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.

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.

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.

Three-Dimensional Computer-Assisted Two-Layer Elastic Models of the Face.

PubMed

Ueda, Koichi; Shigemura, Yuka; Otsuki, Yuki; Fuse, Asuka; Mitsuno, Daisuke

2017-11-01

To make three-dimensional computer-assisted elastic models for the face, we decided on five requirements: (1) an elastic texture like skin and subcutaneous tissue; (2) the ability to take pen marking for incisions; (3) the ability to be cut with a surgical knife; (4) the ability to keep stitches in place for a long time; and (5) a layered structure. After testing many elastic solvents, we have made realistic three-dimensional computer-assisted two-layer elastic models of the face and cleft lip from the computed tomographic and magnetic resonance imaging stereolithographic data. The surface layer is made of polyurethane and the inner layer is silicone. Using this elastic model, we taught residents and young doctors how to make several typical local flaps and to perform cheiloplasty. They could experience realistic simulated surgery and understand three-dimensional movement of the flaps.

Algebraic multigrid methods applied to problems in computational structural mechanics

NASA Technical Reports Server (NTRS)

Mccormick, Steve; Ruge, John

1989-01-01

The development of algebraic multigrid (AMG) methods and their application to certain problems in structural mechanics are described with emphasis on two- and three-dimensional linear elasticity equations and the 'jacket problems' (three-dimensional beam structures). Various possible extensions of AMG are also described. The basic idea of AMG is to develop the discretization sequence based on the target matrix and not the differential equation. Therefore, the matrix is analyzed for certain dependencies that permit the proper construction of coarser matrices and attendant transfer operators. In this manner, AMG appears to be adaptable to structural analysis applications.

Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations

NASA Astrophysics Data System (ADS)

Scerrato, Daria; Giorgio, Ivan; Rizzi, Nicola Luigi

2016-06-01

In this paper, we determine numerically a large class of equilibrium configurations of an elastic two-dimensional continuous pantographic sheet in three-dimensional deformation consisting of two families of fibers which are parabolic prior to deformation. The fibers are assumed (1) to be continuously distributed over the sample, (2) to be endowed of bending and torsional stiffnesses, and (3) tied together at their points of intersection to avoid relative slipping by means of internal (elastic) pivots. This last condition characterizes the system as a pantographic lattice (Alibert and Della Corte in Zeitschrift für angewandte Mathematik und Physik 66(5):2855-2870, 2015; Alibert et al. in Math Mech Solids 8(1):51-73, 2003; dell'Isola et al. in Int J Non-Linear Mech 80:200-208, 2016; Int J Solids Struct 81:1-12, 2016). The model that we employ here, developed by Steigmann and dell'Isola (Acta Mech Sin 31(3):373-382, 2015) and first investigated in Giorgio et al. (Comptes rendus Mecanique 2016, doi: 10.1016/j.crme.2016.02.009), is applicable to fiber lattices in which three-dimensional bending, twisting, and stretching are significant as well as a resistance to shear distortion, i.e., to the angle change between the fibers. Some relevant numerical examples are exhibited in order to highlight the main features of the model adopted: In particular, buckling and post-buckling behaviors of pantographic parabolic lattices are investigated. The fabric of the metamaterial presented in this paper has been conceived to resist more effectively in the extensional bias tests by storing more elastic bending energy and less energy in the deformation of elastic pivots: A comparison with a fabric constituted by beams which are straight in the reference configuration shows that the proposed concept is promising.

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

Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity

NASA Astrophysics Data System (ADS)

Gómez, D.; Nazarov, S. A.; Pérez, M. E.

2018-04-01

We consider a homogenization Winkler-Steklov spectral problem that consists of the elasticity equations for a three-dimensional homogeneous anisotropic elastic body which has a plane part of the surface subject to alternating boundary conditions on small regions periodically placed along the plane. These conditions are of the Dirichlet type and of the Winkler-Steklov type, the latter containing the spectral parameter. The rest of the boundary of the body is fixed, and the period and size of the regions, where the spectral parameter arises, are of order ɛ . For fixed ɛ , the problem has a discrete spectrum, and we address the asymptotic behavior of the eigenvalues {β _k^ɛ }_{k=1}^{∞} as ɛ → 0. We show that β _k^ɛ =O(ɛ ^{-1}) for each fixed k, and we observe a common limit point for all the rescaled eigenvalues ɛ β _k^ɛ while we make it evident that, although the periodicity of the structure only affects the boundary conditions, a band-gap structure of the spectrum is inherited asymptotically. Also, we provide the asymptotic behavior for certain "groups" of eigenmodes.

Development of three-dimensional hollow elastic model for cerebral aneurysm clipping simulation enabling rapid and low cost prototyping.

PubMed

Mashiko, Toshihiro; Otani, Keisuke; Kawano, Ryutaro; Konno, Takehiko; Kaneko, Naoki; Ito, Yumiko; Watanabe, Eiju

2015-03-01

We developed a method for fabricating a three-dimensional hollow and elastic aneurysm model useful for surgical simulation and surgical training. In this article, we explain the hollow elastic model prototyping method and report on the effects of applying it to presurgical simulation and surgical training. A three-dimensional printer using acrylonitrile-butadiene-styrene as a modeling material was used to produce a vessel model. The prototype was then coated with liquid silicone. After the silicone had hardened, the acrylonitrile-butadiene-styrene was melted with xylene and removed, leaving an outer layer as a hollow elastic model. Simulations using the hollow elastic model were performed in 12 patients. In all patients, the clipping proceeded as scheduled. The surgeon's postoperative assessment was favorable in all cases. This method enables easy fabrication at low cost. Simulation using the hollow elastic model is thought to be useful for understanding of three-dimensional aneurysm structure. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

Direct numerical simulation of human phonation

NASA Astrophysics Data System (ADS)

Bodony, Daniel; Saurabh, Shakti

2017-11-01

The generation and propagation of the human voice in three-dimensions is studied using direct numerical simulation. A full body domain is employed for the purpose of directly computing the sound in the region past the speaker's mouth. The air in the vocal tract is modeled as a compressible and viscous fluid interacting with the elastic vocal folds. The vocal fold tissue material properties are multi-layered, with varying stiffness, and a linear elastic transversely isotropic model is utilized and implemented in a quadratic finite element code. The fluid-solid domains are coupled through a boundary-fitted interface and utilize a Poisson equation-based mesh deformation method. A kinematic constraint based on a specified minimum gap between the vocal folds is applied to prevent collision during glottal closure. Both near VF flow dynamics and far-field acoustics have been studied. A comparison is drawn to current two-dimensional simulations as well as to data from the literature. Near field vocal fold dynamics and glottal flow results are studied and in good agreement with previous three-dimensional phonation studies. Far-field acoustic characteristics, when compared to their two-dimensional counterpart, are shown to be sensitive to the dimensionality. Supported by the National Science Foundation (CAREER Award Number 1150439).

Application of a transonic potential flow code to the static aeroelastic analysis of three-dimensional wings

NASA Technical Reports Server (NTRS)

Whitlow, W., Jr.; Bennett, R. M.

1982-01-01

Since the aerodynamic theory is nonlinear, the method requires the coupling of two iterative processes - an aerodynamic analysis and a structural analysis. A full potential analysis code, FLO22, is combined with a linear structural analysis to yield aerodynamic load distributions on and deflections of elastic wings. This method was used to analyze an aeroelastically-scaled wind tunnel model of a proposed executive-jet transport wing and an aeroelastic research wing. The results are compared with the corresponding rigid-wing analyses, and some effects of elasticity on the aerodynamic loading are noted.

A numerical method for determination of source time functions for general three-dimensional rupture propagation

NASA Technical Reports Server (NTRS)

Das, S.

1979-01-01

A method to determine the displacement and the stress on the crack plane for a three-dimensional shear crack of arbitrary shape propagating in an infinite, homogeneous medium which is linearly elastic everywhere off the crack plane is presented. The main idea of the method is to use a representation theorem in which the displacement at any given point on the crack plane is written as an integral of the traction over the whole crack plane. As a test of the accuracy of the numerical technique, the results are compared with known solutions for two simple cases.

High Resolution, Large Deformation 3D Traction Force Microscopy

PubMed Central

López-Fagundo, Cristina; Reichner, Jonathan; Hoffman-Kim, Diane; Franck, Christian

2014-01-01

Traction Force Microscopy (TFM) is a powerful approach for quantifying cell-material interactions that over the last two decades has contributed significantly to our understanding of cellular mechanosensing and mechanotransduction. In addition, recent advances in three-dimensional (3D) imaging and traction force analysis (3D TFM) have highlighted the significance of the third dimension in influencing various cellular processes. Yet irrespective of dimensionality, almost all TFM approaches have relied on a linear elastic theory framework to calculate cell surface tractions. Here we present a new high resolution 3D TFM algorithm which utilizes a large deformation formulation to quantify cellular displacement fields with unprecedented resolution. The results feature some of the first experimental evidence that cells are indeed capable of exerting large material deformations, which require the formulation of a new theoretical TFM framework to accurately calculate the traction forces. Based on our previous 3D TFM technique, we reformulate our approach to accurately account for large material deformation and quantitatively contrast and compare both linear and large deformation frameworks as a function of the applied cell deformation. Particular attention is paid in estimating the accuracy penalty associated with utilizing a traditional linear elastic approach in the presence of large deformation gradients. PMID:24740435

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.

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

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 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.

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.

Bidirectional Elastic Image Registration Using B-Spline Affine Transformation

PubMed Central

Gu, Suicheng; Meng, Xin; Sciurba, Frank C.; Wang, Chen; Kaminski, Naftali; Pu, Jiantao

2014-01-01

A registration scheme termed as B-spline affine transformation (BSAT) is presented in this study to elastically align two images. We define an affine transformation instead of the traditional translation at each control point. Mathematically, BSAT is a generalized form of the affine transformation and the traditional B-Spline transformation (BST). In order to improve the performance of the iterative closest point (ICP) method in registering two homologous shapes but with large deformation, a bi-directional instead of the traditional unidirectional objective / cost function is proposed. In implementation, the objective function is formulated as a sparse linear equation problem, and a sub-division strategy is used to achieve a reasonable efficiency in registration. The performance of the developed scheme was assessed using both two-dimensional (2D) synthesized dataset and three-dimensional (3D) volumetric computed tomography (CT) data. Our experiments showed that the proposed B-spline affine model could obtain reasonable registration accuracy. PMID:24530210

Nonclassical models of the theory of plates and shells

NASA Astrophysics Data System (ADS)

Annin, Boris D.; Volchkov, Yuri M.

2017-11-01

Publications dealing with the study of methods of reducing a three-dimensional problem of the elasticity theory to a two-dimensional problem of the theory of plates and shells are reviewed. Two approaches are considered: the use of kinematic and force hypotheses and expansion of solutions of the three-dimensional elasticity theory in terms of the complete system of functions. Papers where a three-dimensional problem is reduced to a two-dimensional problem with the use of several approximations of each of the unknown functions (stresses and displacements) by segments of the Legendre polynomials are also reviewed.

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

On a 3-D singularity element for computation of combined mode stress intensities

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Kathiresan, K.

1976-01-01

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

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.

Measuring strain and rotation fields at the dislocation core in graphene

NASA Astrophysics Data System (ADS)

Bonilla, L. L.; Carpio, A.; Gong, C.; Warner, J. H.

2015-10-01

Strain fields, dislocations, and defects may be used to control electronic properties of graphene. By using advanced imaging techniques with high-resolution transmission electron microscopes, we have measured the strain and rotation fields about dislocations in monolayer graphene with single-atom sensitivity. These fields differ qualitatively from those given by conventional linear elasticity. However, atom positions calculated from two-dimensional (2D) discrete elasticity and three-dimensional discrete periodized Föppl-von Kármán equations (dpFvKEs) yield fields close to experiments when determined by geometric phase analysis. 2D theories produce symmetric fields whereas those from experiments exhibit asymmetries. Numerical solutions of dpFvKEs provide strain and rotation fields of dislocation dipoles and pairs that also exhibit asymmetries and, compared with experiments, may yield information on out-of-plane displacements of atoms. While discrete theories need to be solved numerically, analytical formulas for strains and rotation about dislocations can be obtained from 2D Mindlin's hyperstress theory. These formulas are very useful for fitting experimental data and provide a template to ascertain the importance of nonlinear and nonplanar effects. Measuring the parameters of this theory, we find two characteristic lengths between three and four times the lattice spacings that control dilatation and rotation about a dislocation. At larger distances from the dislocation core, the elastic fields decay to those of conventional elasticity. Our results may be relevant for strain engineering in graphene and other 2D materials of current interest.

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.

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.

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).

Impact of Wall Shear Stress and Pressure Variation on the Stability of Atherosclerotic Plaque

NASA Astrophysics Data System (ADS)

Taviani, V.; Li, Z. Y.; Sutcliffe, M.; Gillard, J.

Rupture of vulnerable atheromatous plaque in the carotid and coronary arteries often leads to stroke and heart attack respectively. The mechanism of blood flow and plaque rupture in stenotic arteries is still not fully understood. A three dimensional rigid wall model was solved under steady and unsteady conditions assuming a time-varying inlet velocity profile to investigate the relative importance of axial forces and pressure drops in arteries with asymmetric stenosis. Flow-structure interactions were investigated for the same geometry and the results were compared with those retrieved with the corresponding one dimensional models. The Navier-Stokes equations were used as the governing equations for the fluid. The tube wall was assumed linearly elastic, homogeneous isotropic. The analysis showed that wall shear stress is small (less than 3.5%) with respect to pressure drop throughout the cycle even for severe stenosis. On the contrary, the three dimensional behavior of velocity, pressure and wall shear stress is in general very different from that predicted by one dimensional models. This suggests that the primary source of mistakes in one dimensional studies comes from neglecting the three dimensional geometry of the plaque. Neglecting axial forces only involves minor errors.

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.

FIDDLE: A Computer Code for Finite Difference Development of Linear Elasticity in Generalized Curvilinear Coordinates

NASA Technical Reports Server (NTRS)

Kaul, Upender K.

2005-01-01

A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.

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).

AELAS: Automatic ELAStic property derivations via high-throughput first-principles computation

NASA Astrophysics Data System (ADS)

Zhang, S. H.; Zhang, R. F.

2017-11-01

The elastic properties are fundamental and important for crystalline materials as they relate to other mechanical properties, various thermodynamic qualities as well as some critical physical properties. However, a complete set of experimentally determined elastic properties is only available for a small subset of known materials, and an automatic scheme for the derivations of elastic properties that is adapted to high-throughput computation is much demanding. In this paper, we present the AELAS code, an automated program for calculating second-order elastic constants of both two-dimensional and three-dimensional single crystal materials with any symmetry, which is designed mainly for high-throughput first-principles computation. Other derivations of general elastic properties such as Young's, bulk and shear moduli as well as Poisson's ratio of polycrystal materials, Pugh ratio, Cauchy pressure, elastic anisotropy and elastic stability criterion, are also implemented in this code. The implementation of the code has been critically validated by a lot of evaluations and tests on a broad class of materials including two-dimensional and three-dimensional materials, providing its efficiency and capability for high-throughput screening of specific materials with targeted mechanical properties. Program Files doi:http://dx.doi.org/10.17632/f8fwg4j9tw.1 Licensing provisions: BSD 3-Clause Programming language: Fortran Nature of problem: To automate the calculations of second-order elastic constants and the derivations of other elastic properties for two-dimensional and three-dimensional materials with any symmetry via high-throughput first-principles computation. Solution method: The space-group number is firstly determined by the SPGLIB code [1] and the structure is then redefined to unit cell with IEEE-format [2]. Secondly, based on the determined space group number, a set of distortion modes is automatically specified and the distorted structure files are generated. Afterwards, the total energy for each distorted structure is calculated by the first-principles codes, e.g. VASP [3]. Finally, the second-order elastic constants are determined from the quadratic coefficients of the polynomial fitting of the energies vs strain relationships and other elastic properties are accordingly derived. References [1] http://atztogo.github.io/spglib/. [2] A. Meitzler, H.F. Tiersten, A.W. Warner, D. Berlincourt, G.A. Couqin, F.S. Welsh III, IEEE standard on piezoelectricity, Society, 1988. [3] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169.

Constitutive relations in multidimensional isotropic elasticity and their restrictions to subspaces of lower dimensions

NASA Astrophysics Data System (ADS)

Georgievskii, D. V.

2017-07-01

The mechanical meaning and the relationships among material constants in an n-dimensional isotropic elastic medium are discussed. The restrictions of the constitutive relations (Hooke's law) to subspaces of lower dimension caused by the conditions that an m-dimensional strain state or an m-dimensional stress state (1 ≤ m < n) is realized in the medium. Both the terminology and the general idea of the mathematical construction are chosen by analogy with the case n = 3 and m = 2, which is well known in the classical plane problem of elasticity theory. The quintuples of elastic constants of the same medium that enter both the n-dimensional relations and the relations written out for any m-dimensional restriction are expressed in terms of one another. These expressions in terms of the known constants, for example, of a three-dimensional medium, i.e., the classical elastic constants, enable us to judge the material properties of this medium immersed in a space of larger dimension.

Three-dimensional polarization states of monochromatic light fields.

PubMed

Azzam, R M A

2011-11-01

The 3×1 generalized Jones vectors (GJVs) [E(x) E(y) E(z)](t) (t indicates the transpose) that describe the linear, circular, and elliptical polarization states of an arbitrary three-dimensional (3-D) monochromatic light field are determined in terms of the geometrical parameters of the 3-D vibration of the time-harmonic electric field. In three dimensions, there are as many distinct linear polarization states as there are points on the surface of a hemisphere, and the number of distinct 3-D circular polarization states equals that of all two-dimensional (2-D) polarization states on the Poincaré sphere, of which only two are circular states. The subset of 3-D polarization states that results from the superposition of three mutually orthogonal x, y, and z field components of equal amplitude is considered as a function of their relative phases. Interesting contours of equal ellipticity and equal inclination of the normal to the polarization ellipse with respect to the x axis are obtained in 2-D phase space. Finally, the 3×3 generalized Jones calculus, in which elastic scattering (e.g., by a nano-object in the near field) is characterized by the 3-D linear transformation E(s)=T E(i), is briefly introduced. In such a matrix transformation, E(i) and E(s) are the 3×1 GJVs of the incident and scattered waves and T is the 3×3 generalized Jones matrix of the scatterer at a given frequency and for given directions of incidence and scattering.

Numerical modeling of the exterior-to-interior transmission of impulsive sound through three-dimensional, thin-walled elastic structures

NASA Astrophysics Data System (ADS)

Remillieux, Marcel C.; Pasareanu, Stephanie M.; Svensson, U. Peter

2013-12-01

Exterior propagation of impulsive sound and its transmission through three-dimensional, thin-walled elastic structures, into enclosed cavities, are investigated numerically in the framework of linear dynamics. A model was developed in the time domain by combining two numerical tools: (i) exterior sound propagation and induced structural loading are computed using the image-source method for the reflected field (specular reflections) combined with an extension of the Biot-Tolstoy-Medwin method for the diffracted field, (ii) the fully coupled vibro-acoustic response of the interior fluid-structure system is computed using a truncated modal-decomposition approach. In the model for exterior sound propagation, it is assumed that all surfaces are acoustically rigid. Since coupling between the structure and the exterior fluid is not enforced, the model is applicable to the case of a light exterior fluid and arbitrary interior fluid(s). The structural modes are computed with the finite-element method using shell elements. Acoustic modes are computed analytically assuming acoustically rigid boundaries and rectangular geometries of the enclosed cavities. This model is verified against finite-element solutions for the cases of rectangular structures containing one and two cavities, respectively.

Optimized growth and reorientation of anisotropic material based on evolution equations

NASA Astrophysics Data System (ADS)

Jantos, Dustin R.; Junker, Philipp; Hackl, Klaus

2018-07-01

Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton's principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.

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

Dimensional accuracy of pickup implant impression: an in vitro comparison of novel modular versus standard custom trays.

PubMed

Simeone, Piero; Valentini, Pier Paolo; Pizzoferrato, Roberto; Scudieri, Folco

2011-01-01

The purpose of this in vitro study was to compare the dimensional accuracy of the pickup impression technique using a modular individual tray (MIT) and using a standard individual tray (ST) for multiple internal-connection implants. The roles of both materials and geometric misfits were considered. First, because the MIT relies on the stiffness and elasticity of acrylic resin material, a preliminary investigation of the resin volume contraction during curing and polymerization was done. Then, two sets of specimens were tested to compare the accuracy of the MIT (test group) to that of the ST (control group). The linear and angular displacements of the transfer copings were measured and compared during three different stages of the impression procedure. Experimental measurements were performed with a computerized coordinate measuring machine. The curing dynamic of the acrylic resin was strongly dependent on the physical properties of the acrylic material and the powder/liquid ratio. Specifically, an increase in the powder/liquid ratio accelerated resin polymerization (curing time decreases by 70%) and reduced the final volume contraction by 45%. However, the total shrinkage never exceeded the elastic limits of the material; hence, it did not affect the coping's stability. In the test group, linear errors were reduced by 55% and angular errors were reduced by 65%. Linear and angular displacements of the transfer copings were significantly reduced with the MIT technique, which led to higher dimensional accuracy versus the ST group. The MIT approach, in combination with a thin and uniform amount of acrylic resin in the pickup impression technique, showed no significant permanent distortions in multiple misalignment internal-connection implants compared to the ST technique.

Effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures: A paradigm in three dimensions

PubMed Central

Ovtchinnikov, Evgueni E.; Xanthis, Leonidas S.

2000-01-01

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickness is small. In this paper we show an effective way of resolving this difficulty by invoking a special preconditioning technique associated with the effective dimensional reduction algorithm (EDRA). As an example, we present an algorithm for computing the minimal eigenvalue of a thin elastic plate and we show both theoretically and numerically that it is robust with respect to both the thickness and discretization parameters, i.e. the convergence does not deteriorate with diminishing thickness or mesh refinement. This robustness is sine qua non for the efficient computation of large-scale eigenvalue problems for thin elastic structures. PMID:10655469

Physical interpretation and application of principles of ultrasonic nondestructive evaluation of high-performance materials

NASA Technical Reports Server (NTRS)

Miller, James G.

1990-01-01

An ultrasonic measurement system employed in the experimental interrogation of the anisotropic properties (through the measurement of the elastic stiffness constants) of the uniaxial graphite-epoxy composites is presented. The continuing effort for the development of improved visualization techniques for physical parameters is discussed. The background is set for the understanding and visualization of the relationship between the phase and energy/group velocity for propagation in high-performance anisotropic materials by investigating the general requirements imposed by the classical wave equation. The consequences are considered when the physical parameters of the anisotropic material are inserted into the classical wave equation by a linear elastic model. The relationship is described between the phase velocity and the energy/group velocity three dimensional surfaces through graphical techniques.

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.

Adaptive finite element methods for two-dimensional problems in computational fracture mechanics

NASA Technical Reports Server (NTRS)

Min, J. B.; Bass, J. M.; Spradley, L. W.

1994-01-01

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

ZIP3D: An elastic and elastic-plastic finite-element analysis program for cracked bodies

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Newman, J. C., Jr.

1990-01-01

ZIP3D is an elastic and an elastic-plastic finite element program to analyze cracks in three dimensional solids. The program may also be used to analyze uncracked bodies or multi-body problems involving contacting surfaces. For crack problems, the program has several unique features including the calculation of mixed-mode strain energy release rates using the three dimensional virtual crack closure technique, the calculation of the J integral using the equivalent domain integral method, the capability to extend the crack front under monotonic or cyclic loading, and the capability to close or open the crack surfaces during cyclic loading. The theories behind the various aspects of the program are explained briefly. Line-by-line data preparation is presented. Input data and results for an elastic analysis of a surface crack in a plate and for an elastic-plastic analysis of a single-edge-crack-tension specimen are also presented.

Stability of a penny-shaped geothermal reservoir in the earth's crust

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

Abe, H.; Sekine, H.

1982-06-01

The theoretical analysis of a penny-shaped geothermal reservoir in the earth's crust subject to linear tectonic stress gradients has been made on the basis of the three dimensional theory of elasticity. The condition for stability of a reservoir requires K/sub 1/ < K /SUB c/ , where K/sub 1/ and K /SUB c/ are, respectively, the stress intensity factor for the opening mode and the fracture toughness of the surrounding rock. From this condition the upper critical pressure being necessary for the reservoir stability is obtained and is shown graphically.

Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Bigelow, C. A.; Shivakumar, K. N.

1993-01-01

Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonic and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor alpha(sub g) was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of alpha(sub g) were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness.

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

In Vivo Measurement of Age-Related Stiffening in the Crystalline Lens by Brillouin Optical Microscopy

PubMed Central

Scarcelli, Giuliano; Kim, Pilhan; Yun, Seok Hyun

2011-01-01

Abtract The biophysical and biomechanical properties of the crystalline lens (e.g., viscoelasticity) have long been implicated in accommodation and vision problems, such as presbyopia and cataracts. However, it has been difficult to measure such parameters noninvasively. Here, we used in vivo Brillouin optical microscopy to characterize material acoustic properties at GHz frequency and measure the longitudinal elastic moduli of lenses. We obtained three-dimensional elasticity maps of the lenses in live mice, which showed biomechanical heterogeneity in the cortex and nucleus of the lens with high spatial resolution. An in vivo longitudinal study of mice over a period of 2 months revealed a marked age-related stiffening of the lens nucleus. We found remarkably good correlation (log-log linear) between the Brillouin elastic modulus and the Young's modulus measured by conventional mechanical techniques at low frequencies (∼1 Hz). Our results suggest that Brillouin microscopy is potentially useful for basic and animal research and clinical ophthalmology. PMID:21943436

In vivo measurement of age-related stiffening in the crystalline lens by Brillouin optical microscopy.

PubMed

Scarcelli, Giuliano; Kim, Pilhan; Yun, Seok Hyun

2011-09-21

The biophysical and biomechanical properties of the crystalline lens (e.g., viscoelasticity) have long been implicated in accommodation and vision problems, such as presbyopia and cataracts. However, it has been difficult to measure such parameters noninvasively. Here, we used in vivo Brillouin optical microscopy to characterize material acoustic properties at GHz frequency and measure the longitudinal elastic moduli of lenses. We obtained three-dimensional elasticity maps of the lenses in live mice, which showed biomechanical heterogeneity in the cortex and nucleus of the lens with high spatial resolution. An in vivo longitudinal study of mice over a period of 2 months revealed a marked age-related stiffening of the lens nucleus. We found remarkably good correlation (log-log linear) between the Brillouin elastic modulus and the Young's modulus measured by conventional mechanical techniques at low frequencies (~1 Hz). Our results suggest that Brillouin microscopy is potentially useful for basic and animal research and clinical ophthalmology. Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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.

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

NASA Astrophysics Data System (ADS)

Sid, S.; Terrapon, V. E.; Dubief, Y.

2018-02-01

The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to Reτ=85 , which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, Wiτ=40 ,100 , are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed turbulence, eventually leading to flow laminarization. A sufficiently high Schmidt number (weakly diffusive polymers) is necessary to allow self-sustained turbulence to settle. Although EIT can withstand a low amount of diffusion and remains in a nonlaminar chaotic state, adding a finite amount of GAD in the system can have an impact on the dynamics and lead to important quantitative changes, even for Schmidt numbers as large as 102. The use of GAD should therefore be avoided in viscoelastic flow simulations.

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

NASA Astrophysics Data System (ADS)

Peng, Heng; Liu, Yinghua; Chen, Haofeng

2018-05-01

In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

A Flight Dynamics Model for a Multi-Actuated Flexible Rocket Vehicle

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2011-01-01

A comprehensive set of motion equations for a multi-actuated flight vehicle is presented. The dynamics are derived from a vector approach that generalizes the classical linear perturbation equations for flexible launch vehicles into a coupled three-dimensional model. The effects of nozzle and aerosurface inertial coupling, sloshing propellant, and elasticity are incorporated without restrictions on the position, orientation, or number of model elements. The present formulation is well suited to matrix implementation for large-scale linear stability and sensitivity analysis and is also shown to be extensible to nonlinear time-domain simulation through the application of a special form of Lagrange s equations in quasi-coordinates. The model is validated through frequency-domain response comparison with a high-fidelity planar implementation.

Magnetorheological elastomer vibration isolation of tunable three-dimensional locally resonant acoustic metamaterial

NASA Astrophysics Data System (ADS)

Xu, Zhenlong; Tong, Jie; Wu, Fugen

2018-03-01

Magnetorheological elastomers (MREs) are used as cladding in three-dimensional locally resonant acoustic metamaterial (LRAM) cores. The metamaterial units are combined into a vibration isolator. Two types of LRAMs, namely, cubic and spherical kernels, are constructed. The finite element method is used to analyze the elastic band structures, transmittances, and vibration modes of the incident elastic waves. Results show that the central position and width of the LRAM elastic bandgap can be controlled by the application of an external magnetic field; furthermore, they can be adjusted by changing the MRE cladding thickness. These methods contribute to the design of metamaterial MRE vibration isolators.

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.

Simulations of dynamics of plunge and pitch of a three-dimensional flexible wing in a low Reynolds number flow

NASA Astrophysics Data System (ADS)

Qi, Dewei; Liu, Yingming; Shyy, Wei; Aono, Hikaru

2010-09-01

The lattice Boltzmann flexible particle method (LBFPM) is used to simulate fluid-structure interaction and motion of a flexible wing in a three-dimensional space. In the method, a beam with rectangular cross section has been discretized into a chain of rigid segments. The segments are connected through ball and socket joints at their ends and may be bent and twisted. Deformation of flexible structure is treated with a linear elasticity model through bending and twisting. It is demonstrated that the flexible particle method (FPM) can approximate the nonlinear Euler-Bernoulli beam equation without resorting to a nonlinear elasticity model. Simulations of plunge and pitch of flexible wing at Reynolds number Re=136 are conducted in hovering condition by using the LBFPM. It is found that both lift and drag forces increase first, then decrease dramatically as the bending rigidity in spanwise direction decreases and that the lift and drag forces are sensitive to rigidity in a certain range. It is shown that the downwash flows induced by wing tip and trailing vortices in wake area are larger for a flexible wing than for a rigid wing, lead to a smaller effective angle of attack, and result in a larger lift force.

Simulating Fatigue Crack Growth in Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Spievak, Lisa E.; Wawrzynek, Paul A.; Ingraffea, Anthony R.

2000-01-01

The majority of helicopter transmission systems utilize spiral bevel gears to convert the horizontal power from the engine into vertical power for the rotor. Due to the cyclical loading on a gear's tooth, fatigue crack propagation can occur. In rotorcraft applications, a crack's trajectory determines whether the gear failure will be benign or catastrophic for the aircraft. As a result, the capability to predict crack growth in gears is significant. A spiral bevel gear's complex shape requires a three dimensional model of the geometry and cracks. The boundary element method in conjunction with linear elastic fracture mechanics theories is used to predict arbitrarily shaped three dimensional fatigue crack trajectories in a spiral bevel pinion under moving load conditions. The predictions are validated by comparison to experimental results. The sensitivity of the predictions to variations in loading conditions and crack growth rate model parameters is explored. Critical areas that must be understood in greater detail prior to predicting more accurate crack trajectories and crack growth rates in three dimensions are identified.

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

1973-01-01

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

Rotational elasticity

NASA Astrophysics Data System (ADS)

Vassiliev, Dmitri

2017-04-01

We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Simplified computational methods for elastic and elastic-plastic fracture problems

NASA Technical Reports Server (NTRS)

Atluri, Satya N.

1992-01-01

An overview is given of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fractures. Topics covered include analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids, with crack faces being subjected to arbitrary tractions; finite element or boundary element alternating methods for two or three dimensional crack problems; a 'direct stiffness' method for stiffened panels with flexible fasteners and with multiple cracks; multiple site damage near a row of fastener holes; an analysis of cracks with bonded repair patches; methods for the generation of weight functions for two and three dimensional crack problems; and domain-integral methods for elastic-plastic or inelastic crack mechanics.

Estimation of parameters of constant elasticity of substitution production functional model

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi

2017-11-01

Nonlinear model building has become an increasing important powerful tool in mathematical economics. In recent years the popularity of applications of nonlinear models has dramatically been rising up. Several researchers in econometrics are very often interested in the inferential aspects of nonlinear regression models [6]. The present research study gives a distinct method of estimation of more complicated and highly nonlinear model viz Constant Elasticity of Substitution (CES) production functional model. Henningen et.al [5] proposed three solutions to avoid serious problems when estimating CES functions in 2012 and they are i) removing discontinuities by using the limits of the CES function and its derivative. ii) Circumventing large rounding errors by local linear approximations iii) Handling ill-behaved objective functions by a multi-dimensional grid search. Joel Chongeh et.al [7] discussed the estimation of the impact of capital and labour inputs to the gris output agri-food products using constant elasticity of substitution production function in Tanzanian context. Pol Antras [8] presented new estimates of the elasticity of substitution between capital and labour using data from the private sector of the U.S. economy for the period 1948-1998.

Remote Sensing of Three-dimensional Winds with Elastic Lidar: Explanation of Maximum Cross-correlation Method

NASA Astrophysics Data System (ADS)

Buttler, William T.; Soriano, Cecilia; Baldasano, Jose M.; Nickel, George H.

Maximum cross-correlation provides a method toremotely de-ter-mine high-lyre-solved three-dimensional fields of horizontalwinds with e-las-tic li-darthrough-out large volumes of the planetaryboundary layer (PBL). This paperdetails the technique and shows comparisonsbetween elastic lidar winds, remotelysensed laser Doppler velocimeter (LDV) windprofiles, and radiosonde winds.Radiosonde wind data were acquired at Barcelona,Spain, during the BarcelonaAir-Quality Initiative (1992), and the LDVwind data were acquired at SunlandPark, New Mexico during the 1994 Border AreaAir-Quality Study. Comparisonsshow good agreement between the differentinstruments, and demonstrate the methoduseful for air pollution management at thelocal/regional scale. Elastic lidar windscould thus offer insight into aerosol andpollution transport within the PBL. Lidarwind fields might also be used to nudge orimprove initialization and evaluation ofatmospheric meteorological models.

The mathematical formulation of a generalized Hooke's law for blood vessels.

PubMed

Zhang, Wei; Wang, Chong; Kassab, Ghassan S

2007-08-01

It is well known that the stress-strain relationship of blood vessels is highly nonlinear. To linearize the relationship, the Hencky strain tensor is generalized to a logarithmic-exponential (log-exp) strain tensor to absorb the nonlinearity. A quadratic nominal strain potential is proposed to derive the second Piola-Kirchhoff stresses by differentiating the potential with respect to the log-exp strains. The resulting constitutive equation is a generalized Hooke's law. Ten material constants are needed for the three-dimensional orthotropic model. The nondimensional constant used in the log-exp strain definition is interpreted as a nonlinearity parameter. The other nine constants are the elastic moduli with respect to the log-exp strains. In this paper, the proposed linear stress-strain relation is shown to represent the pseudoelastic Fung model very well.

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.

Robust estimation of carotid artery wall motion using the elasticity-based state-space approach.

PubMed

Gao, Zhifan; Xiong, Huahua; Liu, Xin; Zhang, Heye; Ghista, Dhanjoo; Wu, Wanqing; Li, Shuo

2017-04-01

The dynamics of the carotid artery wall has been recognized as a valuable indicator to evaluate the status of atherosclerotic disease in the preclinical stage. However, it is still a challenge to accurately measure this dynamics from ultrasound images. This paper aims at developing an elasticity-based state-space approach for accurately measuring the two-dimensional motion of the carotid artery wall from the ultrasound imaging sequences. In our approach, we have employed a linear elasticity model of the carotid artery wall, and converted it into the state space equation. Then, the two-dimensional motion of carotid artery wall is computed by solving this state-space approach using the H ∞ filter and the block matching method. In addition, a parameter training strategy is proposed in this study for dealing with the parameter initialization problem. In our experiment, we have also developed an evaluation function to measure the tracking accuracy of the motion of the carotid artery wall by considering the influence of the sizes of the two blocks (acquired by our approach and the manual tracing) containing the same carotid wall tissue and their overlapping degree. Then, we have compared the performance of our approach with the manual traced results drawn by three medical physicians on 37 healthy subjects and 103 unhealthy subjects. The results have showed that our approach was highly correlated (Pearson's correlation coefficient equals 0.9897 for the radial motion and 0.9536 for the longitudinal motion), and agreed well (width the 95% confidence interval is 89.62 µm for the radial motion and 387.26 µm for the longitudinal motion) with the manual tracing method. We also compared our approach to the three kinds of previous methods, including conventional block matching methods, Kalman-based block matching methods and the optical flow. Altogether, we have been able to successfully demonstrate the efficacy of our elasticity-model based state-space approach (EBS) for more accurate tracking of the 2-dimensional motion of the carotid artery wall, towards more effective assessment of the status of atherosclerotic disease in the preclinical stage. Copyright © 2017 Elsevier B.V. All rights reserved.

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

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

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

1997-12-01

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

Multigrid finite element method in stress analysis of three-dimensional elastic bodies of heterogeneous structure

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2016-11-01

To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.

Transient Non Lin Deformation in Fractured Rock

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

Sartori, Enrico

1998-10-14

MATLOC is a nonlinear, transient, two-dimensional (planer and axisymmetric), thermal stress, finite-element code designed to determine the deformation within a fractured rock mass. The mass is modeled as a nonlinear anistropic elastic material which can exhibit stress-dependent bi-linear locking behavior.

Nonlinear finite-element analysis of nanoindentation of viral capsids

NASA Astrophysics Data System (ADS)

Gibbons, Melissa M.; Klug, William S.

2007-03-01

Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage ϕ29 . As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young’s moduli of ≈280-360MPa for CCMV and ≈4.5GPa for ϕ29 .

Mechanical behaviour of the human atria.

PubMed

Bellini, Chiara; Di Martino, Elena S; Federico, Salvatore

2013-07-01

This work was aimed at providing a local mechanical characterisation of tissues from the healthy human atria. Thirty-two tissue specimens were harvested from nine adult subjects whose death was not directly related to cardiovascular diseases. Tissues were kept in Tyrode's solution and tested using a planar biaxial device. Results showed that tissues from healthy human atria undergo large deformations under in-plane distributed tensions roughly corresponding to an in vivo pressure of 15 mmHg. The material was modelled as hyperelastic and a Fung-type elastic strain energy potential was chosen. This class of potentials is based on a function of a quadratic form in the components of the Green-Lagrange strain tensor, and it has been previously proved that the fourth-order tensor of this quadratic form is proportional to the linear elasticity tensor of the linearised theory. This has three important consequences: (i) the coefficients in Fung-type potentials have a precise physical meaning; (ii) whenever a microstructural description for the linear elasticity tensor is available, this is automatically inherited by the Fung-type potential; (iii) because of the presence of the linear elasticity tensor in the definition of a Fung-type potential, each of the three normal stresses is coupled with all three normal strains.We propose to include information on the microstructure of the atrium by writing the linear elasticity tensor as the volumetric-fraction-weighed sum of the linear elasticity tensors of the three constituents of the tissue: the ground matrix, the main fibre family and the secondary fibre family. To the best of our knowledge, this is the first time that a Fung-type potential is given a precise structural meaning, based on the directions and the material properties of the fibres. Because of the coupling between normal strains and normal stresses, this structurally-based Fung-type potential allows for discriminating among all testing protocols in planar biaxial stretch.

Three-Dimensional Anisotropic Acoustic and Elastic Full-Waveform Seismic Inversion

NASA Astrophysics Data System (ADS)

Warner, M.; Morgan, J. V.

2013-12-01

Three-dimensional full-waveform inversion is a high-resolution, high-fidelity, quantitative, seismic imaging technique that has advanced rapidly within the oil and gas industry. The method involves the iterative improvement of a starting model using a series of local linearized updates to solve the full non-linear inversion problem. During the inversion, forward modeling employs the full two-way three-dimensional heterogeneous anisotropic acoustic or elastic wave equation to predict the observed raw field data, wiggle-for-wiggle, trace-by-trace. The method is computationally demanding; it is highly parallelized, and runs on large multi-core multi-node clusters. Here, we demonstrate what can be achieved by applying this newly practical technique to several high-density 3D seismic datasets that were acquired to image four contrasting sedimentary targets: a gas cloud above an oil reservoir, a radially faulted dome, buried fluvial channels, and collapse structures overlying an evaporate sequence. We show that the resulting anisotropic p-wave velocity models match in situ measurements in deep boreholes, reproduce detailed structure observed independently on high-resolution seismic reflection sections, accurately predict the raw seismic data, simplify and sharpen reverse-time-migrated reflection images of deeper horizons, and flatten Kirchhoff-migrated common-image gathers. We also show that full-elastic 3D full-waveform inversion of pure pressure data can generate a reasonable shear-wave velocity model for one of these datasets. For two of the four datasets, the inclusion of significant transversely isotropic anisotropy with a vertical axis of symmetry was necessary in order to fit the kinematics of the field data properly. For the faulted dome, the full-waveform-inversion p-wave velocity model recovers the detailed structure of every fault that can be seen on coincident seismic reflection data. Some of the individual faults represent high-velocity zones, some represent low-velocity zones, some have more-complex internal structure, and some are visible merely as offsets between two regions with contrasting velocity. Although this has not yet been demonstrated quantitatively for this dataset, it seems likely that at least some of this fine structure in the recovered velocity model is related to the detailed lithology, strain history and fluid properties within the individual faults. We have here applied this technique to seismic data that were acquired by the extractive industries, however this inversion scheme is immediately scalable and applicable to a much wider range of problems given sufficient quality and density of observed data. Potential targets range from shallow magma chambers beneath active volcanoes, through whole-crustal sections across plate boundaries, to regional and whole-Earth models.

