the proposed system can be utilized to design and fabricate the personalized prosthetic socket in order for releasing the wearing pain caused by the conventional prosthetic socket.

The Differentiation of Adaptive Behaviours: Evidence from High and Low Performers

ERIC Educational Resources Information Center

Kane, Harrison; Oakland, Thomas David

2015-01-01

Background: Professionals who use measures of adaptive behaviour when working with special populations may assume that adaptive behaviour is a consistent and linear construct at various ability levels and thus believe the construct of adaptive behaviour is the same for high and low performers. That is, highly adaptive people simply are assumed to…

Elasticity and critical bending moment of model colloidal aggregates.

PubMed

Pantina, John P; Furst, Eric M

2005-04-08

The bending mechanics of singly bonded colloidal aggregates are measured using laser tweezers. We find that the colloidal bonds are capable of supporting significant torques, providing a direct measurement of the tangential interactions between particles. A critical bending moment marks the limit of linear bending elasticity, past which small-scale rearrangements occur. These mechanical properties underlie the rheology and dynamics of colloidal gels formed by diffusion-limited cluster aggregation, and give critical insight into the contact interactions between Brownian particles.

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

NASA Astrophysics Data System (ADS)

Valášek, J.; Sváček, P.; Horáček, J.

2016-03-01

The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.

Property-Structure-Processing Relations in Polymeric Materials.

DTIC Science & Technology

1981-07-31

increase indefinitely without indicating actual yield value and R which is a measure of the elastic character of the fluid, approaches a limiting value...appears to increase indefinitely without indicating an- actual yield value and R, which is a measure of the elastic character of the fluid, approaches a...a linear graph when log r is plotted against log x; i.e., ,I has a x" behavior at low x. Since a 0 1, this does not correspond to the classical yield

Fatigue-Crack-Growth Structural Analysis

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.

1986-01-01

Elastic and plastic deformations calculated under variety of loading conditions. Prediction of fatigue-crack-growth lives made with FatigueCrack-Growth Structural Analysis (FASTRAN) computer program. As cyclic loads are applied to initial crack configuration, FASTRAN predicts crack length and other parameters until complete break occurs. Loads are tensile or compressive and of variable or constant amplitude. FASTRAN incorporates linear-elastic fracture mechanics with modifications of load-interaction effects caused by crack closure. FASTRAN considered research tool, because of lengthy calculation times. FASTRAN written in FORTRAN IV for batch execution.

Concentration Dependent Physical Properties of Ge1-xSnx Solid Solution

NASA Astrophysics Data System (ADS)

Jivani, A. R.; Jani, A. R.

2011-12-01

Our own proposed potential is used to investigate few physical properties like total energy, bulk modulus, pressure derivative of bulk modulus, elastic constants, pressure derivative of elastic constants, Poisson's ratio and Young's modulus of Ge1-xSnx solid solution with x is atomic concentration of α-Sn. The potential combines linear plus quadratic types of electron-ion interaction. First time screening function proposed by Sarkar et al is used to investigate the properties of the Ge-Sn solid solution system.

Is the time-dependent behaviour of the aortic valve intrinsically quasi-linear?

NASA Astrophysics Data System (ADS)