Random three-dimensional jammed packings of elastic shells acting as force sensors

NASA Astrophysics Data System (ADS)

Jose, Jissy; van Blaaderen, Alfons; Imhof, Arnout

2016-06-01

In a jammed solid of granular particles, the applied stress is in-homogeneously distributed within the packing. A full experimental characterization requires measurement of all the interparticle forces, but so far such measurements are limited to a few systems in two and even fewer in three dimensions. Particles with the topology of (elastic) shells are good local force sensors as relatively large deformations of the shells result from relatively small forces. We recently introduced such fluorescent shells as a model granular system in which force distributions can be determined in three dimensions using confocal microscopy and quantitative image analysis. An interesting aspect about these shells that differentiates them from other soft deformable particles is their buckling behavior at higher compression. This leads to deformations that do not conserve the inner volume of the particle. Here we use this system to accurately measure the contact forces in a three-dimensional packing of shells subjected to a static anisotropic compression and to shear. At small deformations forces are linear, however, for a buckled contact, the restoring force is related to the amount of deformation by a square root law, as follows from the theory of elasticity of shells. Near the unjamming-jamming transition (point J ), we found the probability distribution of the interparticle forces P (f ) to decay nearly exponentially at large forces, with little evidence of long-range force chains in the packings. As the packing density is increased, the tail of the distribution was found to crossover to a Gaussian, in line with other experimental and simulation studies. Under a small shear strain, up to 0.216, applied at an extremely low shear rate, we observed a shear-induced anisotropy in both the pair correlation function and contact force network; however, no appreciable change was seen in the number of contacts per particle.

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.

Forming three-dimensional closed shapes from two-dimensional soft ribbons by controlled buckling

PubMed Central

Aoki, Michio

2018-01-01

Conventional manufacturing techniques—moulding, machining and casting—exist to produce three-dimensional (3D) shapes. However, these industrial processes are typically geared for mass production and are not directly applicable to residential settings, where inexpensive and versatile tools are desirable. Moreover, those techniques are, in general, not adequate to process soft elastic materials. Here, we introduce a new concept of forming 3D closed hollow shapes from two-dimensional (2D) elastic ribbons by controlled buckling. We numerically and experimentally characterize how the profile and thickness of the ribbon determine its buckled shape. We find a 2D master profile with which various elliptical 3D shapes can be formed. More complex natural and artificial hollow shapes, such as strawberry, hourglass and wheel, can also be achieved via strategic design and pattern engraving on the ribbons. The nonlinear response of the post-buckling regime is rationalized through finite-element analysis, which shows good quantitative agreement with experiments. This robust fabrication should complement conventional techniques and provide a rich arena for future studies on the mechanics and new applications of elastic hollow structures. PMID:29515894

Forming three-dimensional closed shapes from two-dimensional soft ribbons by controlled buckling

NASA Astrophysics Data System (ADS)

Aoki, Michio; Juang, Jia-Yang

2018-02-01

Conventional manufacturing techniques-moulding, machining and casting-exist to produce three-dimensional (3D) shapes. However, these industrial processes are typically geared for mass production and are not directly applicable to residential settings, where inexpensive and versatile tools are desirable. Moreover, those techniques are, in general, not adequate to process soft elastic materials. Here, we introduce a new concept of forming 3D closed hollow shapes from two-dimensional (2D) elastic ribbons by controlled buckling. We numerically and experimentally characterize how the profile and thickness of the ribbon determine its buckled shape. We find a 2D master profile with which various elliptical 3D shapes can be formed. More complex natural and artificial hollow shapes, such as strawberry, hourglass and wheel, can also be achieved via strategic design and pattern engraving on the ribbons. The nonlinear response of the post-buckling regime is rationalized through finite-element analysis, which shows good quantitative agreement with experiments. This robust fabrication should complement conventional techniques and provide a rich arena for future studies on the mechanics and new applications of elastic hollow structures.

A simple mechanical system mimicking phase transitions in a one-dimensional medium

NASA Astrophysics Data System (ADS)

Charru, François

1997-11-01

We study a simple mechanical oscillator the bifurcations of which illustrate first- and second-order phase transitions. The phase diagram of the oscillator exhibits a coexistence curve. This curve ends at a critical point, where three critical exponents can be defined. A metronome may be used to illustrate the main results. We then consider a linear array of such oscillators with elastic coupling, which is governed by the damped Klein - Gordon equation. The classical solutions of this equation, such as fronts propagating in an unstable or in a metastable state, can be guessed at and discussed from the point of view of a mechanical model.

Propulsion of flexible polymer structures in a rotating magnetic field.

PubMed

Garstecki, Piotr; Tierno, Pietro; Weibel, Douglas B; Sagués, Francesc; Whitesides, George M

2009-05-20

We demonstrate a new concept for the propulsions of abiological structures at low Reynolds numbers. The approach is based on the design of flexible, planar polymer structures with a permanent magnetic moment. In the presence of an external, uniform, rotating magnetic field these structures deform into three-dimensional shapes that have helical symmetry and translate linearly through fluids at Re between 10(-1) and 10. The mechanism for the motility of these structures involves reversible deformation that breaks their planar symmetry and generates propulsion. These elastic propellers resemble microorganisms that use rotational mechanisms based on flagella and cilia for their motility in fluids at low Re.

An approximation method for configuration optimization of trusses

NASA Technical Reports Server (NTRS)

Hansen, Scott R.; Vanderplaats, Garret N.

1988-01-01

Two- and three-dimensional elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints. Constraints on member stresses and Euler buckling are imposed and multiple static loading conditions are considered. The method presented here utilizes an approximate structural analysis based on first order Taylor series expansions of the member forces. A numerical optimizer minimizes the weight of the truss using information from the approximate structural analysis. Comparisons with results from other methods are made. It is shown that the method of forming an approximate structural analysis based on linearized member forces leads to a highly efficient method of truss configuration optimization.

A numerical approximation to the elastic properties of sphere-reinforced composites

NASA Astrophysics Data System (ADS)

Segurado, J.; Llorca, J.

2002-10-01

Three-dimensional cubic unit cells containing 30 non-overlapping identical spheres randomly distributed were generated using a new, modified random sequential adsortion algorithm suitable for particle volume fractions of up to 50%. The elastic constants of the ensemble of spheres embedded in a continuous and isotropic elastic matrix were computed through the finite element analysis of the three-dimensional periodic unit cells, whose size was chosen as a compromise between the minimum size required to obtain accurate results in the statistical sense and the maximum one imposed by the computational cost. Three types of materials were studied: rigid spheres and spherical voids in an elastic matrix and a typical composite made up of glass spheres in an epoxy resin. The moduli obtained for different unit cells showed very little scatter, and the average values obtained from the analysis of four unit cells could be considered very close to the "exact" solution to the problem, in agreement with the results of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) referring to the size of the representative volume element for elastic composites. They were used to assess the accuracy of three classical analytical models: the Mori-Tanaka mean-field analysis, the generalized self-consistent method, and Torquato's third-order approximation.

Effect of chordwise forces and deformations and deformations due to steady lift on wing flutter

NASA Technical Reports Server (NTRS)

Boyd, W. N.

1977-01-01

This investigation explores the effects of chordwise forces and deformations and steady-state deformation due to lift on the static and dynamic aeroelastic stability of a uniform cantilever wing. Results of this analysis are believed to have practical applications for high-performance sailplanes and certain RPV's. The airfoil cross section is assumed to be symmetric and camber bending is neglected. Motions in vertical bending, fore-and-aft bending, and torsion are considered. A differential equation model is developed, which included the nonlinear elastic bending-torsion coupling that accompanies even moderate deflections. A linearized expansion in small time-dependent deflections is made about a steady flight condition. The stability determinant of the linearized system then contains coefficients that depend on steady displacements. Loads derived from two-dimensional incompressible aerodynamic theory are used to obtain the majority of the results, but cases using three-dimensional subsonic compressible theory are also studied. The stability analysis is carried out in terms of the dynamically uncoupled natural modes of vibration of the uniform cantilever.

Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation

NASA Astrophysics Data System (ADS)

Bokhari, Ashfaque H.; Mahomed, F. M.; Zaman, F. D.

2010-05-01

The complete symmetry group classification of the fourth-order Euler-Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, is obtained. We perform the Lie and Noether symmetry analysis of this problem. In the Lie analysis, the principal Lie algebra which is one dimensional extends in four cases, viz. the linear, exponential, general power law, and a negative fractional power law. It is further shown that two cases arise in the Noether classification with respect to the standard Lagrangian. That is, the linear case for which the Noether algebra dimension is one less than the Lie algebra dimension as well as the negative fractional power law. In the latter case the Noether algebra is three dimensional and is isomorphic to the Lie algebra which is sl(2,R). This exceptional case, although admitting the nonsolvable algebra sl(2,R), remarkably allows for a two-parameter family of exact solutions via the Noether integrals. The Lie reduction gives a second-order ordinary differential equation which has nonlocal symmetry.

Visualising elastic anisotropy: theoretical background and computational implementation

NASA Astrophysics Data System (ADS)

Nordmann, J.; Aßmus, M.; Altenbach, H.

2018-02-01

In this article, we present the technical realisation for visualisations of characteristic parameters of the fourth-order elasticity tensor, which is classified by three-dimensional symmetry groups. Hereby, expressions for spatial representations of uc(Young)'s modulus and bulk modulus as well as plane representations of shear modulus and uc(Poisson)'s ratio are derived and transferred into a comprehensible form to computer algebra systems. Additionally, we present approaches for spatial representations of both latter parameters. These three- and two-dimensional representations are implemented into the software MATrix LABoratory. Exemplary representations of characteristic materials complete the present treatise.

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

NASA Astrophysics Data System (ADS)

Igumnov, Leonid; Ipatov, Aleksandr; Belov, Aleksandr; Petrov, Andrey

2015-09-01

The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.

Discrete Breathers in One-Dimensional Diatomic Granular Crystals

NASA Astrophysics Data System (ADS)

Boechler, N.; Theocharis, G.; Job, S.; Kevrekidis, P. G.; Porter, Mason A.; Daraio, C.

2010-06-01

We report the experimental observation of modulational instability and discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characterize their effective linear spectrum both theoretically and experimentally. We then illustrate theoretically and numerically the modulational instability of the lower edge of the optical band. This leads to the dynamical formation of long-lived breather structures, whose families of solutions we compute throughout the linear spectral gap. Finally, we experimentally observe the manifestation of the modulational instability and the resulting generation of localized breathing modes with quantitative characteristics that agree with our numerical results.

Differentiation of benign from malignant solid breast masses: comparison of two-dimensional and three-dimensional shear-wave elastography.

PubMed

Lee, Su Hyun; Chang, Jung Min; Kim, Won Hwa; Bae, Min Sun; Cho, Nariya; Yi, Ann; Koo, Hye Ryoung; Kim, Seung Ja; Kim, Jin You; Moon, Woo Kyung

2013-04-01

To prospectively compare the diagnostic performances of two-dimensional (2D) and three-dimensional (3D) shear-wave elastography (SWE) for differentiating benign from malignant breast masses. B-mode ultrasound and SWE were performed for 134 consecutive women with 144 breast masses before biopsy. Quantitative elasticity values (maximum and mean elasticity in the stiffest portion of mass, Emax and Emean; lesion-to-fat elasticity ratio, Erat) were measured with both 2D and 3D SWE. The area under the receiver operating characteristic curve (AUC), sensitivity and specificity of B-mode, 2D, 3D SWE and combined data of B-mode and SWE were compared. Sixty-seven of the 144 breast masses (47 %) were malignant. Overall, higher elasticity values of 3D SWE than 2D SWE were noted for both benign and malignant masses. The AUC for 2D and 3D SWE were not significantly different: Emean, 0.938 vs 0.928; Emax, 0.939 vs 0.930; Erat, 0.907 vs 0.871. Either 2D or 3D SWE significantly improved the specificity of B-mode ultrasound from 29.9 % (23 of 77) up to 71.4 % (55 of 77) and 63.6 % (49 of 77) without a significant change in sensitivity. Two-dimensional and 3D SWE performed equally in distinguishing benign from malignant masses and both techniques improved the specificity of B-mode ultrasound.

Vibration control of multiferroic fibrous composite plates using active constrained layer damping

NASA Astrophysics Data System (ADS)

Kattimani, S. C.; Ray, M. C.

2018-06-01

Geometrically nonlinear vibration control of fiber reinforced magneto-electro-elastic or multiferroic fibrous composite plates using active constrained layer damping treatment has been investigated. The piezoelectric (BaTiO3) fibers are embedded in the magnetostrictive (CoFe2O4) matrix forming magneto-electro-elastic or multiferroic smart composite. A three-dimensional finite element model of such fiber reinforced magneto-electro-elastic plates integrated with the active constrained layer damping patches is developed. Influence of electro-elastic, magneto-elastic and electromagnetic coupled fields on the vibration has been studied. The Golla-Hughes-McTavish method in time domain is employed for modeling a constrained viscoelastic layer of the active constrained layer damping treatment. The von Kármán type nonlinear strain-displacement relations are incorporated for developing a three-dimensional finite element model. Effect of fiber volume fraction, fiber orientation and boundary conditions on the control of geometrically nonlinear vibration of the fiber reinforced magneto-electro-elastic plates is investigated. The performance of the active constrained layer damping treatment due to the variation of piezoelectric fiber orientation angle in the 1-3 Piezoelectric constraining layer of the active constrained layer damping treatment has also been emphasized.

Three dimensional dynamics of a flexible Motorised Momentum Exchange Tether

NASA Astrophysics Data System (ADS)

Ismail, N. A.; Cartmell, M. P.

2016-03-01

This paper presents a new flexural model for the three dimensional dynamics of the Motorised Momentum Exchange Tether (MMET) concept. This study has uncovered the relationships between planar and nonplanar motions, and the effect of the coupling between these two parameters on pragmatic circular and elliptical orbits. The tether sub-spans are modelled as stiffened strings governed by partial differential equations of motion, with specific boundary conditions. The tether sub-spans are flexible and elastic, thereby allowing three dimensional displacements. The boundary conditions lead to a specific frequency equation and the eigenvalues from this provide the natural frequencies of the orbiting flexible motorised tether when static, accelerating in monotonic spin, and at terminal angular velocity. A rotation transformation matrix has been utilised to get the position vectors of the system's components in an assumed inertial frame. Spatio-temporal coordinates are transformed to modal coordinates before applying Lagrange's equations, and pre-selected linear modes are included to generate the equations of motion. The equations of motion contain inertial nonlinearities which are essentially of cubic order, and these show the potential for intricate intermodal coupling effects. A simulation of planar and non-planar motions has been undertaken and the differences in the modal responses, for both motions, and between the rigid body and flexible models are highlighted and discussed.

Shear-wave elasticity measurements of three-dimensional cell cultures for mechanobiology

PubMed Central

Kuo, Po-Ling; Charng, Ching-Che; Wu, Po-Chen

2017-01-01

ABSTRACT Studying mechanobiology in three-dimensional (3D) cell cultures better recapitulates cell behaviors in response to various types of mechanical stimuli in vivo. Stiffening of the extracellular matrix resulting from cell remodeling potentiates many pathological conditions, including advanced cancers. However, an effective tool for measuring the spatiotemporal changes in elastic properties of such 3D cell cultures without directly contacting the samples has not been reported previously. We describe an ultrasonic shear-wave-based platform for quantitatively evaluating the spatiotemporal dynamics of the elasticity of a matrix remodeled by cells cultured in 3D environments. We used this approach to measure the elasticity changes of 3D matrices grown with highly invasive lung cancer cells and cardiac myoblasts, and to delineate the principal mechanism underlying the stiffening of matrices remodeled by these cells. The described approach can be a useful tool in fields investigating and manipulating the mechanotransduction of cells in 3D contexts, and also has potential as a drug-screening platform. PMID:27505887

Nonlinear elasticity in rocks: A comprehensive three-dimensional description

DOE PAGES

Lott, Martin; Remillieux, Marcel; Garnier, Vincent; ...

2017-07-17

Here we study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency “pump” wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe” wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists ofmore » the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) $P$ and (shear) $S$ waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.« less

An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels.

PubMed

Fambri, Francesco; Dumbser, Michael; Casulli, Vincenzo

2014-11-01

Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea of the method consists in a splitting of the pressure into a hydrostatic and a non-hydrostatic part, where first a small quasi-one-dimensional nonlinear system is solved for the hydrostatic pressure and only in a second step the fully three-dimensional non-hydrostatic pressure is computed from a three-dimensional nonlinear system as a correction to the hydrostatic one. The resulting algorithm is robust, efficient, locally and globally mass conservative, and applies to hydrostatic and non-hydrostatic flows in one, two and three space dimensions. These features are illustrated on nontrivial test cases for flows in tubes with circular or elliptical cross section where the exact analytical solution is known. Test cases of steady and pulsatile flows in uniformly curved rigid and elastic tubes are presented. Wherever possible, axial velocity development and secondary flows are shown and compared with previously published results. Copyright © 2014 John Wiley & Sons, Ltd.

Noninvasive evaluation of left ventricular elastance according to pressure-volume curves modeling in arterial hypertension.

PubMed

Bonnet, Benjamin; Jourdan, Franck; du Cailar, Guilhem; Fesler, Pierre

2017-08-01

End-systolic left ventricular (LV) elastance ( E es ) has been previously calculated and validated invasively using LV pressure-volume (P-V) loops. Noninvasive methods have been proposed, but clinical application remains complex. The aims of the present study were to 1 ) estimate E es according to modeling of the LV P-V curve during ejection ("ejection P-V curve" method) and validate our method with existing published LV P-V loop data and 2 ) test the clinical applicability of noninvasively detecting a difference in E es between normotensive and hypertensive subjects. On the basis of the ejection P-V curve and a linear relationship between elastance and time during ejection, we used a nonlinear least-squares method to fit the pressure waveform. We then computed the slope and intercept of time-varying elastance as well as the volume intercept (V 0 ). As a validation, 22 P-V loops obtained from previous invasive studies were digitized and analyzed using the ejection P-V curve method. To test clinical applicability, ejection P-V curves were obtained from 33 hypertensive subjects and 32 normotensive subjects with carotid tonometry and real-time three-dimensional echocardiography during the same procedure. A good univariate relationship ( r 2  = 0.92, P < 0.005) and good limits of agreement were found between the invasive calculation of E es and our new proposed ejection P-V curve method. In hypertensive patients, an increase in arterial elastance ( E a ) was compensated by a parallel increase in E es without change in E a / E es In addition, the clinical reproducibility of our method was similar to that of another noninvasive method. In conclusion, E es and V 0 can be estimated noninvasively from modeling of the P-V curve during ejection. This approach was found to be reproducible and sensitive enough to detect an expected increase in LV contractility in hypertensive patients. Because of its noninvasive nature, this methodology may have clinical implications in various disease states. NEW & NOTEWORTHY The use of real-time three-dimensional echocardiography-derived left ventricular volumes in conjunction with carotid tonometry was found to be reproducible and sensitive enough to detect expected differences in left ventricular elastance in arterial hypertension. Because of its noninvasive nature, this methodology may have clinical implications in various disease states. Copyright © 2017 the American Physiological Society.

Mixed-mode fracture mechanics parameters of elliptical interface cracks in anisotropic bimaterials

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

Xue, Y.; Qu, J.

1999-07-01

Two-dimensional interface cracks in anisotropic bimaterials have been studied extensively in the literature. However, solutions to three-dimensional interface cracks in anisotropic bimaterials are not available, except for circular (penny-shaped) cracks. In this paper, an elliptical crack on the interface between two anisotropic elastic half-spaces is considered. A formal solution is obtained by using the Stroh method in two dimensional elasticity in conjunction with the Fourier transform method. To illustrate the solution procedure, an elliptical delamination in a cross-ply composite is solved. Numerical results of the stress intensity factors and energy release rate along the crack front are obtained terms ofmore » the interfacial matrix M. It is found that the fields near the crack front are often in mixed mode, due to material anisotropy and the three dimensional nature of the crack front.« less

Coarse-grained mechanics of viral shells

NASA Astrophysics Data System (ADS)

Klug, William S.; Gibbons, Melissa M.

2008-03-01

We present an approach for creating three-dimensional finite element models of viral capsids from atomic-level structural data (X-ray or cryo-EM). The models capture heterogeneous geometric features and are used in conjunction with three-dimensional nonlinear continuum elasticity to simulate nanoindentation experiments as performed using atomic force microscopy. The method is extremely flexible; able to capture varying levels of detail in the three-dimensional structure. Nanoindentation simulations are presented for several viruses: Hepatitis B, CCMV, HK97, and φ29. In addition to purely continuum elastic models a multiscale technique is developed that combines finite-element kinematics with MD energetics such that large-scale deformations are facilitated by a reduction in degrees of freedom. Simulations of these capsid deformation experiments provide a testing ground for the techniques, as well as insight into the strength-determining mechanisms of capsid deformation. These methods can be extended as a framework for modeling other proteins and macromolecular structures in cell biology.

The load separation technique in the elastic-plastic fracture analysis of two- and three-dimensional geometries

NASA Technical Reports Server (NTRS)

Sharobeam, Monir H.

1994-01-01

Load separation is the representation of the load in the test records of geometries containing cracks as a multiplication of two separate functions: a crack geometry function and a material deformation function. Load separation is demonstrated in the test records of several two-dimensional geometries such as compact tension geometry, single edge notched bend geometry, and center cracked tension geometry and three-dimensional geometries such as semi-elliptical surface crack. The role of load separation in the evaluation of the fracture parameter J-integral and the associated factor eta for two-dimensional geometries is discussed. The paper also discusses the theoretical basis and the procedure for using load separation as a simplified yet accurate approach for plastic J evaluation in semi-elliptical surface crack which is a three-dimensional geometry. The experimental evaluation of J, and particularly J(sub pl), for three-dimensional geometries is very challenging. A few approaches have been developed in this regard and they are either complex or very approximate. The paper also presents the load separation as a mean to identify the blunting and crack growth regions in the experimental test records of precracked specimens. Finally, load separation as a methodology in elastic-plastic fracture mechanics is presented.

Some remarks on elastic crack-tip stress fields.

NASA Technical Reports Server (NTRS)

Rice, J. R.

1972-01-01

It is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear elastic body in plane strain, then the stress intensity factor for any other symmetrical load system whatsoever on the same body may be directly determined. The result is closely related to Bueckner's (1970) weight function, through which the stress intensity factor is expressed as a sum of work-like products between applied forces and values of the weight function at their points of application. An example of the method is given wherein the solution for a crack in a remotely uniform stress field is used to generate the expression for the stress intensity factor due to an arbitrary traction distribution on the faces of a crack. A corresponding theory is developed in an appendix for three-dimensional crack problems, although this appears to be directly useful chiefly for problems in which there is axial symmetry.

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

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

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. Themore » notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.« less

Free and Forced Vibrations of Thick-Walled Anisotropic Cylindrical Shells

NASA Astrophysics Data System (ADS)

Marchuk, A. V.; Gnedash, S. V.; Levkovskii, S. A.

2017-03-01

Two approaches to studying the free and forced axisymmetric vibrations of cylindrical shell are proposed. They are based on the three-dimensional theory of elasticity and division of the original cylindrical shell with concentric cross-sectional circles into several coaxial cylindrical shells. One approach uses linear polynomials to approximate functions defined in plan and across the thickness. The other approach also uses linear polynomials to approximate functions defined in plan, but their variation with thickness is described by the analytical solution of a system of differential equations. Both approaches have approximation and arithmetic errors. When determining the natural frequencies by the semi-analytical finite-element method in combination with the divide and conqure method, it is convenient to find the initial frequencies by the finite-element method. The behavior of the shell during free and forced vibrations is analyzed in the case where the loading area is half the shell thickness

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1997-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic responses of axial-flow turbo-machinery blading.The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to a far-field eigenanalysis, is also described. The linearized aerodynamic and numerical models have been implemented into a three-dimensional linearized unsteady flow code, called LINFLUX. This code has been applied to selected, benchmark, unsteady, subsonic flows to establish its accuracy and to demonstrate its current capabilities. The unsteady flows considered, have been chosen to allow convenient comparisons between the LINFLUX results and those of well-known, two-dimensional, unsteady flow codes. Detailed numerical results for a helical fan and a three-dimensional version of the 10th Standard Cascade indicate that important progress has been made towards the development of a reliable and useful, three-dimensional, prediction capability that can be used in aeroelastic and aeroacoustic design studies.

The asymptotic homogenization elasticity tensor properties for composites with material discontinuities

NASA Astrophysics Data System (ADS)

Penta, Raimondo; Gerisch, Alf

2017-01-01

The classical asymptotic homogenization approach for linear elastic composites with discontinuous material properties is considered as a starting point. The sharp length scale separation between the fine periodic structure and the whole material formally leads to anisotropic elastic-type balance equations on the coarse scale, where the arising fourth rank operator is to be computed solving single periodic cell problems on the fine scale. After revisiting the derivation of the problem, which here explicitly points out how the discontinuity in the individual constituents' elastic coefficients translates into stress jump interface conditions for the cell problems, we prove that the gradient of the cell problem solution is minor symmetric and that its cell average is zero. This property holds for perfect interfaces only (i.e., when the elastic displacement is continuous across the composite's interface) and can be used to assess the accuracy of the computed numerical solutions. These facts are further exploited, together with the individual constituents' elastic coefficients and the specific form of the cell problems, to prove a theorem that characterizes the fourth rank operator appearing in the coarse-scale elastic-type balance equations as a composite material effective elasticity tensor. We both recover known facts, such as minor and major symmetries and positive definiteness, and establish new facts concerning the Voigt and Reuss bounds. The latter are shown for the first time without assuming any equivalence between coarse and fine-scale energies ( Hill's condition), which, in contrast to the case of representative volume elements, does not identically hold in the context of asymptotic homogenization. We conclude with instructive three-dimensional numerical simulations of a soft elastic matrix with an embedded cubic stiffer inclusion to show the profile of the physically relevant elastic moduli (Young's and shear moduli) and Poisson's ratio at increasing (up to 100 %) inclusion's volume fraction, thus providing a proxy for the design of artificial elastic composites.

A new global approach to obtain three-dimensional displacement maps by integrating GPS and DInSAR data

NASA Astrophysics Data System (ADS)

Guglielmino, F.; Nunnari, G.; Puglisi, G.; Spata, A.

2009-04-01

We propose a new technique, based on the elastic theory, to efficiently produce an estimate of three-dimensional surface displacement maps by integrating sparse Global Position System (GPS) measurements of deformations and Differential Interferometric Synthetic Aperture Radar (DInSAR) maps of movements of the Earth's surface. The previous methodologies known in literature, for combining data from GPS and DInSAR surveys, require two steps: the first, in which sparse GPS measurements are interpolated in order to fill in GPS displacements at the DInSAR grid, and the second, to estimate the three-dimensional surface displacement maps by using a suitable optimization technique. One of the advantages of the proposed approach is that both these steps are unified. We propose a linear matrix equation which accounts for both GPS and DInSAR data whose solution provide simultaneously the strain tensor, the displacement field and the rigid body rotation tensor throughout the entire investigated area. The mentioned linear matrix equation is solved by using the Weighted Least Square (WLS) thus assuring both numerical robustness and high computation efficiency. The proposed methodology was tested on both synthetic and experimental data, these last from GPS and DInSAR measurements carried out on Mt. Etna. The goodness of the results has been evaluated by using standard errors. These tests also allow optimising the choice of specific parameters of this algorithm. This "open" structure of the method will allow in the near future to take account of other available data sets, such as additional interferograms, or other geodetic data (e.g. levelling, tilt, etc.), in order to achieve even higher accuracy.

Force system generated by elastic archwires with vertical V bends: a three-dimensional analysis.

PubMed

Upadhyay, Madhur; Shah, Raja; Peterson, Donald; Asaki, Takafumi; Yadav, Sumit; Agarwal, Sachin

2017-04-01

Our previous understanding of V-bend mechanics is primarily from two-dimensional (2D) analysis of archwire bracket interactions in the second order. These analyses do not take into consideration the three-dimensional (3D) nature of orthodontic appliances involving the third order. To quantify the force system generated in a 3D two bracket set up involving the molar and incisors with vertical V-bends. Maxillary molar and incisor brackets were arranged in a dental arch form and attached to load cells capable of measuring forces and moments in all three planes (x, y, and z) of space. Symmetrical V-bends (right and left sides) were placed at 11 different locations along rectangular beta-titanium archwires of various sizes at an angle of 150degrees. Each wire was evaluated for the 11 bend positions. Specifically, the vertical forces (Fz) and anterio-posterior moments (Mx) were analysed. Descriptive statistics were used to interpret the results. With increasing archwire size, Fz and Mx increased at the two brackets (P < 0.05). The vertical forces were linear and symmetric in nature, increasing in magnitude as the bends moved closer to either bracket. The Mx curves were asymmetric and non-linear displaying higher magnitudes for molar bracket. As the bends were moved closer to either bracket a distinct flattening of the incisor Mx curve was noted, implying no change in its magnitude. This article provides critical information on V-bend mechanics involving second order and third order archwire-bracket interactions. A model for determining this force system is described that might allow for easier translation to actual clinical practice. © The Author 2016. Published by Oxford University Press on behalf of the European Orthodontic Society. All rights reserved. For permissions, please email: journals.permissions@oup.com

Analytical Solution for the Aeroelastic Response of a Two-Dimensional Elastic Plate in Axial Flow

NASA Astrophysics Data System (ADS)

Medina, Cory; Kang, Chang-Kwon

2017-11-01

The aeroelastic response of an elastic plate in an unsteady flow describes many engineering problems from bio-locomotion, deforming airfoils, to energy harvesting. However, the analysis is challenging because the shape of the plate is a priori unknown. This study presents an analytical model that can predict the two-way tightly coupled aeroelastic response of a two-dimensional elastic plate including the effects of plate curvature along the flow direction. The plate deforms due to the dynamic balance of wing inertia, elastic restoring force, and aerodynamic force. The coupled model utilizes the linearized Euler-Bernoulli beam theory for the structural model and thin airfoil theory as presented by Theodorsen, which assumes incompressible potential flow, for the aerodynamic model. The coupled equations of motion are solved via Galerkin's method, where closed form solutions for the plate deformation are obtained by deriving the unsteady aerodynamic pressure with respect to the plate normal functions, expressed in a Chebyshev polynomial expansion. Stability analysis is performed for a range of mass ratios obtaining the flutter velocities and corresponding frequencies and the results agree well with the results reported in the literature.

Continuum modeling of three-dimensional truss-like space structures

NASA Technical Reports Server (NTRS)

Nayfeh, A. H.; Hefzy, M. S.

1978-01-01

A mathematical and computational analysis capability has been developed for calculating the effective mechanical properties of three-dimensional periodic truss-like structures. Two models are studied in detail. The first, called the octetruss model, is a three-dimensional extension of a two-dimensional model, and the second is a cubic model. Symmetry considerations are employed as a first step to show that the specific octetruss model has four independent constants and that the cubic model has two. The actual values of these constants are determined by averaging the contributions of each rod element to the overall structure stiffness. The individual rod member contribution to the overall stiffness is obtained by a three-dimensional coordinate transformation. The analysis shows that the effective three-dimensional elastic properties of both models are relatively close to each other.

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.

Space Shuttle Orbiter Wing-Leading-Edge Panel Thermo-Mechanical Analysis for Entry Conditions

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.; Song, Kyongchan; Raju, Ivatury S.

2010-01-01

Linear elastic, thermo-mechanical stress analyses of the Space Shuttle Orbiter wing-leading-edge panels is presented for entry heating conditions. The wing-leading-edge panels are made from reinforced carbon-carbon and serve as a part of the overall thermal protection system. Three-dimensional finite element models are described for three configurations: integrated configuration, an independent single-panel configuration, and a local lower-apex joggle segment. Entry temperature conditions are imposed and the through-the-thickness response is examined. From the integrated model, it was concluded that individual panels can be analyzed independently since minimal interaction between adjacent components occurred. From the independent single-panel model, it was concluded that increased through-the-thickness stress levels developed all along the chord of a panel s slip-side joggle region, and hence isolated local joggle sections will exhibit the same trend. From the local joggle models, it was concluded that two-dimensional plane-strain models can be used to study the influence of subsurface defects along the slip-side joggle region of these panels.

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

Compressive elasticity of three-dimensional nanofiber matrix directs mesenchymal stem cell differentiation to vascular cells with endothelial or smooth muscle cell markers.

PubMed

Wingate, K; Bonani, W; Tan, Y; Bryant, S J; Tan, W

2012-04-01

The importance of mesenchymal stem cells (MSC) in vascular regeneration is becoming increasingly recognized. However, few in vitro studies have been performed to identify the effects of environmental elasticity on the differentiation of MSC into vascular cell types. Electrospinning and photopolymerization techniques were used to fabricate a three-dimensional (3-D) polyethylene glycol dimethacrylate nanofiber hydrogel matrix with tunable elasticity for use as a cellular substrate. Compression testing demonstrated that the elastic modulus of the hydrated 3-D matrices ranged from 2 to 15 kPa, similar to the in vivo elasticity of the intima basement membrane and media layer. MSC seeded on rigid matrices (8-15 kPa) showed an increase in cell area compared with those seeded on soft matrices (2-5 kPa). Furthermore, the matrix elasticity guided the cells to express different vascular-specific phenotypes with high differentiation efficiency. Around 95% of MSC seeded on the 3-D matrices with an elasticity of 3 kPa showed Flk-1 endothelial markers within 24h, while only 20% of MSC seeded on the matrices with elasticity >8 kPa demonstrated Flk-1 marker. In contrast, ∼80% of MSC seeded on 3-D matrices with elasticity >8 kPa demonstrated smooth muscle α-actin marker within 24h, while fewer than 10% of MSC seeded on 3-D matrices with elasticity <5 kPa showed α-actin markers. The ability to control MSC differentiation into either endothelial or smooth muscle-like cells based purely on the local elasticity of the substrate could be a powerful tool for vascular tissue regeneration. Copyright © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

[Stress distribution in press-fit orthodontic microimplant bone interface].

PubMed

Wu, Jian-chao; Huang, Ji-na; Zhao, Shi-fang; Xu, Xue-jun

2006-12-01

The goal of this study is to analyse the stress distribution in the press-fit microimplant-bone interface and its indications for immediate loading of orthodontic microimplant. Three-dimensional finite element models were created of a 20 mm section of posterior mandible simplified in isosceles trapezoid shape, 30 mm in height, 10mm in upper side width, 14 mm in lower side width,with a single microimplant, 1.2 mm in diameter, 6 mm in length embedded in the bone. The cortical bone thickness was assumed as 1.6 mm. Cortical and cancellous bone were modeled as transversely isotropic and linearly elastic materials. Titanium was modeled as isotropic and linearly elastic material. Perfect bonding was assumed at microimplant- bone interfaces. ANSYS 9.0 finite element analysis software was used to generate the simplified finite element models of the local mandible-implant complex. 0 mm, 0.05 mm and 0.1 mm press-fit were arbitrarily set to the implant-bone interface to mimic the situation of immediate placement of microimplant. Stresses in the microimplant-bone interface were calculated under these "press-fit". Stresses distributed mainly in the cortical bone interface. At Omm press-fit, the stress was 0 MPa. For 0.05mm press-fit, the stress was 1648 MPa in mesio-distal direction, 1782MPa in occluso-gingival direction;and for 0.1 mm, it reached 2012MPa in mesio-distal direction, 2110MPa in occluso-gingival direction. As the "press-fit" increased, the stresses increased accordingly. Values of initial stress in the microimplant-bone interface due to press-fit generated by immediately placed microimplant were very high in these limited and simplified three dimensional finite element models. It reminded us that the initial stress be taken into consideration when immediate loading of the microimplant is planned. Supported by Research Fund of Health Bureau of Zhejiang Province (2005B104).

Stress concentrations for straight-shank and countersunk holes in plates subjected to tension, bending, and pin loading

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Newman, J. C., Jr.

1992-01-01

A three dimensional stress concentration analysis was conducted on straight shank and countersunk (rivet) holes in a large plate subjected to various loading conditions. Three dimensional finite element analysis were performed with 20 node isoparametric elements. The plate material was assumed to be linear elastic and isotropic, with a Poisson ratio of 0.3. Stress concentration along the bore of the hole were computed for several ratios of hole radius to plate thickness (0.1 to 2.5) and ratios of countersink depth to plate thickness (0.25 to 1). The countersink angles were varied from 80 to 100 degrees in some typical cases, but the angle was held constant at 100 degrees for most cases. For straight shank holes, three types of loading were considered: remote tension, remote bending, and wedge loading in the hole. Results for remote tension and wedge loading were used to estimate stress concentration for simulated rivet in pin loading. For countersunk holes only remote tension and bending were considered. Based on the finite element results, stress concentration equations were developed. Whenever possible, the present results were compared with other numerical solutions and experimental results from the literature.

Boundary-integral methods in elasticity and plasticity. [solutions of boundary value problems

NASA Technical Reports Server (NTRS)

Mendelson, A.

1973-01-01

Recently developed methods that use boundary-integral equations applied to elastic and elastoplastic boundary value problems are reviewed. Direct, indirect, and semidirect methods using potential functions, stress functions, and displacement functions are described. Examples of the use of these methods for torsion problems, plane problems, and three-dimensional problems are given. It is concluded that the boundary-integral methods represent a powerful tool for the solution of elastic and elastoplastic problems.

Solution-adaptive finite element method in computational fracture mechanics

NASA Technical Reports Server (NTRS)

Min, J. B.; Bass, J. M.; Spradley, L. W.

1993-01-01

Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.

Crack growth in bonded elastic half planes

NASA Technical Reports Server (NTRS)

Goree, J. G.

1975-01-01

Two solutions were developed for the two dimensional problem of bonded linearly elastic half-planes. For each solution, numerical results are presented for the stress intensity factors, strain energy release rate, stresses, and displacements. The behavior predicted by the studies was investigated experimentally using polymers for the material pairs. Close agreement was found for the critical stress intensity factor at fracture for the perpendicular crack near the interface. Fracture along the interface proved to be inconclusive due to difficulties in obtaining a brittle bond. Some interesting and predictable behavior regarding the potential for the crack to cross the interface was observed and is discussed.

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions.

PubMed

Solares, Santiago D

2016-01-01

Significant progress has been accomplished in the development of experimental contact-mode and dynamic-mode atomic force microscopy (AFM) methods designed to measure surface material properties. However, current methods are based on one-dimensional (1D) descriptions of the tip-sample interaction forces, thus neglecting the intricacies involved in the material behavior of complex samples (such as soft viscoelastic materials) as well as the differences in material response between the surface and the bulk. In order to begin to address this gap, a computational study is presented where the sample is simulated using an enhanced version of a recently introduced model that treats the surface as a collection of standard-linear-solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young's modulus. Relevant cases are discussed for single- and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface indentation profiles and tip-sample interaction force curves, as well as their implications with regards to experimental interpretation. A variety of phenomena are examined in detail, which highlight the need for further development of more physically accurate sample models that are specifically designed for AFM simulation. A multifrequency AFM simulation tool based on the above sample model is provided as supporting information.

Isotropic-resolution linear-array-based photoacoustic computed tomography through inverse Radon transform

NASA Astrophysics Data System (ADS)

Li, Guo; Xia, Jun; Li, Lei; Wang, Lidai; Wang, Lihong V.

2015-03-01

Linear transducer arrays are readily available for ultrasonic detection in photoacoustic computed tomography. They offer low cost, hand-held convenience, and conventional ultrasonic imaging. However, the elevational resolution of linear transducer arrays, which is usually determined by the weak focus of the cylindrical acoustic lens, is about one order of magnitude worse than the in-plane axial and lateral spatial resolutions. Therefore, conventional linear scanning along the elevational direction cannot provide high-quality three-dimensional photoacoustic images due to the anisotropic spatial resolutions. Here we propose an innovative method to achieve isotropic resolutions for three-dimensional photoacoustic images through combined linear and rotational scanning. In each scan step, we first elevationally scan the linear transducer array, and then rotate the linear transducer array along its center in small steps, and scan again until 180 degrees have been covered. To reconstruct isotropic three-dimensional images from the multiple-directional scanning dataset, we use the standard inverse Radon transform originating from X-ray CT. We acquired a three-dimensional microsphere phantom image through the inverse Radon transform method and compared it with a single-elevational-scan three-dimensional image. The comparison shows that our method improves the elevational resolution by up to one order of magnitude, approaching the in-plane lateral-direction resolution. In vivo rat images were also acquired.

Tensile behaviors of three-dimensionally free-formable titanium mesh plates for bone graft applications

NASA Astrophysics Data System (ADS)

He, Jianmei

2017-11-01

Present metal artificial bones for bone grafts have the problems like too heavy and excessive elastic modulus compared with natural bones. In this study, three-dimensionally (3D) free-formable titanium mesh plates for bone graft applications was introduced to improve these problems. Fundamental mesh shapes and patterns were designed under different base shapes and design parameters through three dimensional CAD tools from higher flexibility and strength points of view. Based on the designed mesh shape and patterns, sample specimens of titanium mesh plates with different base shapes and design variables were manufactured through laser processing. Tensile properties of the sample titanium mesh plates like volume density, tensile elastic modulus were experimentally and analytically evaluated. Experimental results showed that such titanium mesh plates had much higher flexibility and their mechanical properties could be controlled to close to the natural bones. More details on the mechanical properties of titanium mesh plates including compression, bending, torsion and durability will be carried out in future study.

Significance of rotating ground motions on nonlinear behavior of symmetric and asymmetric buildings in near fault sites

USGS Publications Warehouse

Kalkan, Erol; ,

2012-01-01

Building codes in the U.S. require at least two horizontal ground motion components for three-dimensional (3D) response history analysis (RHA) of structures. For sites within 5 km of an active fault, these records should be rotated to fault-normal/fault-parallel (FN/FP) directions, and two RHA analyses should be performed separately (when FN and then FP are aligned with transverse direction of the structural axes). It is assumed that this approach will lead to two sets of responses that envelope the range of possible responses over all non-redundant rotation angles. This assumption is examined here using 3D computer models of a single-story structure having symmetric (that is, torsionally-stiff) and asymmetric (that is, torsionally flexible) layouts subjected to an ensemble of bi-directional near-fault strong ground motions with and without apparent velocity pulses. In this parametric study, the elastic vibration period of the structures is varied from 0.2 to 5 seconds, and yield strength reduction factors R is varied from a value that leads to linear-elastic design to 3 and 5. The influence that the rotation angle of the ground motion has on several engineering demand parameters (EDPs) is examined in linear-elastic and nonlinear-inelastic domains to form a benchmark for evaluating the use of the FN/FP directions as well as the maximum-direction (MD) ground motion, a new definition of horizontal ground motions for use in the seismic design of structures according to the 2009 NEHRP Provisions and Commentary.