Anssari-Benam, Afshin

2014-05-01

The widely popular quasi-linear viscoelasticity (QLV) theory has been employed extensively in the literature for characterising the time-dependent behaviour of many biological tissues, including the aortic valve (AV). However, in contrast to other tissues, application of QLV to AV data has been met with varying success, with studies reporting discrepancies in the values of the associated quantified parameters for data collected from different timescales in experiments. Furthermore, some studies investigating the stress-relaxation phenomenon in valvular tissues have suggested discrete relaxation spectra, as an alternative to the continuous spectrum proposed by the QLV. These indications put forward a more fundamental question: Is the time-dependent behaviour of the aortic valve intrinsically quasi-linear? In other words, can the inherent characteristics of the tissue that govern its biomechanical behaviour facilitate a quasi-linear time-dependent behaviour? This paper attempts to address these questions by presenting a mathematical analysis to derive the expressions for the stress-relaxation G( t) and creep J( t) functions for the AV tissue within the QLV theory. The principal inherent characteristic of the tissue is incorporated into the QLV formulation in the form of the well-established gradual fibre recruitment model, and the corresponding expressions for G( t) and J( t) are derived. The outcomes indicate that the resulting stress-relaxation and creep functions do not appear to voluntarily follow the observed experimental trends reported in previous studies. These results highlight that the time-dependent behaviour of the AV may not be quasi-linear, and more suitable theoretical criteria and models may be required to explain the phenomenon based on tissue's microstructure, and for more accurate estimation of the associated material parameters. In general, these results may further be applicable to other planar soft tissues of the same class, i.e. with the same representation for fibre recruitment mechanism and discrete time-dependent spectra.

Miniaturized Stretchable and High-Rate Linear Supercapacitors

NASA Astrophysics Data System (ADS)

Zhu, Wenjun; Zhang, Yang; Zhou, Xiaoshuang; Xu, Jiang; Liu, Zunfeng; Yuan, Ningyi; Ding, Jianning

2017-07-01

Linear stretchable supercapacitors have attracted much attention because they are well suited to applications in the rapidly expanding field of wearable electronics. However, poor conductivity of the electrode material, which limits the transfer of electrons in the axial direction of the linear supercapacitors, leads to a serious loss of capacity at high rates. To solve this problem, we use gold nanoparticles to decorate aligned multiwall carbon nanotube to fabricate stretchable linear electrodes. Furthermore, we have developed fine stretchable linear supercapacitors, which exhibited an extremely high elasticity up to 400% strain with a high capacitance of about 8.7 F g-1 at the discharge current of 1 A g-1.

Miniaturized Stretchable and High-Rate Linear Supercapacitors.

PubMed

Zhu, Wenjun; Zhang, Yang; Zhou, Xiaoshuang; Xu, Jiang; Liu, Zunfeng; Yuan, Ningyi; Ding, Jianning

2017-12-01

Linear stretchable supercapacitors have attracted much attention because they are well suited to applications in the rapidly expanding field of wearable electronics. However, poor conductivity of the electrode material, which limits the transfer of electrons in the axial direction of the linear supercapacitors, leads to a serious loss of capacity at high rates. To solve this problem, we use gold nanoparticles to decorate aligned multiwall carbon nanotube to fabricate stretchable linear electrodes. Furthermore, we have developed fine stretchable linear supercapacitors, which exhibited an extremely high elasticity up to 400% strain with a high capacitance of about 8.7 F g -1 at the discharge current of 1 A g -1 .

Temperature dependence of single-crystal elastic constants of flux-grown alpha-GaPO(4).

PubMed

Armand, P; Beaurain, M; Rufflé, B; Menaert, B; Papet, P

2009-06-01

The lattice parameter change with respect to temperature (T) has been measured using high-temperature powder X-ray diffraction techniques for high-temperature flux-grown GaPO(4) single crystals with the alpha-quartz structure. The lattice and the volume linear thermal expansion coefficients in the temperature range 303-1173 K were computed from the X-ray data. The percentage linear thermal expansions along the a and c axes at 1173 K are 1.5 and 0.51, respectively. The temperature dependence of the mass density rho of flux-grown GaPO(4) single crystals was evaluated using the volume thermal expansion coefficient alpha(V)(T) = 3.291 x 10(-5) - 2.786 x 10(-8) [T] + 4.598 x 10(-11)[T](2). Single-crystal high-resolution Brillouin spectroscopy measurements have been carried out at ambient pressure from 303 to 1123 K to determine the elastic constants C(IJ) of high-temperature flux-grown GaPO(4) material. The single-crystal elastic moduli were calculated using the sound velocities via the measured Brillouin frequency shifts Deltanu(B). These are, to our knowledge, the highest temperatures at which single-crystal elastic constants of alpha-GaPO(4) have been measured. Most of the room-temperature elastic constant values measured on flux-grown GaPO(4) material are higher than the ones found for hydrothermally grown GaPO(4) single crystals. The fourth-order temperature coefficients of both the Brillouin frequency shifts T(nuB)((n)) and the single-crystal elastic moduli T(C(IJ))((n)) were obtained. The first-order temperature coefficients of the C(IJ) are in excellent agreement with previous reports on low-temperature hydrothermally grown alpha-GaPO(4) single crystals, while small discrepancies in the higher-order temperature coefficients are observed. This is explained in terms of the OH content in the GaPO(4) network, which is an important parameter in the crystal thermal behavior.