Cell mechanics, structure, and function are regulated by the stiffness of the three-dimensional microenvironment.

PubMed

Chen, J; Irianto, J; Inamdar, S; Pravincumar, P; Lee, D A; Bader, D L; Knight, M M

2012-09-19

This study adopts a combined computational and experimental approach to determine the mechanical, structural, and metabolic properties of isolated chondrocytes cultured within three-dimensional hydrogels. A series of linear elastic and hyperelastic finite-element models demonstrated that chondrocytes cultured for 24 h in gels for which the relaxation modulus is <5 kPa exhibit a cellular Young's modulus of ∼5 kPa. This is notably greater than that reported for isolated chondrocytes in suspension. The increase in cell modulus occurs over a 24-h period and is associated with an increase in the organization of the cortical actin cytoskeleton, which is known to regulate cell mechanics. However, there was a reduction in chromatin condensation, suggesting that changes in the nucleus mechanics may not be involved. Comparison of cells in 1% and 3% agarose showed that cells in the stiffer gels rapidly develop a higher Young's modulus of ∼20 kPa, sixfold greater than that observed in the softer gels. This was associated with higher levels of actin organization and chromatin condensation, but only after 24 h in culture. Further studies revealed that cells in stiffer gels synthesize less extracellular matrix over a 28-day culture period. Hence, this study demonstrates that the properties of the three-dimensional microenvironment regulate the mechanical, structural, and metabolic properties of living cells. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

I-Wire Heart-on-a-Chip II: Biomechanical analysis of contractile, three-dimensional cardiomyocyte tissue constructs.

PubMed

Schroer, Alison K; Shotwell, Matthew S; Sidorov, Veniamin Y; Wikswo, John P; Merryman, W David

2017-01-15

This companion study presents the biomechanical analysis of the "I-Wire" platform using a modified Hill model of muscle mechanics that allows for further characterization of construct function and response to perturbation. The I-Wire engineered cardiac tissue construct (ECTC) is a novel experimental platform to investigate cardiac cell mechanics during auxotonic contraction. Whereas passive biomaterials often exhibit nonlinear and dissipative behavior, active tissue equivalents, such as ECTCs, also expend metabolic energy to perform mechanical work that presents additional challenges in quantifying their properties. The I-Wire model uses the passive mechanical response to increasing applied tension to measure the inherent stress and resistance to stretch of the construct before, during, and after treatments. Both blebbistatin and isoproterenol reduced prestress and construct stiffness; however, blebbistatin treatment abolished subsequent force-generating potential while isoproterenol enhanced this property. We demonstrate that the described model can replicate the response of these constructs to intrinsic changes in force-generating potential in response to both increasing frequency of stimulation and decreasing starting length. This analysis provides a useful mathematical model of the I-Wire platform, increases the number of parameters that can be derived from the device, and serves as a demonstration of quantitative characterization of nonlinear, active biomaterials. We anticipate that this quantitative analysis of I-Wire constructs will prove useful for qualifying patient-specific cardiomyocytes and fibroblasts prior to their utilization for cardiac regenerative medicine. Passive biomaterials may have non-linear elasticity and losses, but engineered muscle tissue also exhibits time- and force-dependent contractions. Historically, mathematical muscle models include series-elastic, parallel-elastic, contractile, and viscous elements. While hearts-on-a-chip can demonstrate in vitro the contractile properties of engineered cardiac constructs and their response to drugs, most of these use cellular monolayers that cannot be readily probed with controlled forces. The I-Wire platform described in the preceding paper by Sidorov et al. addresses these limitations with three-dimensional tissue constructs to which controlled forces can be applied. In this companion paper, we show how to characterize I-Wire constructs using a non-linear, active Hill model, which should be useful for qualifying cells prior to their use in cardiac regenerative medicine. Copyright © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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.

Linking a completely three-dimensional nanostrain to a structural transformation eigenstrain.

PubMed

Tirry, Wim; Schryvers, Dominique

2009-09-01

Ni-Ti is one of the most popular shape-memory alloys, a phenomenon resulting from a martensitic transformation. Commercial Ni-Ti-based alloys are often thermally treated to contain Ni(4)Ti(3) precipitates. The presence of these precipitates can introduce an extra transformation step related to the so-called R-phase. It is believed that the strain field surrounding the precipitates, caused by the matrix-precipitate lattice mismatch, lies at the origin of this intermediate transformation step. Atomic-resolution transmission electron microscopy in combination with geometrical phase analysis is used to measure the elastic strain field surrounding these precipitates. By combining measurements from two different crystallographic directions, the three-dimensional strain matrix is determined from two-dimensional measurements. Comparison of the measured strain matrix to the eigenstrain of the R-phase shows that both are very similar and that the introduction of the R-phase might indeed compensate the elastic strain introduced by the precipitate.

Linking a completely three-dimensional nanostrain to a structural transformation eigenstrain

NASA Astrophysics Data System (ADS)

Tirry, Wim; Schryvers, Dominique

2009-09-01

Ni-Ti is one of the most popular shape-memory alloys, a phenomenon resulting from a martensitic transformation. Commercial Ni-Ti-based alloys are often thermally treated to contain Ni4Ti3 precipitates. The presence of these precipitates can introduce an extra transformation step related to the so-called R-phase. It is believed that the strain field surrounding the precipitates, caused by the matrix-precipitate lattice mismatch, lies at the origin of this intermediate transformation step. Atomic-resolution transmission electron microscopy in combination with geometrical phase analysis is used to measure the elastic strain field surrounding these precipitates. By combining measurements from two different crystallographic directions, the three-dimensional strain matrix is determined from two-dimensional measurements. Comparison of the measured strain matrix to the eigenstrain of the R-phase shows that both are very similar and that the introduction of the R-phase might indeed compensate the elastic strain introduced by the precipitate.

Direct Linear Transformation Method for Three-Dimensional Cinematography

ERIC Educational Resources Information Center

Shapiro, Robert

1978-01-01

The ability of Direct Linear Transformation Method for three-dimensional cinematography to locate points in space was shown to meet the accuracy requirements associated with research on human movement. (JD)

Stress Regression Analysis of Asphalt Concrete Deck Pavement Based on Orthogonal Experimental Design and Interlayer Contact

NASA Astrophysics Data System (ADS)

Wang, Xuntao; Feng, Jianhu; Wang, Hu; Hong, Shidi; Zheng, Supei

2018-03-01

A three-dimensional finite element box girder bridge and its asphalt concrete deck pavement were established by ANSYS software, and the interlayer bonding condition of asphalt concrete deck pavement was assumed to be contact bonding condition. Orthogonal experimental design is used to arrange the testing plans of material parameters, and an evaluation of the effect of different material parameters in the mechanical response of asphalt concrete surface layer was conducted by multiple linear regression model and using the results from the finite element analysis. Results indicated that stress regression equations can well predict the stress of the asphalt concrete surface layer, and elastic modulus of waterproof layer has a significant influence on stress values of asphalt concrete surface layer.

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

NASA Astrophysics Data System (ADS)

Gambolati, Giuseppe; Teatini, Pietro

1996-01-01

A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.

Microtubule organization in three-dimensional confined geometries: evaluating the role of elasticity through a combined in vitro and modeling approach.

PubMed

Cosentino Lagomarsino, Marco; Tanase, Catalin; Vos, Jan W; Emons, Anne Mie C; Mulder, Bela M; Dogterom, Marileen

2007-02-01

Microtubules or microtubule bundles in cells often grow longer than the size of the cell, which causes their shape and organization to adapt to constraints imposed by the cell geometry. We test the reciprocal role of elasticity and confinement in the organization of growing microtubules in a confining box-like geometry, in the absence of other (active) microtubule organizing processes. This is inspired, for example, by the cortical microtubule array of elongating plant cells, where microtubules are typically organized in an aligned array transverse to the cell elongation axis. The method we adopt is a combination of analytical calculations, in which the polymers are modeled as inextensible filaments with bending elasticity confined to a two-dimensional surface that defines the limits of a three-dimensional space, and in vitro experiments, in which microtubules are polymerized from nucleation seeds in microfabricated chambers. We show that these features are sufficient to organize the polymers in aligned, coiling configurations as for example observed in plant cells. Though elasticity can account for the regularity of these arrays, it cannot account for a transverse orientation of microtubules to the cell's long axis. We therefore conclude that an additional active, force-generating process is necessary to create a coiling configuration perpendicular to the long axis of the cell.

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.

Software For Three-Dimensional Stress And Thermal Analyses

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Wilson, R. B.; Hopkins, D. A.

1994-01-01

BEST3D is advanced engineering software system for three-dimensional thermal and stress analyses, particularly of components of hot sections of gas-turbine engines. Utilizes boundary element method, offering, in many situations, more accuracy, efficiency, and ease of use than finite element method. Performs engineering analyses of following types: elastic, heat transfer, plastic, forced vibration, free vibration, and transient elastodynamic. Written in FORTRAN 77.

Three-dimensional Stress Analysis Using the Boundary Element Method

NASA Technical Reports Server (NTRS)

Wilson, R. B.; Banerjee, P. K.

1984-01-01

The boundary element method is to be extended (as part of the NASA Inelastic Analysis Methods program) to the three-dimensional stress analysis of gas turbine engine hot section components. The analytical basis of the method (as developed in elasticity) is outlined, its numerical implementation is summarized, and the approaches to be followed in extending the method to include inelastic material response indicated.

Fractonic line excitations: An inroad from three-dimensional elasticity theory

NASA Astrophysics Data System (ADS)

Pai, Shriya; Pretko, Michael

2018-06-01

We demonstrate the existence of a fundamentally new type of excitation, fractonic lines, which are linelike excitations with the restricted mobility properties of fractons. These excitations, described using an amalgamation of higher-form gauge theories with symmetric tensor gauge theories, see direct physical realization as the topological lattice defects of ordinary three-dimensional quantum crystals. Starting with the more familiar elasticity theory, we show how theory maps onto a rank-4 tensor gauge theory, with phonons corresponding to gapless gauge modes and disclination defects corresponding to linelike charges. We derive flux conservation laws which lock these linelike excitations in place, analogous to the higher moment charge conservation laws of fracton theories. This way of encoding mobility restrictions of lattice defects could shed light on melting transitions in three dimensions. This new type of extended object may also be a useful tool in the search for improved quantum error-correcting codes in three dimensions.

Elastic and failure response of imperfect three-dimensional metallic lattices: the role of geometric defects induced by Selective Laser Melting

NASA Astrophysics Data System (ADS)

Liu, Lu; Kamm, Paul; García-Moreno, Francisco; Banhart, John; Pasini, Damiano

2017-10-01

This paper examines three-dimensional metallic lattices with regular octet and rhombicuboctahedron units fabricated with geometric imperfections via Selective Laser Sintering. We use X-ray computed tomography to capture morphology, location, and distribution of process-induced defects with the aim of studying their role in the elastic response, damage initiation, and failure evolution under quasi-static compression. Testing results from in-situ compression tomography show that each lattice exhibits a distinct failure mechanism that is governed not only by cell topology but also by geometric defects induced by additive manufacturing. Extracted from X-ray tomography images, the statistical distributions of three sets of defects, namely strut waviness, strut thickness variation, and strut oversizing, are used to develop numerical models of statistically representative lattices with imperfect geometry. Elastic and failure responses are predicted within 10% agreement from the experimental data. In addition, a computational study is presented to shed light into the relationship between the amplitude of selected defects and the reduction of elastic properties compared to their nominal values. The evolution of failure mechanisms is also explained with respect to strut oversizing, a parameter that can critically cause failure mode transitions that are not visible in defect-free lattices.

Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

NASA Astrophysics Data System (ADS)

Kharibegashvili, S. S.; Jokhadze, O. M.

2014-04-01

A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles.

The molecular kink paradigm for rubber elasticity: Numerical simulations of explicit polyisoprene networks at low to moderate tensile strains

NASA Astrophysics Data System (ADS)

Hanson, David E.

2011-08-01

Based on recent molecular dynamics and ab initio simulations of small isoprene molecules, we propose a new ansatz for rubber elasticity. We envision a network chain as a series of independent molecular kinks, each comprised of a small number of backbone units, and the strain as being imposed along the contour of the chain. We treat chain extension in three distinct force regimes: (Ia) near zero strain, where we assume that the chain is extended within a well defined tube, with all of the kinks participating simultaneously as entropic elastic springs, (II) when the chain becomes sensibly straight, giving rise to a purely enthalpic stretching force (until bond rupture occurs) and, (Ib) a linear entropic regime, between regimes Ia and II, in which a force limit is imposed by tube deformation. In this intermediate regime, the molecular kinks are assumed to be gradually straightened until the chain becomes a series of straight segments between entanglements. We assume that there exists a tube deformation tension limit that is inversely proportional to the chain path tortuosity. Here we report the results of numerical simulations of explicit three-dimensional, periodic, polyisoprene networks, using these extension-only force models. At low strain, crosslink nodes are moved affinely, up to an arbitrary node force limit. Above this limit, non-affine motion of the nodes is allowed to relax unbalanced chain forces. Our simulation results are in good agreement with tensile stress vs. strain experiments.

The molecular kink paradigm for rubber elasticity: numerical simulations of explicit polyisoprene networks at low to moderate tensile strains.

PubMed

Hanson, David E

2011-08-07

Based on recent molecular dynamics and ab initio simulations of small isoprene molecules, we propose a new ansatz for rubber elasticity. We envision a network chain as a series of independent molecular kinks, each comprised of a small number of backbone units, and the strain as being imposed along the contour of the chain. We treat chain extension in three distinct force regimes: (Ia) near zero strain, where we assume that the chain is extended within a well defined tube, with all of the kinks participating simultaneously as entropic elastic springs, (II) when the chain becomes sensibly straight, giving rise to a purely enthalpic stretching force (until bond rupture occurs) and, (Ib) a linear entropic regime, between regimes Ia and II, in which a force limit is imposed by tube deformation. In this intermediate regime, the molecular kinks are assumed to be gradually straightened until the chain becomes a series of straight segments between entanglements. We assume that there exists a tube deformation tension limit that is inversely proportional to the chain path tortuosity. Here we report the results of numerical simulations of explicit three-dimensional, periodic, polyisoprene networks, using these extension-only force models. At low strain, crosslink nodes are moved affinely, up to an arbitrary node force limit. Above this limit, non-affine motion of the nodes is allowed to relax unbalanced chain forces. Our simulation results are in good agreement with tensile stress vs. strain experiments.

Singularity computations

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1976-01-01

An approach is described for singularity computations based on a numerical method for elastoplastic flow to delineate radial and angular distribution of field quantities and measure the intensity of the singularity. The method is applicable to problems in solid mechanics and lends itself to certain types of heat flow and fluid motion studies. Its use is not limited to linear, elastic, small strain, or two-dimensional situations.

Free Oscillations of a Fluid-filled Cavity in an Infinite Elastic Medium

NASA Astrophysics Data System (ADS)

Sakuraba, A.

2016-12-01

Volcanic low-frequency earthquakes and tremor have been widely recognized as a good indicator of hidden activities of volcanoes. It is likely that existence or movement of underground magma and geothermal fluids play a crucial role in their generation mechanisms, but there are still many unknowns. This presentation aims to give a fundamental contribution to understanding and interpreting volcanic low-frequency seismic events. The problem we consider is to compute eigen modes of free oscillations of a fluid-filled cavity surrounded by an infinite linearly elastic medium. A standard boundary element method is used to solve fluid and elastic motion around a cavity of arbitrary shape. Nonlinear advection term is neglected, but viscosity is generally considered in a fluid medium. Of a great importance is to find not only characteristic frequencies but attenuation properties of the oscillations, the latter being determined by both viscous dissipation in the fluid cavity and elastic wave radiation to infinity. One of the simplest cases may be resonance of a fluid-filled crack, which has been studied numerically (Chouet, JGR 1986; Yamamoto and Kawakatsu, GJI 2008) and analytically (Maeda and Kumagai, GRL 2013). In the present study, we generally consider a three-dimensional cavity with emphasis on treating the crack model and other simplest models such as spherical and cylindrical resonators as the extreme cases. In order to reduce computational costs, we assume symmetries about three orthogonal planes and calculate the eigen modes separately for each symmetry. The current status of this project is that the computational code has been checked through comparison to eigen modes of a spherical inviscid cavity (Sakuraba et al., EPS 2002), and another comparison to resonance of a fluid-filled crack is undertook.

Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals

PubMed Central

Ackerman, Paul J.; van de Lagemaat, Jao; Smalyukh, Ivan I.

2015-01-01

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains that exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields. PMID:25607778

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

Ackerman, P. J.; van de Lagemaat, J.; Smalyukh, I. I.

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains thatmore » exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields.« less

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

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.

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.

Hydroelastic behaviour of a structure exposed to an underwater explosion

PubMed Central

Colicchio, G.; Greco, M.; Brocchini, M.; Faltinsen, O. M.

2015-01-01

The hydroelastic interaction between an underwater explosion and an elastic plate is investigated num- erically through a domain-decomposition strategy. The three-dimensional features of the problem require a large computational effort, which is reduced through a weak coupling between a one-dimensional radial blast solver, which resolves the blast evolution far from the boundaries, and a three-dimensional compressible flow solver used where the interactions between the compression wave and the boundaries take place and the flow becomes three-dimensional. The three-dimensional flow solver at the boundaries is directly coupled with a modal structural solver that models the response of the solid boundaries like elastic plates. This enables one to simulate the fluid–structure interaction as a strong coupling, in order to capture hydroelastic effects. The method has been applied to the experimental case of Hung et al. (2005 Int. J. Impact Eng. 31, 151–168 (doi:10.1016/j.ijimpeng.2003.10.039)) with explosion and structure sufficiently far from other boundaries and successfully validated in terms of the evolution of the acceleration induced on the plate. It was also used to investigate the interaction of an underwater explosion with the bottom of a close-by ship modelled as an orthotropic plate. In the application, the acoustic phase of the fluid–structure interaction is examined, highlighting the need of the fluid–structure coupling to capture correctly the possible inception of cavitation. PMID:25512585

Nanoparticulate delivery of agents for induced elastogenesis in three-dimensional collagenous matrices.

PubMed

Venkataraman, Lavanya; Sivaraman, Balakrishnan; Vaidya, Pratik; Ramamurthi, Anand

2016-12-01

The degradation of elastic matrix in the infrarenal aortic wall is a critical parameter underlying the formation and progression of abdominal aortic aneurysms. It is mediated by the chronic overexpression of matrix metalloprotease (MMP)-2 and MMP-9, leading to a progressive loss of elasticity and weakening of the aortic wall. Delivery of therapeutic agents to inhibit MMPs, while concurrently coaxing cell-based regenerative repair of the elastic matrix represents a potential strategy for slowing or arresting abdominal aortic aneurysm growth. Previous studies have demonstrated elastogenic induction of healthy and aneurysmal aortic smooth muscle cells and inhibition of MMPs, following exogenous delivery of elastogenic factors such as transforming growth factor (TGF)-β1, as well as MMP-inhibitors such as doxycycline (DOX) in two-dimensional culture. Based on these findings, and others that demonstrated elastogenic benefits of nanoparticulate delivery of these agents in two-dimensional culture, poly(lactide-co-glycolide) nanoparticles were developed for localized, controlled and sustained delivery of DOX and TGF-β1 to human aortic smooth muscle cells within a three-dimensional gels of type I collagen, which closely simulate the arterial tissue microenvironment. DOX and TGF-β1 released from these nanoparticles influenced elastogenic outcomes positively within the collagen constructs over 21 days of culture, which were comparable to that induced by exogenous supplementation of DOX and TGF-β1 within the culture medium. However, this was accomplished at doses ~20-fold lower than the exogenous dosages of the agents, illustrating that their localized, controlled and sustained delivery from nanoparticles embedded within a three-dimensional scaffold is an efficient strategy for directed elastogenesis. Copyright © 2014 John Wiley & Sons, Ltd. Copyright © 2014 John Wiley & Sons, Ltd.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Sensitivity analysis on the effective stiffness properties of 3-D orthotropic honeycomb cores

NASA Astrophysics Data System (ADS)

Karakoç, Alp

2018-01-01

The present study investigates the influences of representative volume element RVE mesh and material parameters, here cell wall elastic moduli, on the effective stiffness properties of three dimensional orthotropic honeycomb cores through strain driven computational homogenization in the finite element framework. For this purpose, case studies were carried out, for which hexagonal cellular RVEs were generated, meshed with eight node linear brick finite elements of varying numbers. Periodic boundary conditions were then implemented on the RVE boundaries by using one-to-one nodal match for the corresponding corners, edges and surfaces for the imposed macroscopic strains. As a novelty, orthotropic material properties were assigned for each cell wall by means of the transformation matrices following the cell wall orientations. Thereafter, simulations were conducted and volume averaged macroscopic stresses were obtained. Eventually, effective stiffness properties were obtained, through which RVE sensitivity analysis was carried out. The investigations indicate that there is a strong relation between number of finite elements and most of the effective stiffness parameters. In addition to this, cell wall elastic moduli also play critical role on the effective properties of the investigated materials.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

A Review of the Proposed K (sub Isi) Offset-Secant Method for Size-Independent Linear-Elastic Toughness Evaluation

NASA Technical Reports Server (NTRS)

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

2017-01-01

The proposed size-independent linear-elastic fracture toughness, K (sub Isi), for potential inclusion in ASTM E399 targets a consistent 0.5 millimeters crack extension for all specimen sizes through an offset secant that is a function of the specimen ligament length. The K (sub Isi) method also includes an increase in allowable deformation, and the removal of the P (sub max)/P (sub Q) criterion. A finite element study of the K (sub Isi) test method confirms the viability of the increased deformation limit, but has also revealed a few areas of concern. Findings: 1. The deformation limit, b (sub o) greater than or equal to 1.1 times (K (sub I) divided by delta (sub ys) squared) maintains a K-dominant crack tip field with limited plastic contribution to the fracture energy; 2. The three dimensional effects on compliance and the shape of the force versus CMOD (Crack-Mouth Opening Displacement) trace are significant compared to a plane strain assumption; 3. The non-linearity in the force versus CMOD trace at deformations higher than the current limit of 2.5 times (K (sub I) divided by delta (sub ys) squared) is sufficient to introduce error or even "false calls" regarding crack extension when using a constant offset secant line. This issue is more significant for specimens with W (width) greater than or equal to 2 inches; 4. A non-linear plasticity correction factor in the offset secant may improve the viability of the method at deformations between 2.5 times (K (sub I) divided by delta (sub ys) squared) and 1.1 times (K (sub I) divided by delta (sub ys) squared).

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.

Three-dimensional finite-element elastic analysis of a thermally cycled single-edge wedge geometry specimen

NASA Technical Reports Server (NTRS)

Bizon, P. T.; Hill, R. J.; Guilliams, B. P.; Drake, S. K.; Kladden, J. L.

1979-01-01

An elastic stress analysis was performed on a wedge specimen (prismatic bar with single-wedge cross section) subjected to thermal cycles in fluidized beds. Seven different combinations consisting of three alloys (NASA TAZ-8A, 316 stainless steel, and A-286) and four thermal cycling conditions were analyzed. The analyses were performed as a joint effort of two laboratories using different models and computer programs (NASTRAN and ISO3DQ). Stress, strain, and temperature results are presented.

Intensity of joints associated with an extensional fault zone: an estimation by poly3d .

NASA Astrophysics Data System (ADS)

Minelli, G.

2003-04-01

The presence and frequency of joints in sedimentary rocks strongly affects the mechanical and fluid flow properties of the host layers. Joints intensity is evaluated by spacing, S, the distance between neighbouring fractures, or by density, D = 1/S. Joint spacing in layered rocks is often linearly related to layer thickness T, with typical values of 0.5 T < S < 2.0 T . On the other hand, some field cases display very tight joints with S << T and nonlinear relations between spacing and thickness , most of these cases are related to joint system “genetically” related to a nearby fault zone. The present study by using the code Poly3D (Rock Fracture Project at Stanford), numerically explores the effect of the stress distribution in the neighbour of an extensional fault zone with respect to the mapped intensity of joints both in the hanging wall and in the foot wall of it (WILLEMSE, E. J. M., 1997; MARTEL, S. J, AND BOGER, W. A,; 1998). Poly3D is a C language computer program that calculates the displacements, strains and stresses induced in an elastic whole or half-space by planar, polygonal-shaped elements of displacement discontinuity (WILLEMSE, E. J. M., POLLARD, D. D., 2000) Dislocations of varying shapes may be combined to yield complex three-dimensional surfaces well-suited for modeling fractures, faults, and cavities in the earth's crust. The algebraic expressions for the elastic fields around a polygonal element are derived by superposing the solution for an angular dislocation in an elastic half-space. The field data have been collected in a quarry located close to Noci town (Puglia) by using the scan line methodology. In this quarry a platform limestone with a regular bedding with very few shale or marly intercalations displaced by a normal fault are exposed. The comparison between the mapped joints intensity and the calculated stress around the fault displays a good agreement. Nevertheless the intrinsic limitations (isotropic medium and elastic behaviour) of this project encourages other application of Poly3d. References WILLEMSE, E. J. M., 1997, Segmented normal faults: Correspondence between three-dimensional mechanical models and field data: Journal of Geophysical Research, v. 102, p. 675-692. MARTEL, S. J, AND BOGER, W. A, 1998, Geometry and mechanics of secondary fracturing around small three-dimensional faults in granitic rock: Journal of Geophysical Research, v. 103, p. 21,299-21,314. WILLEMSE, E. J. M., POLLARD, D. D., 2000, Normal fault growth: evolution of tipline shapes and slip distribution: in Lehner, F.K. &Urai, J.L. (eds.), Aspects of Tectonic Faulting, Springer -Verlag , Berlin, p. 193-226.

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

Three-dimensional modeling of flexible pavements : executive summary, August 2001.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Three dimensional modeling of flexible pavements : final report, March 2002.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Enhancing elastic stress relaxation in SiGe/Si heterostructures by Si pillar necking

NASA Astrophysics Data System (ADS)

Isa, F.; Salvalaglio, M.; Arroyo Rojas Dasilva, Y.; Jung, A.; Isella, G.; Erni, R.; Timotijevic, B.; Niedermann, P.; Gröning, P.; Montalenti, F.; von Känel, H.

2016-10-01

We demonstrate that the elastic stress relaxation mechanism in micrometre-sized, highly mismatched heterostructures may be enhanced by employing patterned substrates in the form of necked pillars, resulting in a significant reduction of the dislocation density. Compositionally graded Si1-xGex crystals were grown by low energy plasma enhanced chemical vapour deposition, resulting in tens of micrometres tall, three-dimensional heterostructures. The patterned Si(001) substrates consist of micrometre-sized Si pillars either with the vertical {110} or isotropically under-etched sidewalls resulting in narrow necks. The structural properties of these heterostructures were investigated by defect etching and transmission electron microscopy. We show that the dislocation density, and hence the competition between elastic and plastic stress relaxation, is highly influenced by the shape of the substrate necks and their proximity to the mismatched epitaxial material. The SiGe dislocation density increases monotonically with the crystal width but is significantly reduced by the substrate under-etching. The drop in dislocation density is interpreted as a direct effect of the enhanced compliance of the under-etched Si pillars, as confirmed by the three-dimensional finite element method simulations of the elastic energy distribution.

Modified equations of finite-size layered plates made of orthotropic material. Comparison of the results of numerical calculations with analytical solutions

NASA Astrophysics Data System (ADS)

Volchkov, Yu. M.

2017-09-01

This paper describes the modified bending equations of layered orthotropic plates in the first approximation. The approximation of the solution of the equation of the three-dimensional theory of elasticity by the Legendre polynomial segments is used to obtain differential equations of the elastic layer. For the approximation of equilibrium equations and boundary conditions of three-dimensional theory of elasticity, several approximations of each desired function (stresses and displacements) are used. The stresses at the internal points of the plate are determined from the defining equations for the orthotropic material, averaged with respect to the plate thickness. The construction of the bending equations of layered plates for each layer is carried out with the help of the elastic layer equations and the conjugation conditions on the boundaries between layers, which are conditions for the continuity of normal stresses and displacements. The numerical solution of the problem of bending of the rectangular layered plate obtained with the help of modified equations is compared with an analytical solution. It is determined that the maximum error in determining the stresses does not exceed 3 %.

Equilibrium structures of carbon diamond-like clusters and their elastic properties

NASA Astrophysics Data System (ADS)

Lisovenko, D. S.; Baimova, Yu. A.; Rysaeva, L. Kh.; Gorodtsov, V. A.; Dmitriev, S. V.

2017-04-01

Three-dimensional carbon diamond-like phases consisting of sp 3-hybridized atoms, obtained by linking of carcasses of fullerene-like molecules, are studied by methods of molecular dynamics modeling. For eight cubic and one hexagonal diamond-like phases on the basis of four types of fullerene-like molecules, equilibrium configurations are found and the elastic constants are calculated. The results obtained by the method of molecular dynamics are used for analytical calculations of the elastic characteristics of the diamond- like phases with the cubic and hexagonal anisotropy. It is found that, for a certain choice of the dilatation axis, three of these phases have negative Poisson's ratio, i.e., are partial auxetics. The variability of the engineering elasticity coefficients (Young's modulus, Poisson's ratio, shear modulus, and bulk modulus) is analyzed.

Geometric charges in theories of elasticity and plasticity

NASA Astrophysics Data System (ADS)

Moshe, Michael

The mechanics of many natural systems is governed by localized sources of stresses. Examples include ''plastic events'' that occur in amorphous solids under external stress, defects formation in crystalline material, and force-dipoles applied by cells adhered to an elastic substrate. Recent developments in a geometric formulation of elasticity theory paved the way for a unifying mathematical description of such singular sources of stress, as ''elastic charges''. In this talk I will review basic results in this emerging field, focusing on the geometry and mechanics of elastic charges in two-dimensional solid bodies. I will demonstrate the applicability of this new approach in three different problems: failure of an amorphous solid under load, mechanics of Kirigami, and wrinkle patterns in geometrically-incompatible elastic sheets.

Buckling analysis of Big Dee Vacuum Vessel

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

Lightner, S.; Gallix, R.

1983-12-01

A simplified three-dimensional shell buckling analysis of the GA Technologies Inc., Big Dee Vacuum Vessel (V/V) was performed using the finite element program TRICO. A coarse-mesh linear elastic model, which accommodated the support boundary conditions, was used to determine the buckling mode shape under a uniform external pressure. Using this buckling mode shape, refined models were used to calculate the linear buckling load (P/sub crit/) more accurately. Several different designs of the Big Dee V/V were considered in this analysis. The supports for the V/V were equally-spaced radial pins at the outer diameter of the mid-plane. For all the casesmore » considered, the buckling mode was axisymmetric in the toroidal direction. Therefore, it was possible to use only a small angular sector of a toric shell for the refined analysis. P/sub crit/ for the Big Dee is about 60 atm for a uniform external pressure. Also investigated in this analysis were the effects of geometrical imperfections and non-uniform pressure distributions.« less

Vestibular coriolis effect differences modeled with three-dimensional linear-angular interactions.

PubMed

Holly, Jan E

2004-01-01

The vestibular coriolis (or "cross-coupling") effect is traditionally explained by cross-coupled angular vectors, which, however, do not explain the differences in perceptual disturbance under different acceleration conditions. For example, during head roll tilt in a rotating chair, the magnitude of perceptual disturbance is affected by a number of factors, including acceleration or deceleration of the chair rotation or a zero-g environment. Therefore, it has been suggested that linear-angular interactions play a role. The present research investigated whether these perceptual differences and others involving linear coriolis accelerations could be explained under one common framework: the laws of motion in three dimensions, which include all linear-angular interactions among all six components of motion (three angular and three linear). The results show that the three-dimensional laws of motion predict the differences in perceptual disturbance. No special properties of the vestibular system or nervous system are required. In addition, simulations were performed with angular, linear, and tilt time constants inserted into the model, giving the same predictions. Three-dimensional graphics were used to highlight the manner in which linear-angular interaction causes perceptual disturbance, and a crucial component is the Stretch Factor, which measures the "unexpected" linear component.

Modeling of Melt-Infiltrated SiC/SiC Composite Properties

NASA Technical Reports Server (NTRS)

Mital, Subodh K.; Bednarcyk, Brett A.; Arnold, Steven M.; Lang, Jerry

2009-01-01

The elastic properties of a two-dimensional five-harness melt-infiltrated silicon carbide fiber reinforced silicon carbide matrix (MI SiC/SiC) ceramic matrix composite (CMC) were predicted using several methods. Methods used in this analysis are multiscale laminate analysis, micromechanics-based woven composite analysis, a hybrid woven composite analysis, and two- and three-dimensional finite element analyses. The elastic properties predicted are in good agreement with each other as well as with the available measured data. However, the various methods differ from each other in three key areas: (1) the fidelity provided, (2) the efforts required for input data preparation, and (3) the computational resources required. Results also indicate that efficient methods are also able to provide a reasonable estimate of local stress fields.

Elasticity of fractal materials using the continuum model with non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Tangle-Free Finite Element Mesh Motion for Ablation Problems

NASA Technical Reports Server (NTRS)

Droba, Justin

2016-01-01

In numerical simulations involving boundaries that evolve in time, the primary challenge is updating the computational mesh to reflect the physical changes in the domain. In particular, the fundamental objective for any such \\mesh motion" scheme is to maintain mesh quality and suppress unphysical geometric anamolies and artifacts. External to a physical process of interest, mesh motion is an added component that determines the specifics of how to move the mesh given certain limited information from the main system. This paper develops a set of boundary conditions designed to eliminate tangling and internal collision within the context of PDE-based mesh motion (linear elasticity). These boundary conditions are developed for two- and three-dimensional meshes. The paper presents detailed algorithms for commonly occuring topological scenarios and explains how to apply them appropriately. Notably, the techniques discussed herein make use of none of the specifics of any particular formulation of mesh motion and thus are more broadly applicable. The two-dimensional algorithms are validated by an extensive verification procedure. Finally, many examples of diverse geometries in both two- and three-dimensions are shown to showcase the capabilities of the tangle-free boundary conditions.

Investigation of optimal method for inducing harmonic motion in tissue using a linear ultrasound phased array--a simulation study.

PubMed

Heikkilä, Janne; Hynynen, Kullervo

2006-04-01

Many noninvasive ultrasound techniques have been developed to explore mechanical properties of soft tissues. One of these methods, Localized Harmonic Motion Imaging (LHMI), has been proposed to be used for ultrasound surgery monitoring. In LHMI, dynamic ultrasound radiation-force stimulation induces displacements in a target that can be measured using pulse-echo imaging and used to estimate the elastic properties of the target. In this initial, simulation study, the use of a one-dimensional phased array is explored for the induction of the tissue motion. The study compares three different dual-frequency and amplitude-modulated single-frequency methods for the inducing tissue motion. Simulations were computed in a homogeneous soft-tissue volume. The Rayleigh integral was used in the simulations of the ultrasound fields and the tissue displacements were computed using a finite-element method (FEM). The simulations showed that amplitude-modulated sonication using a single frequency produced the largest vibration amplitude of the target tissue. These simulations demonstrate that the properties of the tissue motion are highly dependent on the sonication method and that it is important to consider the full three-dimensional distribution of the ultrasound field for controlling the induction of tissue motion.

A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation

NASA Technical Reports Server (NTRS)

Crivelli, Luis A.; Felippa, Carlos A.

1992-01-01

A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.

Three-dimensional finite element models of the human pubic symphysis with viscohyperelastic soft tissues.

PubMed

Li, Zuoping; Alonso, Jorge E; Kim, Jong-Eun; Davidson, James S; Etheridge, Brandon S; Eberhardt, Alan W

2006-09-01

Three-dimensional finite element (FE) models of human pubic symphyses were constructed from computed tomography image data of one male and one female cadaver pelvis. The pubic bones, interpubic fibrocartilaginous disc and four pubic ligaments were segmented semi-automatically and meshed with hexahedral elements using automatic mesh generation schemes. A two-term viscoelastic Prony series, determined by curve fitting results of compressive creep experiments, was used to model the rate-dependent effects of the interpubic disc and the pubic ligaments. Three-parameter Mooney-Rivlin material coefficients were calculated for the discs using a heuristic FE approach based on average experimental joint compression data. Similarly, a transversely isotropic hyperelastic material model was applied to the ligaments to capture average tensile responses. Linear elastic isotropic properties were assigned to bone. The applicability of the resulting models was tested in bending simulations in four directions and in tensile tests of varying load rates. The model-predicted results correlated reasonably with the joint bending stiffnesses and rate-dependent tensile responses measured in experiments, supporting the validity of the estimated material coefficients and overall modeling approach. This study represents an important and necessary step in the eventual development of biofidelic pelvis models to investigate symphysis response under high-energy impact conditions, such as motor vehicle collisions.

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.

Elastic Characterization of Transversely Isotropic Soft Materials by Dynamic Shear and Asymmetric Indentation

PubMed Central

Namani, R.; Feng, Y.; Okamoto, R. J.; Jesuraj, N.; Sakiyama-Elbert, S. E.; Genin, G. M.; Bayly, P. V.

2012-01-01

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B = 11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20–40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08 ± 0. 42 kPa (mean ± std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58 ± 0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material. PMID:22757501

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: Coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions

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

Solares, Santiago D.

Significant progress has been accomplished in the development of experimental contact-mode and dynamic-mode atomic force microscopy (AFM) methods designed to measure surface material properties. However, current methods are based on one-dimensional (1D) descriptions of the tip-sample interaction forces, thus neglecting the intricacies involved in the material behavior of complex samples (such as soft viscoelastic materials) as well as the differences in material response between the surface and the bulk. In order to begin to address this gap, a computational study is presented where the sample is simulated using an enhanced version of a recently introduced model that treats the surfacemore » as a collection of standard-linear-solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young's modulus. Relevant cases are discussed for single-and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface indentation profiles and tip-sample interaction force curves, as well as their implications with regards to experimental interpretation. A variety of phenomena are examined in detail, which highlight the need for further development of more physically accurate sample models that are specifically designed for AFM simulation. As a result, a multifrequency AFM simulation tool based on the above sample model is provided as supporting information.« less

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: Coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions

DOE PAGES

Solares, Santiago D.

2016-04-15

Significant progress has been accomplished in the development of experimental contact-mode and dynamic-mode atomic force microscopy (AFM) methods designed to measure surface material properties. However, current methods are based on one-dimensional (1D) descriptions of the tip-sample interaction forces, thus neglecting the intricacies involved in the material behavior of complex samples (such as soft viscoelastic materials) as well as the differences in material response between the surface and the bulk. In order to begin to address this gap, a computational study is presented where the sample is simulated using an enhanced version of a recently introduced model that treats the surfacemore » as a collection of standard-linear-solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young's modulus. Relevant cases are discussed for single-and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface indentation profiles and tip-sample interaction force curves, as well as their implications with regards to experimental interpretation. A variety of phenomena are examined in detail, which highlight the need for further development of more physically accurate sample models that are specifically designed for AFM simulation. As a result, a multifrequency AFM simulation tool based on the above sample model is provided as supporting information.« less

The limits of hamiltonian structures in three-dimensional elasticity, shells, and rods

NASA Astrophysics Data System (ADS)

Ge, Z.; Kruse, H. P.; Marsden, J. E.

1996-01-01

This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material and derive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame.

Three-dimensional vs. two-dimensional shear-wave elastography of the testes - preliminary study on a healthy collective.

PubMed

Marcon, J; Trottmann, M; Rübenthaler, J; D'Anastasi, M; Stief, C G; Reiser, M F; Clevert, D A

2016-01-01

Shear wave elastography (SWE) and its derivative Supersonic Shear Imaging (SSI) are newer techniques for the determination of tissue elasticity by measuring the velocity of generated shear waves (SWV), which correlates positively with tissue stiffness.The techniques are integrated into many modern ultrasound systems and have been examined in the evaluation of viscoelastic properties of different organ systems. Two-dimensional shear wave elastography (2D SWE) of the testes has been found to be a useful tool in recent studies which included the determination of standard values in healthy volunteers. Three-dimensional shear wave elastography (3D SWE) is the latest development in elastography and is made possible by generation of a multiplanar three-dimensional map via volumetric acquisition with a special ultrasound transducer. This technique allows the assessment of tissue elasticity in a three-dimensional, fully accessible organ map.The aim of this preliminary study was to both evaluate the feasibility of 3D SWE and to compare 2D and 3D SWE standard values in the testes of healthy subjects. We examined the testes of healthy male volunteers (n = 32) with a mean age of 51.06±17.75 years (range 25-77 years) by B-mode ultrasound, 2D and 3D SWE techniques in September of 2016. Volunteers with a history of testicular pathologies were excluded. For all imaging procedures the SL15-4 linear transducer (bandwidth 4-15 MHz) as well as the SLV16-4 volumetric probe (bandwidth 4-16 MHz) of the Aixplorer® ultrasound device (SuperSonic Imagine, Aix-en-Provence, France) were used. Seven regions of interest (ROI, Q-Box®) within the testes were evaluated for SWV using both procedures. SWV values were described in m/s. Results were statistically evaluated using univariateanalysis. Mean SWV values were 1.05 m/s for the 2D SWE and 1.12 m/s for the 3D SWE.Comparisons of local areas delivered no statistically significant differences (p = 0.11 to p = 0.66), except for the region in the central portion in the superior part of the coronal plane (p = 0.03). Testicular volume was significanty higher by a mean of 1.72 ml when measured with 3D SWE (p = 0.001). 3D SWE proved to be a feasible diagnostic tool in the assessment of testicular tissue, providing the examiner with a fully accessible three-dimensional map in a multiplanar or multislice view. With this technique a more precise testicular imaging - especially if combined with the display of tissue stiffness in SWE - is available and therefore could improve the diagnostic work-up of scrotal masses or the routine investigation of infertile men. Further studies for a better understanding in the context of various testicular pathologies will be required.