Association between suicidal behaviour and impaired glucose metabolism in depressive disorders.

PubMed

Koponen, Hannu; Kautiainen, Hannu; Leppänen, Esa; Mäntyselkä, Pekka; Vanhala, Mauno

2015-07-22

Disturbances in lipid metabolism have been linked to suicidal behaviour, but little is known about the association between suicide risk and abnormal glucose metabolism in depression. Hyperglycaemia and hyperinsulinaemia may increase the risk of depression and also the risk for suicide, we therefore studied associations between suicidal behaviour and disturbances in glucose metabolism in depressive patients who had been referred to depression nurse case managers. Patients aged 35 years and older (N = 448, mean age 51 years) who were experiencing a new depressive episode, who were referred to depression nurse case managers in 2008-2009 and who scored ≥10 on the Beck Depression Inventory were enrolled in this study. The study was conducted in municipalities within the Central Finland Hospital District (catchment area of 274 000 inhabitants) as part of the Finnish Depression and Metabolic Syndrome in Adults study. The patients' psychiatric diagnoses and suicidal behaviour were confirmed by the Mini-International Neuropsychiatric Interview. Blood samples, for glucose and lipid determinations, were drawn from participants after 12 h of fasting, which was followed by a 2-hour oral glucose tolerance test (OGTT) when blood was drawn at 0 and 2 h. Insulin resistance was measured by the Quantitative Insulin Sensitivity Check Index (QUICKI) method. Suicidal ideation (49 %) and previous suicide attempts (16 %) were common in patients with major depressive disorder or dysthymia. Patients with depression and suicidal behaviour had higher blood glucose concentrations at baseline and at 2 hours in the OGTT. Glucose levels associated positively with the prevalence of suicidal behaviour, and the linearity was significant at baseline (p for linearity: 0.012, adjusted for age and sex) and for 2-hour OGTT glucose (p for linearity: 0.004, adjusted for age and sex). QUICKI levels associated with suicidal behavior (p for linearity across tertiles of QUICKI: 0.026). Total and LDL cholesterol and triglyceride levels were also higher in those patients with suicidal behaviour. Multivariate analysis revealed that blood glucose levels, BDI scores and antidepressive medications associated with suicidal behaviour. Insulin resistance and disturbances in glucose and lipid metabolism may be more common in middle-aged depressive patients with suicidal behaviour.

Forces and torques on rigid inclusions in an elastic environment: Resulting matrix-mediated interactions, displacements, and rotations

NASA Astrophysics Data System (ADS)

Puljiz, Mate; Menzel, Andreas M.

2017-05-01

Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

Acoustic and elastic multiple scattering and radiation from cylindrical structures

NASA Astrophysics Data System (ADS)

Amirkulova, Feruza Abdukadirovna

Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an incident wave to produce zero total field over a finite spatial region. The approach precisely determines the necessary source amplitudes and enables a cloaked region to be determined using Graf's theorem. To apply the approach, the infinite series of multipole expansions are truncated, and the accuracy of cloaking is studied by modifying the truncation parameter.

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure

PubMed Central

Dong, Juncai; Zhu, Hailiang; Chen, Dongliang

2015-01-01

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed. PMID:26099720

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure.

PubMed

Dong, Juncai; Zhu, Hailiang; Chen, Dongliang

2015-06-23

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed.

Effects of Host-rock Fracturing on Elastic-deformation Source Models of Volcano Deflation.