Elastic plastic fracture mechanics methodology for surface cracks

NASA Astrophysics Data System (ADS)

Ernst, Hugo A.; Boatwright, D. W.; Curtin, W. J.; Lambert, D. M.

1993-08-01

The Elastic Plastic Fracture Mechanics (EPFM) Methodology has evolved significantly in the last several years. Nevertheless, some of these concepts need to be extended further before the whole methodology can be safely applied to structural parts. Specifically, there is a need to include the effect of constraint in the characterization of material resistance to crack growth and also to extend these methods to the case of 3D defects. As a consequence, this project was started as a 36 month research program with the general objective of developing an EPFM methodology to assess the structural reliability of pressure vessels and other parts of interest to NASA containing defects. This report covers a computer modelling algorithm used to simulate the growth of a semi-elliptical surface crack; the presentation of a finite element investigation that compared the theoretical (HRR) stress field to that produced by elastic and elastic-plastic models; and experimental efforts to characterize three dimensional aspects of fracture present in 'two dimensional', or planar configuration specimens.

Elastic plastic fracture mechanics methodology for surface cracks

NASA Technical Reports Server (NTRS)

Ernst, Hugo A.; Boatwright, D. W.; Curtin, W. J.; Lambert, D. M.

1993-01-01

The Elastic Plastic Fracture Mechanics (EPFM) Methodology has evolved significantly in the last several years. Nevertheless, some of these concepts need to be extended further before the whole methodology can be safely applied to structural parts. Specifically, there is a need to include the effect of constraint in the characterization of material resistance to crack growth and also to extend these methods to the case of 3D defects. As a consequence, this project was started as a 36 month research program with the general objective of developing an EPFM methodology to assess the structural reliability of pressure vessels and other parts of interest to NASA containing defects. This report covers a computer modelling algorithm used to simulate the growth of a semi-elliptical surface crack; the presentation of a finite element investigation that compared the theoretical (HRR) stress field to that produced by elastic and elastic-plastic models; and experimental efforts to characterize three dimensional aspects of fracture present in 'two dimensional', or planar configuration specimens.

A Simplified Mesh Deformation Method Using Commercial Structural Analysis Software

NASA Technical Reports Server (NTRS)

Hsu, Su-Yuen; Chang, Chau-Lyan; Samareh, Jamshid

2004-01-01

Mesh deformation in response to redefined or moving aerodynamic surface geometries is a frequently encountered task in many applications. Most existing methods are either mathematically too complex or computationally too expensive for usage in practical design and optimization. We propose a simplified mesh deformation method based on linear elastic finite element analyses that can be easily implemented by using commercially available structural analysis software. Using a prescribed displacement at the mesh boundaries, a simple structural analysis is constructed based on a spatially varying Young s modulus to move the entire mesh in accordance with the surface geometry redefinitions. A variety of surface movements, such as translation, rotation, or incremental surface reshaping that often takes place in an optimization procedure, may be handled by the present method. We describe the numerical formulation and implementation using the NASTRAN software in this paper. The use of commercial software bypasses tedious reimplementation and takes advantage of the computational efficiency offered by the vendor. A two-dimensional airfoil mesh and a three-dimensional aircraft mesh were used as test cases to demonstrate the effectiveness of the proposed method. Euler and Navier-Stokes calculations were performed for the deformed two-dimensional meshes.

Entropic Elasticity in the Giant Muscle Protein Titin

NASA Astrophysics Data System (ADS)

Morgan, Ian; Saleh, Omar

Intrinsically disordered proteins (IDPs) are a large and functionally important class of proteins that lack a fixed three-dimensional structure. Instead, they adopt a conformational ensemble of states which facilitates their biological function as molecular linkers, springs, and switches. Due to their conformational flexibility, it can be difficult to study IDPs using typical experimental methods. To overcome this challenge, we use a high-resolution single-molecule magnetic stretching technique to quantify IDP flexibility. We apply this technique to the giant muscle protein titin, measuring its elastic response at low forces. We present results demonstrating that titin's native elastic response derives from the combined entropic elasticity of its ordered and disordered domains.

Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum

NASA Astrophysics Data System (ADS)

Sander, Oliver; Schiela, Anton

2014-12-01

We formulate the static mechanical coupling of a geometrically exact Cosserat rod to a nonlinearly elastic continuum. In this setting, appropriate coupling conditions have to connect a one-dimensional model with director variables to a three-dimensional model without directors. Two alternative coupling conditions are proposed, which correspond to two different configuration trace spaces. For both, we show existence of solutions of the coupled problems, using the direct method of the calculus of variations. From the first-order optimality conditions, we also derive the corresponding conditions for the dual variables. These are then interpreted in mechanical terms.

Hydroelastic behaviour of a structure exposed to an underwater explosion.

PubMed

Colicchio, G; Greco, M; Brocchini, M; Faltinsen, O M

2015-01-28

The hydroelastic interaction between an underwater explosion and an elastic plate is investigated num- erically through a domain-decomposition strategy. The three-dimensional features of the problem require a large computational effort, which is reduced through a weak coupling between a one-dimensional radial blast solver, which resolves the blast evolution far from the boundaries, and a three-dimensional compressible flow solver used where the interactions between the compression wave and the boundaries take place and the flow becomes three-dimensional. The three-dimensional flow solver at the boundaries is directly coupled with a modal structural solver that models the response of the solid boundaries like elastic plates. This enables one to simulate the fluid-structure interaction as a strong coupling, in order to capture hydroelastic effects. The method has been applied to the experimental case of Hung et al. (2005 Int. J. Impact Eng. 31, 151-168 (doi:10.1016/j.ijimpeng.2003.10.039)) with explosion and structure sufficiently far from other boundaries and successfully validated in terms of the evolution of the acceleration induced on the plate. It was also used to investigate the interaction of an underwater explosion with the bottom of a close-by ship modelled as an orthotropic plate. In the application, the acoustic phase of the fluid-structure interaction is examined, highlighting the need of the fluid-structure coupling to capture correctly the possible inception of cavitation. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Influence of cross-link structure, density and mechanical properties in the mesoscale deformation mechanisms of collagen fibrils

PubMed Central

Depalle, Baptiste; Qin, Zhao; Shefelbine, Sandra J.; Buehler, Markus J.

2015-01-01

Collagen is a ubiquitous protein with remarkable mechanical properties. It is highly elastic, shows large fracture strength and enables substantial energy dissipation during deformation. Most of the connective tissue in humans consists of collagen fibrils composed of a staggered array of tropocollagen molecules, which are connected by intermolecular cross-links. In this study, we report a three-dimensional coarse-grained model of collagen and analyze the influence of enzymatic cross-links on the mechanics of collagen fibrils. Two representatives immature and mature cross-links are implemented in the mesoscale model using a bottom-up approach. By varying the number, type and mechanical properties of cross-links in the fibrils and performing tensile test on the models, we systematically investigate the deformation mechanisms of cross-linked collagen fibrils. We find that cross-linked fibrils exhibit a three phase behavior, which agrees closer with experimental results than what was obtained using previous models. The fibril mechanical response is characterized by: (i) an initial elastic deformation corresponding to the collagen molecule uncoiling, (ii) a linear regime dominated by molecule sliding and (iii) the second stiffer elastic regime related to the stretching of the backbone of the tropocollagen molecules until the fibril ruptures. Our results suggest that both cross-link density and type dictate the stiffness of large deformation regime by increasing the number of interconnected molecules while cross-links mechanical properties determine the failure strain and strength of the fibril. These findings reveal that cross-links play an essential role in creating an interconnected fibrillar material of tunable toughness and strength. PMID:25153614

BOPACE 3-D (the Boeing Plastic Analysis Capability for 3-dimensional Solids Using Isoparametric Finite Elements)

NASA Technical Reports Server (NTRS)

Vos, R. G.; Straayer, J. W.

1975-01-01

The BOPACE 3-D is a finite element computer program, which provides a general family of three-dimensional isoparametric solid elements, and includes a new algorithm for improving the efficiency of the elastic-plastic-creep solution procedure. Theoretical, user, and programmer oriented sections are presented to describe the program.

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).

Three-dimensional shape transformations of hydrogel sheets induced by small-scale modulation of internal stresses

NASA Astrophysics Data System (ADS)

Wu, Zi Liang; Moshe, Michael; Greener, Jesse; Therien-Aubin, Heloise; Nie, Zhihong; Sharon, Eran; Kumacheva, Eugenia

2013-03-01

Although Nature has always been a common source of inspiration in the development of artificial materials, only recently has the ability of man-made materials to produce complex three-dimensional (3D) structures from two-dimensional sheets been explored. Here we present a new approach to the self-shaping of soft matter that mimics fibrous plant tissues by exploiting small-scale variations in the internal stresses to form three-dimensional morphologies. We design single-layer hydrogel sheets with chemically distinct, fibre-like regions that exhibit differential shrinkage and elastic moduli under the application of external stimulus. Using a planar-to-helical three-dimensional shape transformation as an example, we explore the relation between the internal architecture of the sheets and their transition to cylindrical and conical helices with specific structural characteristics. The ability to engineer multiple three-dimensional shape transformations determined by small-scale patterns in a hydrogel sheet represents a promising step in the development of programmable soft matter.

Novel Three-Dimensional Interphase Characterisation of Polymer Nanocomposites Using Nanoscaled Topography.

PubMed

Mousa, Mohanad; Dong, Yu

2018-06-19

Mechanical properties of polymer nanocomposites depend primarily on nanointerphases as transitional zones between nanoparticles and surrounding matrices. Due to the difficulty in the quantitative characterisation of nanointerphases, previous literatures generally deemed such interphases as one-dimensional uniform zones around nanoparticles by assumption for analytical or theoretical modelling. We hereby have demonstrated for the first time direct three-dimensional topography and physical measurement of nanophase mechanical properties between nanodimeter bamboo charcoals (NBCs) and poly (vinyl alcohol) (PVA) in polymer nanocomposites. Topographical features, nanomechanical properties and dimensions of nanointerphases were systematically determined via peak force quantitative nanomechanical tapping mode (PFQNM). Significantly different mechanical properties of nanointerphases were revealed as opposed to those of individual NBCs and PVA matrices. Non-uniform irregular three-dimensional structures and shapes of nanointerphases are manifested around individual NBCs, which can be greatly influenced by nanoparticle size and roughness, and nanoparticle dispersion and distribution. Elastic moduli of nanointerphases were experimentally determined in range from 25.32 ±3.4 to 66.3±3.2 GPa. Additionally, it is clearly shown that the interphase modulus strongly depends on interphase surface area SAInterphase and interphase volume VInterphase. Different NBC distribution patterns from fully to partially embedded nanoparticles are proven to yield a remarkable reduction in elastic moduli of nanointerphases. © 2018 IOP Publishing Ltd.

Contribution of human skin topography to the characterization of dynamic skin tension during senescence: morpho-mechanical approach

NASA Astrophysics Data System (ADS)

Zahouani, H.; Djaghloul, M.; Vargiolu, R.; Mezghani, S.; Mansori, M. E. L.

2014-03-01

The structuring of the dermis with a network of collagen and elastic fibres gives a three-dimensional structure to the skin network with directions perpendicular and parallel to the skin surface. This three-dimensional morphology prints on the surface of the stratum corneum a three dimensional network of lines which express the mechanical tension of the skin at rest. To evaluate the changes of skin morphology, we used a three-dimensional confocal microscopy and characterization of skin imaging of volar forearm microrelief. We have accurately characterize the role of skin line network during chronological aging with the identification of depth scales on the network of lines (z <= 60μm) and the network of lines covering Langer's lines (z > 60 microns). During aging has been highlighted lower rows for elastic fibres, the decrease weakened the tension and results in enlargement of the plates of the microrelief, which gives us a geometric pertinent indicator to quantify the loss of skin tension and assess the stage of aging. The study of 120 Caucasian women shows that ageing in the volar forearm zone results in changes in the morphology of the line network organisation. The decrease in secondary lines (z <= 60 μm) is counterbalanced by an increase in the depth of the primary lines (z > 60 μm) and an accentuation of the anisotropy index.

Three-dimensional analysis of alveolar wall destruction in the early stage of pulmonary emphysema.

PubMed

Kobayashi, Yukihiro; Uehara, Takeshi; Kawasaki, Kenji; Sugano, Mitsutoshi; Matsumoto, Takehisa; Matsumoto, Gou; Honda, Takayuki

2015-03-01

The morphological mechanism of alveolar wall destruction during pulmonary emphysema has not been clarified. The aim of this study was to elucidate this process three-dimensionally. Lung specimens from five patients with pulmonary emphysema were used, and five controls with normal alveolar structure were also examined. Sections 150 μm thick were stained with hematoxylin and eosin, elastica, and silver impregnation, and immunostained with selected antibodies. We examined these sections three-dimensionally using a laser confocal microscope and a light microscope. There were only a few Kohn's pores and no fenestrae in the normal alveoli from the controls. In the lungs of the emphysema patients a small rupture appeared in the extremely thin alveolar wall among the alveolar capillaries. This rupture enlarged to form a circle surrounded by the capillaries, which was called an alveolar fenestra. Two neighboring fenestrae fused by breakdown of the collapsed or cord-like capillary between them to form a large fenestra. The large fenestrae fused repeatedly to become larger, and these were bordered by thick elastic fibers constructing an alveolar framework. Alveolar wall destruction during emphysema could start from small ruptures of the alveolar wall that become fenestrae surrounded by capillaries, which fuse repeatedly to become larger fenestrae rimmed with elastic fibers. The alveolar capillary network could initially prevent enlargement of the fenestrae, and the thick elastic fibers constituting the alveolar framework could secondarily prevent destruction of the alveolar wall structure. © 2014 Wiley Periodicals, Inc.

Elastic plastic fracture mechanics methodology for surface cracks

NASA Technical Reports Server (NTRS)

Ernst, Hugo A.; Lambert, D. M.

1994-01-01

The Elastic Plastic Fracture Mechanics Methodology has evolved significantly in the last several years. Nevertheless, some of these concepts need to be extended further before the whole methodology can be safely applied to structural parts. Specifically, there is a need to include the effect of constraint in the characterization of material resistance to crack growth and also to extend these methods to the case of 3D defects. As a consequence, this project was started as a 36 month research program with the general objective of developing an elastic plastic fracture mechanics methodology to assess the structural reliability of pressure vessels and other parts of interest to NASA which may contain flaws. The project is divided into three tasks that deal with (1) constraint and thickness effects, (2) three-dimensional cracks, and (3) the Leak-Before-Burst (LBB) criterion. This report period (March 1994 to August 1994) is a continuation of attempts to characterize three dimensional aspects of fracture present in 'two dimensional' or planar configuration specimens (Chapter Two), especially, the determination of, and use of, crack face separation data. Also, included, are a variety of fracture resistance testing results (J(m)R-curve format) and a discussion regarding two materials of NASA interest (6061-T651 Aluminum alloy and 1N718-STA1 nickel-base super alloy) involving a bases for like constraint in terms of ligament dimensions, and their comparison to the resulting J(m)R-curves (Chapter Two).

Interaction of Lamb Waves with Fatigue Cracks in Aluminum

DTIC Science & Technology

2011-09-01

Interaction of Lamb Waves with Fatigue Cracks in Aluminum E. D. SWENSON, C. T. OWENS and C. ALLEN ABSTRACT Elastic waves can travel across...the interaction of Lamb waves with both open and closed low-cycle fatigue cracks in aluminum plates using a three-dimensional laser Doppler vibrometer...and antisymmetric Lamb wave modes differ upon encountering fatigue cracks. INTRODUCTION The use of guided elastic waves (Lamb waves) has shown

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.

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.

Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial.

PubMed

Zhu, R; Liu, X N; Hu, G K; Sun, C T; Huang, G L

2014-11-24

Negative refraction of elastic waves has been studied and experimentally demonstrated in three- and two-dimensional phononic crystals, but Bragg scattering is impractical for low-frequency wave control because of the need to scale the structures to manageable sizes. Here we present an elastic metamaterial with chiral microstructure made of a single-phase solid material that aims to achieve subwavelength negative refraction of elastic waves. Both negative effective mass density and modulus are observed owing to simultaneous translational and rotational resonances. We experimentally demonstrate negative refraction of the longitudinal elastic wave at the deep-subwavelength scale in the metamaterial fabricated in a stainless steel plate. The experimental measurements are in good agreement with numerical simulations. Moreover, wave mode conversion related with negative refraction is revealed and discussed. The proposed elastic metamaterial may thus be used as a flat lens for elastic wave focusing.

Biopolymer Chain Elasticity: a novel concept and a least deformation energy principle predicts backbone and overall folding of DNA TTT hairpins in agreement with NMR distances

PubMed Central

Pakleza, Christophe; Cognet, Jean A. H.

2003-01-01

A new molecular modelling methodology is presented and shown to apply to all published solution structures of DNA hairpins with TTT in the loop. It is based on the theory of elasticity of thin rods and on the assumption that single-stranded B-DNA behaves as a continuous, unshearable, unstretchable and flexible thin rod. It requires four construction steps: (i) computation of the tri-dimensional trajectory of the elastic line, (ii) global deformation of single-stranded helical DNA onto the elastic line, (iii) optimisation of the nucleoside rotations about the elastic line, (iv) energy minimisation to restore backbone bond lengths and bond angles. This theoretical approach called ‘Biopolymer Chain Elasticity’ (BCE) is capable of reproducing the tri-dimensional course of the sugar–phosphate chain and, using NMR-derived distances, of reproducing models close to published solution structures. This is shown by computing three different types of distance criteria. The natural description provided by the elastic line and by the new parameter, Ω, which corresponds to the rotation angles of nucleosides about the elastic line, offers a considerable simplification of molecular modelling of hairpin loops. They can be varied independently from each other, since the global shape of the hairpin loop is preserved in all cases. PMID:12560506

Elastic metamaterials for tuning circular polarization of electromagnetic waves

PubMed Central

Zárate, Yair; Babaee, Sahab; Kang, Sung H.; Neshev, Dragomir N.; Shadrivov, Ilya V.; Bertoldi, Katia; Powell, David A.

2016-01-01

Electromagnetic resonators are integrated with advanced elastic material to develop a new type of tunable metamaterial. An electromagnetic-elastic metamaterial able to switch on and off its electromagnetic chiral response is experimentally demonstrated. Such tunability is attained by harnessing the unique buckling properties of auxetic elastic materials (buckliballs) with embedded electromagnetic resonators. In these structures, simple uniaxial compression results in a complex but controlled pattern of deformation, resulting in a shift of its electromagnetic resonance, and in the structure transforming to a chiral state. The concept can be extended to the tuning of three-dimensional materials constructed from the meta-molecules, since all the components twist and deform into the same chiral configuration when compressed. PMID:27320212

Elastic metamaterials for tuning circular polarization of electromagnetic waves.

PubMed

Zárate, Yair; Babaee, Sahab; Kang, Sung H; Neshev, Dragomir N; Shadrivov, Ilya V; Bertoldi, Katia; Powell, David A

2016-06-20

Electromagnetic resonators are integrated with advanced elastic material to develop a new type of tunable metamaterial. An electromagnetic-elastic metamaterial able to switch on and off its electromagnetic chiral response is experimentally demonstrated. Such tunability is attained by harnessing the unique buckling properties of auxetic elastic materials (buckliballs) with embedded electromagnetic resonators. In these structures, simple uniaxial compression results in a complex but controlled pattern of deformation, resulting in a shift of its electromagnetic resonance, and in the structure transforming to a chiral state. The concept can be extended to the tuning of three-dimensional materials constructed from the meta-molecules, since all the components twist and deform into the same chiral configuration when compressed.

Wave dispersion and propagation in state-based peridynamics

NASA Astrophysics Data System (ADS)

Butt, Sahir N.; Timothy, Jithender J.; Meschke, Günther

2017-11-01

Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models in cases, where discontinuities, such as cracks, are present in the deformation field. However, the nonlocal characteristics of peridynamics leads to a dispersive dynamic response of the medium. In this study we focus on the dispersion properties of a state-based linear peridynamic solid model and specifically investigate the role of the peridynamic horizon. We derive the dispersion relation for one, two and three dimensional cases and investigate the effect of horizon size, mesh size (lattice spacing) and the influence function on the dispersion properties. We show how the influence function can be used to minimize wave dispersion at a fixed lattice spacing and demonstrate it qualitatively by wave propagation analysis in one- and two-dimensional models of elastic solids. As a main contribution of this paper, we propose to associate peridynamic non-locality expressed by the horizon with a characteristic length scale related to the material microstructure. To this end, the dispersion curves obtained from peridynamics are compared with experimental data for two kinds of sandstone.