PubMed

Holohan, Eoghan P; Sudhaus, Henriette; Walter, Thomas R; Schöpfer, Martin P J; Walsh, John J

2017-09-08

Volcanoes commonly inflate or deflate during episodes of unrest or eruption. Continuum mechanics models that assume linear elastic deformation of the Earth's crust are routinely used to invert the observed ground motions. The source(s) of deformation in such models are generally interpreted in terms of magma bodies or pathways, and thus form a basis for hazard assessment and mitigation. Using discontinuum mechanics models, we show how host-rock fracturing (i.e. non-elastic deformation) during drainage of a magma body can progressively change the shape and depth of an elastic-deformation source. We argue that this effect explains the marked spatio-temporal changes in source model attributes inferred for the March-April 2007 eruption of Piton de la Fournaise volcano, La Reunion. We find that pronounced deflation-related host-rock fracturing can: (1) yield inclined source model geometries for a horizontal magma body; (2) cause significant upward migration of an elastic-deformation source, leading to underestimation of the true magma body depth and potentially to a misinterpretation of ascending magma; and (3) at least partly explain underestimation by elastic-deformation sources of changes in sub-surface magma volume.

Mechanical characterization of new micro-composites composed by natural clay matrix and PEG 6000 fillers

NASA Astrophysics Data System (ADS)

El Jai, Mostapha; Akhrif, Iatimad; Mesrar, Laila; Jabrane, Raouf

2018-05-01

The aim of this paper is to characterize mechanically the new micro-composites that have been developed in our laboratories. The composites are composed by natural clay (as a matrix) with variant percentages of Polyethylene Glycol 6000 (PEG 6000) as micro-fillers. We used the compression test for the measurement of the static parameters such as elasticity modulus in elastic region and the hardening coefficient which permits to describe the plasticity behaviour of the materials. An additional energetic approach is proposed in order to quantify the evolution of the plasticity of the reinforced materials, caused by the PEG 6000, for different percentages of this polymer.

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.

Elasto-Plastic Analysis of Tee Joints Using HOT-SMAC

NASA Technical Reports Server (NTRS)

Arnold, Steve M. (Technical Monitor); Bednarcyk, Brett A.; Yarrington, Phillip W.

2004-01-01

The Higher Order Theory - Structural/Micro Analysis Code (HOT-SMAC) software package is applied to analyze the linearly elastic and elasto-plastic response of adhesively bonded tee joints. Joints of this type are finding an increasing number of applications with the increased use of composite materials within advanced aerospace vehicles, and improved tools for the design and analysis of these joints are needed. The linearly elastic results of the code are validated vs. finite element analysis results from the literature under different loading and boundary conditions, and new results are generated to investigate the inelastic behavior of the tee joint. The comparison with the finite element results indicates that HOT-SMAC is an efficient and accurate alternative to the finite element method and has a great deal of potential as an analysis tool for a wide range of bonded joints.

Heat kernel for the elliptic system of linear elasticity with boundary conditions

NASA Astrophysics Data System (ADS)

Taylor, Justin; Kim, Seick; Brown, Russell

2014-10-01

We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are Hölder continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are Hölder continuous up to the boundary, then the corresponding heat kernel has a Gaussian bound. In particular, if the domain is a two dimensional Lipschitz domain satisfying a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary condition, then we show that the heat kernel has a Gaussian bound. As an application, we construct Green's function for elliptic mixed problem in such a domain.

System and method to create three-dimensional images of non-linear acoustic properties in a region remote from a borehole

DOEpatents

Vu, Cung; Nihei, Kurt T.; Schmitt, Denis P.; Skelt, Christopher; Johnson, Paul A.; Guyer, Robert; TenCate, James A.; Le Bas, Pierre-Yves

2013-01-01

In some aspects of the disclosure, a method for creating three-dimensional images of non-linear properties and the compressional to shear velocity ratio in a region remote from a borehole using a conveyed logging tool is disclosed. In some aspects, the method includes arranging a first source in the borehole and generating a steered beam of elastic energy at a first frequency; arranging a second source in the borehole and generating a steerable beam of elastic energy at a second frequency, such that the steerable beam at the first frequency and the steerable beam at the second frequency intercept at a location away from the borehole; receiving at the borehole by a sensor a third elastic wave, created by a three wave mixing process, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole; determining a location of a three wave mixing region based on the arrangement of the first and second sources and on properties of the third wave signal; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and determining at a plurality of azimuths, inclinations and longitudinal locations within the borehole. The method is additionally used to generate three dimensional images of the ratio of compressional to shear acoustic velocity of the same volume surrounding the borehole.

Comparative study of sea ice dynamics simulations with a Maxwell elasto-brittle rheology and the elastic-viscous-plastic rheology in NEMO-LIM3

NASA Astrophysics Data System (ADS)

Raulier, Jonathan; Dansereau, Véronique; Fichefet, Thierry; Legat, Vincent; Weiss, Jérôme

2017-04-01

Sea ice is a highly dynamical environment characterized by a dense mesh of fractures or leads, constantly opening and closing over short time scales. This characteristic geomorphology is linked to the existence of linear kinematic features, which consist of quasi-linear patterns emerging from the observed strain rate field of sea ice. Standard rheologies used in most state-of-the-art sea ice models, like the well-known elastic-viscous-plastic rheology, are thought to misrepresent those linear kinematic features and the observed statistical distribution of deformation rates. Dedicated rheologies built to catch the processes known to be at the origin of the formation of leads are developed but still need evaluations on the global scale. One of them, based on a Maxwell elasto-brittle formulation, is being integrated in the NEMO-LIM3 global ocean-sea ice model (www.nemo-ocean.eu; www.elic.ucl.ac.be/lim). In the present study, we compare the results of the sea ice model LIM3 obtained with two different rheologies: the elastic-viscous-plastic rheology commonly used in LIM3 and a Maxwell elasto-brittle rheology. This comparison is focused on the statistical characteristics of the simulated deformation rate and on the ability of the model to reproduce the existence of leads within the ice pack. The impact of the lead representation on fluxes between ice, atmosphere and ocean is also assessed.

On relative distortion in fingerprint comparison.

PubMed

Kalka, Nathan D; Hicklin, R Austin

2014-11-01

When fingerprints are deposited, non-uniform pressure in conjunction with the inherent elasticity of friction ridge skin often causes linear and non-linear distortions in the ridge and valley structure. The effects of these distortions must be considered during analysis of fingerprint images. Even when individual prints are not notably distorted, relative distortion between two prints can have a serious impact on comparison. In this paper we discuss several metrics for quantifying and visualizing linear and non-linear fingerprint deformations, and software tools to assist examiners in accounting for distortion in fingerprint comparisons. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Influence of isotopic disorder on solid state amorphization and polyamorphism in solid H2O -D2O solutions

NASA Astrophysics Data System (ADS)

Gromnitskaya, E. L.; Danilov, I. V.; Lyapin, A. G.; Brazhkin, V. V.

2015-10-01

We present a low-temperature and high-pressure ultrasonic study of elastic properties of isotopic H2O-D2O solid solutions, comparing their properties with those of the isotopically pure H2O and D2O ices. Measurements were carried out for solid state amorphization (SSA) from 1h to high-density amorphous (HDA) ice upon compression up to 1.8 GPa at 77 K and for the temperature-induced (77 -190 K ) u-HDA (unrelaxed HDA) → e-HDA (expanded HDA) → low-density amorphous (LDA )→1 c cascade of ice transformations near room pressure. There are many similarities in the elasticity behaviour of H2O ,D2O , and H2O-D2O solid solutions, including the softening of the shear elastic modulus as a precursor of SSA and the HDA →LDA transition. We have found significant isotopic effects during H/D substitution, including elastic softening of H2O -D2O solid solutions with respect to the isotopically pure ices in the case of the bulk moduli of ices 1c and 1h and for both bulk and shear elastic moduli of HDA ice at high pressures (>1 GPa ) . This softening is related to the configurational isotopic disorder in the solid solutions. At low pressures, the isotope concentration dependence of the elastic moduli of u-HDA ice changes remarkably and becomes monotonic with pronounced change of the bulk modulus (≈20 %) .

Minimally invasive estimation of ventricular dead space volume through use of Frank-Starling curves.

PubMed

Davidson, Shaun; Pretty, Chris; Pironet, Antoine; Desaive, Thomas; Janssen, Nathalie; Lambermont, Bernard; Morimont, Philippe; Chase, J Geoffrey

2017-01-01

This paper develops a means of more easily and less invasively estimating ventricular dead space volume (Vd), an important, but difficult to measure physiological parameter. Vd represents a subject and condition dependent portion of measured ventricular volume that is not actively participating in ventricular function. It is employed in models based on the time varying elastance concept, which see widespread use in haemodynamic studies, and may have direct diagnostic use. The proposed method involves linear extrapolation of a Frank-Starling curve (stroke volume vs end-diastolic volume) and its end-systolic equivalent (stroke volume vs end-systolic volume), developed across normal clinical procedures such as recruitment manoeuvres, to their point of intersection with the y-axis (where stroke volume is 0) to determine Vd. To demonstrate the broad applicability of the method, it was validated across a cohort of six sedated and anaesthetised male Pietrain pigs, encompassing a variety of cardiac states from healthy baseline behaviour to circulatory failure due to septic shock induced by endotoxin infusion. Linear extrapolation of the curves was supported by strong linear correlation coefficients of R = 0.78 and R = 0.80 average for pre- and post- endotoxin infusion respectively, as well as good agreement between the two linearly extrapolated y-intercepts (Vd) for each subject (no more than 7.8% variation). Method validity was further supported by the physiologically reasonable Vd values produced, equivalent to 44.3-53.1% and 49.3-82.6% of baseline end-systolic volume before and after endotoxin infusion respectively. This method has the potential to allow Vd to be estimated without a particularly demanding, specialised protocol in an experimental environment. Further, due to the common use of both mechanical ventilation and recruitment manoeuvres in intensive care, this method, subject to the availability of multi-beat echocardiography, has the potential to allow for estimation of Vd in a clinical environment.

The effect of pore size and porosity on mechanical properties and biological response of porous titanium scaffolds.

PubMed

Torres-Sanchez, C; Al Mushref, F R A; Norrito, M; Yendall, K; Liu, Y; Conway, P P

2017-08-01

The effect of pore size and porosity on elastic modulus, strength, cell attachment and cell proliferation was studied for Ti porous scaffolds manufactured via powder metallurgy and sintering. Porous scaffolds were prepared in two ranges of porosities so that their mechanical properties could mimic those of cortical and trabecular bone respectively. Space-holder engineered pore size distributions were carefully determined to study the impact that small changes in pore size may have on mechanical and biological behaviour. The Young's moduli and compressive strengths were correlated with the relative porosity. Linear, power and exponential regressions were studied to confirm the predictability in the characterisation of the manufactured scaffolds and therefore establish them as a design tool for customisation of devices to suit patients' needs. The correlations were stronger for the linear and the power law regressions and poor for the exponential regressions. The optimal pore microarchitecture (i.e. pore size and porosity) for scaffolds to be used in bone grafting for cortical bone was set to <212μm with volumetric porosity values of 27-37%, and for trabecular tissues to 300-500μm with volumetric porosity values of 54-58%. The pore size range 212-300μm with volumetric porosity values of 38-56% was reported as the least favourable to cell proliferation in the longitudinal study of 12days of incubation. Copyright © 2017 Elsevier B.V. All rights reserved.

On the diffusion and self-trapping of surface dimers

NASA Astrophysics Data System (ADS)

Kappus, W.

The theory of elastic interactions between surface atoms which are caused by substrate strains is applied to the interaction of dimers on the (211) surface of tungsten. From the comparison of theoretical and experimental interactions which were derived from the diffusion behaviour of dimers, conclusions are drawn on the nature of the adatom-substrate bond.

On the diffusion and self-trapping of surface dimers

NASA Astrophysics Data System (ADS)

Kappus, W.

1982-03-01

The theory of elastic interactions between surface atoms which are caused by substrate strains is applied to the interaction of dimers on the (211) surface of tungsten. From the comparison of theoretical and experimental interactions which were derived from the diffusion behaviour of dimers, conclusions are drawn on the nature of the adatom-substrate bond.

Understanding the Physics of Bungee Jumping

ERIC Educational Resources Information Center

Heck, Andre; Uylings, Peter; Kedzierska, Ewa

2010-01-01

Changing mass phenomena like the motion of a falling chain, the behaviour of a falling elastic bar or spring, and the motion of a bungee jumper surprise many a physicist. In this article we discuss the first phase of bungee jumping, when the bungee jumper falls, but the bungee rope is still slack. In instructional material this phase is often…

Rheological study of in-situ crosslinkable hydrogels based on hyaluronanic acid, collagen and sericin.

PubMed

Vulpe, Raluca; Le Cerf, Didier; Dulong, Virginie; Popa, Marcel; Peptu, Catalina; Verestiuc, Liliana; Picton, Luc

2016-12-01

The elaboration of chemically crosslinked hydrogels based on collagen (C), hyaluronanic acid (HA) and sericin (S) with different polymer ratios was investigated by in-situ rheology. This reaction was performed via amide or ester bond reaction activated by carbodiimide, in pure water. Prior to molecule crosslinking, the rheological behaviour of the biopolymers (alone or in mixture) was characterized in a semi-dilute concentration regime. Both flow and dynamic measurements showed that uncrosslinked collagen alone appears to be rather elastic with yield stress properties, whereas uncrosslinked HA alone appears to be rather shear thinning and viscoelastic in agreement with entangled polymer behaviour. Sericin exhibited Newtonian low viscosity behaviour according to its very low molar mass. Before crosslinking, HA exhibited viscoelastic behaviour at concentrations above the critical entangled concentration (C*) in the mixtures, thus HA shows promise as a matrix for future crosslinked networks, whereas sericin did not significantly modify the rheology. During the reaction, followed by rheology, the kinetics were slower for pure HA systems compared with the mixtures (i.e., with added collagen and/or to a lesser extent sericin). At the same time, the final network of hydrogels (i.e., the elastic modulus) was more structured in the mixture based systems. This result is explained by ester bonds (the only possibility for pure HA systems), which are less favourable and reactive than amide bonds (possible with sericin and collagen). The presence of collagen in the HA matrix reinforced the hydrogel network. SEM studies confirmed the structure of the hydrogels, and in vitro degradability was globally consistent with the effect of the selected enzyme according to the hydrogel composition. All the elaborated hydrogels were non-cytotoxic in vitro. Copyright © 2016 Elsevier B.V. All rights reserved.

Water Holding as Determinant for the Elastically Stored Energy in Protein-Based Gels.

PubMed

Pouvreau, Laurice; van Wijlen, Emke; Klok, Jan; Urbonaite, Vaida; Munialo, Claire D; de Jongh, Harmen H J

2016-04-01

To evaluate the importance of the water holding capacity for the elastically stored energy of protein gels, a range of gels were created from proteins from different origin (plant: pea and soy proteins, and animal: whey, blood plasma, egg white proteins, and ovalbumin) varying in network morphology set by the protein concentration, pH, ionic strength, or the presence of specific ions. The results showed that the observed positive and linear relation between water holding (WH) and elastically stored energy (RE) is generic for globular protein gels studied. The slopes of this relation are comparable for all globular protein gels (except for soy protein gels) whereas the intercept is close to 0 for most of the systems except for ovalbumin and egg white gels. The slope and intercept obtained allows one to predict the impact of tuning WH, by gel morphology or network stiffness, on the mechanical deformation of the protein-based gel. Addition of charged polysaccharides to a protein system leads to a deviation from the linear relation between WH and RE and this deviation coincides with a change in phase behavior. © 2016 Institute of Food Technologists®