Self-Assembly and Electrostriction of Arrays and Chains of Hopfion Particles in Chiral Liquid Crystals

DOE PAGES

Ackerman, P. J.; van de Lagemaat, J.; Smalyukh, I. I.

2015-01-21

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains thatmore » exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields.« less

Capillary origami: spontaneous wrapping of a droplet with an elastic sheet.

PubMed

Py, Charlotte; Reverdy, Paul; Doppler, Lionel; Bico, José; Roman, Benoît; Baroud, Charles N

2007-04-13

The interaction between elasticity and capillarity is used to produce three-dimensional structures through the wrapping of a liquid droplet by a planar sheet. The final encapsulated 3D shape is controlled by tailoring the initial geometry of the flat membrane. Balancing interfacial energy with elastic bending energy provides a critical length scale below which encapsulation cannot occur, which is verified experimentally. This length is found to depend on the thickness as h3/2, a scaling favorable to miniaturization which suggests a new way of mass production of 3D micro- or nanoscale objects.

Nonlinear Site Response Validation Studies Using KIK-net Strong Motion Data

NASA Astrophysics Data System (ADS)

Asimaki, D.; Shi, J.

2014-12-01

Earthquake simulations are nowadays producing realistic ground motion time-series in the range of engineering design applications. Of particular significance to engineers are simulations of near-field motions and large magnitude events, for which observations are scarce. With the engineering community slowly adopting the use of simulated ground motions, site response models need to be re-evaluated in terms of their capabilities and limitations to 'translate' the simulated time-series from rock surface output to structural analyses input. In this talk, we evaluate three one-dimensional site response models: linear viscoelastic, equivalent linear and nonlinear. We evaluate the performance of the models by comparing predictions to observations at 30 downhole stations of the Japanese network KIK-Net that have recorded several strong events, including the 2011 Tohoku earthquake. Velocity profiles are used as the only input to all models, while additional parameters such as quality factor, density and nonlinear dynamic soil properties are estimated from empirical correlations. We quantify the differences of ground surface predictions and observations in terms of both seismological and engineering intensity measures, including bias ratios of peak ground response and visual comparisons of elastic spectra, and inelastic to elastic deformation ratio for multiple ductility ratios. We observe that PGV/Vs,30 — as measure of strain— is a better predictor of site nonlinearity than PGA, and that incremental nonlinear analyses are necessary to produce reliable estimates of high-frequency ground motion components at soft sites. We finally discuss the implications of our findings on the parameterization of nonlinear amplification factors in GMPEs, and on the extensive use of equivalent linear analyses in probabilistic seismic hazard procedures.

A Variational Principle for Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Spangler, Jan L.

2003-01-01

A variational principle is formulated for the inverse problem of full-field reconstruction of three-dimensional plate/shell deformations from experimentally measured surface strains. The formulation is based upon the minimization of a least squares functional that uses the complete set of strain measures consistent with linear, first-order shear-deformation theory. The formulation, which accommodates for transverse shear deformation, is applicable for the analysis of thin and moderately thick plate and shell structures. The main benefit of the variational principle is that it is well suited for C(sup 0)-continuous displacement finite element discretizations, thus enabling the development of robust algorithms for application to complex civil and aeronautical structures. The methodology is especially aimed at the next generation of aerospace vehicles for use in real-time structural health monitoring systems.

Recent Progress in the p and h-p Version of the Finite Element Method.

DTIC Science & Technology

1987-07-01

code PROBE which was developed recently by NOETIC Technologies, St. Louis £54]. PROBE solves two dimensional problems of linear elasticity, stationary...of the finite element method was studied in detail from various point of view. We will mention here some essential illustrative results. In one...28) Bathe, K. J., Brezzi, F., Studies of finite element procedures - the INF-SUP condition, equivalent forms and applications in Reliability of

A Comparison of Curing Process-Induced Residual Stresses and Cure Shrinkage in Micro-Scale Composite Structures with Different Constitutive Laws

NASA Astrophysics Data System (ADS)

Li, Dongna; Li, Xudong; Dai, Jianfeng; Xi, Shangbin

2018-02-01

In this paper, three kinds of constitutive laws, elastic, "cure hardening instantaneously linear elastic (CHILE)" and viscoelastic law, are used to predict curing process-induced residual stress for the thermoset polymer composites. A multi-physics coupling finite element analysis (FEA) model implementing the proposed three approaches is established in COMSOL Multiphysics-Version 4.3b. The evolution of thermo-physical properties with temperature and degree of cure (DOC), which improved the accuracy of numerical simulations, and cure shrinkage are taken into account for the three models. Subsequently, these three proposed constitutive models are implemented respectively in a 3D micro-scale composite laminate structure. Compared the differences between these three numerical results, it indicates that big error in residual stress and cure shrinkage generates by elastic model, but the results calculated by the modified CHILE model are in excellent agreement with those estimated by the viscoelastic model.

Tracer particles in two-dimensional elastic networks diffuse logarithmically slow

NASA Astrophysics Data System (ADS)

Lizana, Ludvig; Ambjörnsson, Tobias; Lomholt, Michael A.

2017-01-01

Several experiments on tagged molecules or particles in living systems suggest that they move anomalously slow—their mean squared displacement (MSD) increase slower than linearly with time. Leading models aimed at understanding these experiments predict that the MSD grows as a power law with a growth exponent that is smaller than unity. However, in some experiments the growth is so slow (fitted exponent  ˜0.1-0.2) that they hint towards other mechanisms at play. In this paper, we theoretically demonstrate how in-plane collective modes excited by thermal fluctuations in a two dimensional membrane lead to logarithmic time dependence for the the tracer particle’s MSD.

Structural relaxation driven increase in elastic modulus for a bulk metallic glass

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

Arora, Harpreet Singh; Aditya, Ayyagari V.; Mukherjee, Sundeep, E-mail: sundeep.mukherjee@unt.edu

2015-01-07

The change in elastic modulus as a function of temperature was investigated for a zirconium-based bulk metallic glass. High temperature nano-indentation was done over a wide temperature range from room temperature to the glass-transition. At higher temperature, there was a transition from inhomogeneous to homogeneous deformation, with a decrease in serrated flow and an increase in creep displacement. Hardness was found to decrease, whereas elastic modulus was found to increase with temperature. The increase in elastic modulus for metallic glass at higher temperature was explained by diffusive rearrangement of atoms resulting in free volume annihilation. This is in contrast tomore » elastic modulus increase with temperature for silicate glasses due to compaction of its open three dimensional coordinated structure without any atomic diffusion.« less

Development of a linearized unsteady Euler analysis for turbomachinery blade rows

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Kousen, Kenneth A.

1995-01-01

A linearized unsteady aerodynamic analysis for axial-flow turbomachinery blading is described in this report. The linearization is based on the Euler equations of fluid motion and is motivated by the need for an efficient aerodynamic analysis that can be used in predicting the aeroelastic and aeroacoustic responses of blade rows. The field equations and surface conditions required for inviscid, nonlinear and linearized, unsteady aerodynamic analyses of three-dimensional flow through a single, blade row operating within a cylindrical duct, are derived. An existing numerical algorithm for determining time-accurate solutions of the nonlinear unsteady flow problem is described, and a numerical model, based upon this nonlinear flow solver, is formulated for the first-harmonic linear unsteady problem. The linearized aerodynamic and numerical models have been implemented into a first-harmonic unsteady flow code, called LINFLUX. At present this code applies only to two-dimensional flows, but an extension to three-dimensions is planned as future work. The three-dimensional aerodynamic and numerical formulations are described in this report. Numerical results for two-dimensional unsteady cascade flows, excited by prescribed blade motions and prescribed aerodynamic disturbances at inlet and exit, are also provided to illustrate the present capabilities of the LINFLUX analysis.

Offset-electrode profile acquisition strategy for electrical resistivity tomography

NASA Astrophysics Data System (ADS)

Robbins, Austin R.; Plattner, Alain

2018-04-01

We present an electrode layout strategy that allows electrical resistivity profiles to image the third dimension close to the profile plane. This "offset-electrode profile" approach involves laterally displacing electrodes away from the profile line in an alternating fashion and then inverting the resulting data using three-dimensional electrical resistivity tomography software. In our synthetic and field surveys, the offset-electrode method succeeds in revealing three-dimensional structures in the vicinity of the profile plane, which we could not achieve using three-dimensional inversions of linear profiles. We confirm and explain the limits of linear electrode profiles through a discussion of the three-dimensional sensitivity patterns: For a homogeneous starting model together with a linear electrode layout, all sensitivities remain symmetric with respect to the profile plane through each inversion step. This limitation can be overcome with offset-electrode layouts by breaking the symmetry pattern among the sensitivities. Thanks to freely available powerful three-dimensional resistivity tomography software and cheap modern computing power, the requirement for full three-dimensional calculations does not create a significant burden and renders the offset-electrode approach a cost-effective method. By offsetting the electrodes in an alternating pattern, as opposed to laying the profile out in a U-shape, we minimize shortening the profile length.

Manipulating sonic band gaps at will: vibrational density of states in three-dimensional acoustic metamaterial composites

NASA Astrophysics Data System (ADS)

Terao, Takamichi

2018-04-01

Vibrational properties of elastic composites containing a mass-in-mass microstructure embedded in a solid matrix are numerically studied. Using a lattice model, we investigate the vibrational density of states in three-dimensional composite structures where resonant particles are randomly dispersed. By dispersing such particles in the system, a sonic band gap appears. It is confirmed that this band gap can be introduced in a desired frequency regime by changing the parameters of resonant particles and the frequency width of this band gap can be controlled by varying the concentration of the resonant particles to be dispersed. In addition, multiple sonic band gaps can be realized using different species of resonant particles. These results enable us to suggest an alternative method to fabricate devices that can inhibit the propagation of elastic waves with specific frequencies using acoustic metamaterials.

Microwave imaging by three-dimensional Born linearization of electromagnetic scattering

NASA Astrophysics Data System (ADS)

Caorsi, S.; Gragnani, G. L.; Pastorino, M.

1990-11-01

An approach to microwave imaging is proposed that uses a three-dimensional vectorial form of the Born approximation to linearize the equation of electromagnetic scattering. The inverse scattering problem is numerically solved for three-dimensional geometries by means of the moment method. A pseudoinversion algorithm is adopted to overcome ill conditioning. Results show that the method is well suited for qualitative imaging purposes, while its capability for exactly reconstructing the complex dielectric permittivity is affected by the limitations inherent in the Born approximation and in ill conditioning.

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.

Deformation behaviors of three-dimensional graphene honeycombs under out-of-plane compression: Atomistic simulations and predictive modeling

NASA Astrophysics Data System (ADS)

Meng, Fanchao; Chen, Cheng; Hu, Dianyin; Song, Jun

2017-12-01

Combining atomistic simulations and continuum modeling, a comprehensive study of the out-of-plane compressive deformation behaviors of equilateral three-dimensional (3D) graphene honeycombs was performed. It was demonstrated that under out-of-plane compression, the honeycomb exhibits two critical deformation events, i.e., elastic mechanical instability (including elastic buckling and structural transformation) and inelastic structural collapse. The above events were shown to be strongly dependent on the honeycomb cell size and affected by the local atomic bonding at the cell junction. By treating the 3D graphene honeycomb as a continuum cellular solid, and accounting for the structural heterogeneity and constraint at the junction, a set of analytical models were developed to accurately predict the threshold stresses corresponding to the onset of those deformation events. The present study elucidates key structure-property relationships of 3D graphene honeycombs under out-of-plane compression, and provides a comprehensive theoretical framework to predictively analyze their deformation responses, and more generally, offers critical new knowledge for the rational bottom-up design of 3D networks of two-dimensional nanomaterials.

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.

Directional asymmetry of the nonlinear wave phenomena in a three-dimensional granular phononic crystal under gravity.

PubMed

Merkel, A; Tournat, V; Gusev, V

2014-08-01

We report the experimental observation of the gravity-induced asymmetry for the nonlinear transformation of acoustic waves in a noncohesive granular phononic crystal. Because of the gravity, the contact precompression increases with depth inducing space variations of not only the linear and nonlinear elastic moduli but also of the acoustic wave dissipation. We show experimentally and explain theoretically that, in contrast to symmetric propagation of linear waves, the amplitude of the nonlinearly self-demodulated wave depends on whether the propagation of the waves is in the direction of the gravity or in the opposite direction. Among the observed nonlinear processes, we report frequency mixing of the two transverse-rotational modes belonging to the optical band of vibrations and propagating with negative phase velocities, which results in the excitation of a longitudinal wave belonging to the acoustic band of vibrations and propagating with positive phase velocity. We show that the measurements of the gravity-induced asymmetry in the nonlinear acoustic phenomena can be used to compare the in-depth distributions of the contact nonlinearity and of acoustic absorption.

An accurate boundary element method for the exterior elastic scattering problem in two dimensions

NASA Astrophysics Data System (ADS)

Bao, Gang; Xu, Liwei; Yin, Tao

2017-11-01

This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller [1] boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula [2] is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.

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.

Biomechanical implications of cortical elastic properties of the macaque mandible.

PubMed

Dechow, Paul C; Panagiotopoulou, Olga; Gharpure, Poorva

2017-10-01

Knowledge of the variation in the elastic properties of mandibular cortical bone is essential for modeling bone function. Our aim was to characterize the elastic properties of rhesus macaque mandibular cortical bone and compare these to the elastic properties from mandibles of dentate humans and baboons. Thirty cylindrical samples were harvested from each of six adult female rhesus monkey mandibles. Assuming orthotropy, axes of maximum stiffness in the plane of the cortical plate were derived from ultrasound velocity measurements. Further velocity measurements with longitudinal and transverse ultrasonic transducers along with measurements of bone density were used to compute three-dimensional cortical elastic properties using equations based on Hooke's law. Results showed regional variations in the elastic properties of macaque mandibular cortical bone that have both similarities and differences with that of humans and baboons. So far, the biological and structural basis of these differences is poorly understood. Copyright © 2017 Elsevier GmbH. All rights reserved.

Linear stability theory and three-dimensional boundary layer transition

NASA Technical Reports Server (NTRS)

Spall, Robert E.; Malik, Mujeeb R.

1992-01-01

The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes.

The simulation of shock- and impact-driven flows with Mie-Gruneisen equations of state

NASA Astrophysics Data System (ADS)

Ward, Geoffrey M.

An investigation of shock- and impact-driven flows with Mie-Gruneisen equation of state derived from a linear shock-particle speed Hugoniot relationship is presented. Cartesian mesh methods using structured adaptive refinement are applied to simulate several flows of interest in an Eulerian frame of reference. The flows central to the investigation include planar Richtmyer-Meshkov instability, the impact of a sphere with a plate, and an impact-driven Mach stem. First, for multicomponent shock-driven flows, a dimensionally unsplit, spatially high-order, hybrid, center-difference, limiter methodology is developed. Effective switching between center-difference and upwinding schemes is achieved by a set of robust tolerance and Lax-entropy-based criteria [49]. Oscillations that result from such a mixed stencil scheme are minimized by requiring that the upwinding method approaches the center-difference method in smooth regions. The solver is then applied to investigate planar Richtmyer-Meshkov instability in the context of an equation of state comparison. Comparisons of simulations with materials modeled by isotropic stress Mie-Gruneisen equations of state derived from a linear shock-particle speed Hugoniot relationship [36,52] to those of perfect gases are made with the intention of exposing the role of the equation of state. First, results for single- and triple-mode planar Richtmyer-Meshkov instability between mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Gruneisen equations of state are presented for the case of a reflected shock. The single-mode case is explored for incident shock Mach numbers of 1.5 and 2.5. Additionally, examined is single-mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. Vorticity distribution and corrugation centerline shortly after shock interaction is also examined. The formation of incipient weak shock waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected. Next, the ghost fluid method [83] is explored for application to impact-driven flows with Mie-Gruneisen equations of state in a vacuum. Free surfaces are defined utilizing a level-set approach. The level-set is reinitialized to the signed distance function periodically by solution to a Hamilton-Jacobi differential equation in artificial time. Flux reconstruction along each Cartesian direction of the domain is performed by subdividing in a way that allows for robust treatment of grid-scale sized voids. Ghost cells in voided regions near the material-vacuum interface are determined from surface-normal Riemann problem solution. The method is then applied to several impact problems of interest. First, a one-dimensional impact problem is examined in Mie-Gruneisen aluminum with simple point erosion used to model separation by spallation under high tension. A similar three-dimensional axisymmetric simulation of two rods impacting is then performed without a model for spallation. Further results for three-dimensional axisymmetric simulation of a sphere hitting a plate are then presented. Finally, a brief investigation of the assumptions utilized in modeling solids as isotropic fluids is undertaken. An Eulerian solver approach to handling elastic and elastic-plastic solids is utilized for comparison to the simple fluid model assumption. First, in one dimension an impact problem is examined for elastic, elastic-plastic, and fluid equations of state for aluminum. The results demonstrate that in one dimension the fluid models the plastic shock structure of the flow well. Further investigation is made using a three-dimensional axisymmetric simulation of an impact problem involving a copper cylinder surrounded by aluminum. An aluminum slab impact drives a faster shock in the outer aluminum region yielding a Mach reflection in the copper. The results demonstrate similar plastic shock structures. Several differences are also notable that include a lack of roll-up instability at the material interface and slip-line emanating from the Mach stem's triple point. (Abstract shortened by UMI.)

Influence of cross-link structure, density and mechanical properties in the mesoscale deformation mechanisms of collagen fibrils.

PubMed

Depalle, Baptiste; Qin, Zhao; Shefelbine, Sandra J; Buehler, Markus J

2015-12-01

Collagen is a ubiquitous protein with remarkable mechanical properties. It is highly elastic, shows large fracture strength and enables substantial energy dissipation during deformation. Most of the connective tissue in humans consists of collagen fibrils composed of a staggered array of tropocollagen molecules, which are connected by intermolecular cross-links. In this study, we report a three-dimensional coarse-grained model of collagen and analyze the influence of enzymatic cross-links on the mechanics of collagen fibrils. Two representatives immature and mature cross-links are implemented in the mesoscale model using a bottom-up approach. By varying the number, type and mechanical properties of cross-links in the fibrils and performing tensile test on the models, we systematically investigate the deformation mechanisms of cross-linked collagen fibrils. We find that cross-linked fibrils exhibit a three phase behavior, which agrees closer with experimental results than what was obtained using previous models. The fibril mechanical response is characterized by: (i) an initial elastic deformation corresponding to the collagen molecule uncoiling, (ii) a linear regime dominated by molecule sliding and (iii) the second stiffer elastic regime related to the stretching of the backbone of the tropocollagen molecules until the fibril ruptures. Our results suggest that both cross-link density and type dictate the stiffness of large deformation regime by increasing the number of interconnected molecules while cross-links mechanical properties determine the failure strain and strength of the fibril. These findings reveal that cross-links play an essential role in creating an interconnected fibrillar material of tunable toughness and strength. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

Simulation of the zero-temperature behavior of a three-dimensional elastic medium

NASA Astrophysics Data System (ADS)

McNamara, David; Middleton, A. Alan; Zeng, Chen

1999-10-01

We have performed numerical simulation of a three-dimensional elastic medium, with scalar displacements, subject to quenched disorder. In the absence of topological defects this system is equivalent to a (3+1)-dimensional interface subject to a periodic pinning potential. We have applied an efficient combinatorial optimization algorithm to generate exact ground states for this interface representation. Our results indicate that this Bragg glass is characterized by power law divergences in the structure factor S(k)~Ak-3. We have found numerically consistent values of the coefficient A for two lattice discretizations of the medium, supporting universality for A in the isotropic systems considered here. We also examine the response of the ground state to the change in boundary conditions that corresponds to introducing a single dislocation loop encircling the system. The rearrangement of the ground state caused by this change is equivalent to the domain wall of elastic deformations which span the dislocation loop. Our results indicate that these domain walls are highly convoluted, with a fractal dimension df=2.60(5). We also discuss the implications of the domain wall energetics for the stability of the Bragg glass phase. Elastic excitations similar to these domain walls arise when the pinning potential is slightly perturbed. As in other disordered systems, perturbations of relative strength δ introduce a new length scale L*~δ-1/ζ beyond which the perturbed ground state becomes uncorrelated with the reference (unperturbed) ground state. We have performed a scaling analysis of the response of the ground state to the perturbations and obtain ζ=0.385(40). This value is consistent with the scaling relation ζ=df/2-θ, where θ characterizes the scaling of the energy fluctuations of low energy excitations.

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2015-07-20

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less

Soft tissue strain measurement using an optical method

NASA Astrophysics Data System (ADS)

Toh, Siew Lok; Tay, Cho Jui; Goh, Cho Hong James

2008-11-01

Digital image correlation (DIC) is a non-contact optical technique that allows the full-field estimation of strains on a surface under an applied deformation. In this project, the application of an optimized DIC technique is applied, which can achieve efficiency and accuracy in the measurement of two-dimensional deformation fields in soft tissue. This technique relies on matching the random patterns recorded in images to directly obtain surface displacements and to get displacement gradients from which the strain field can be determined. Digital image correlation is a well developed technique that has numerous and varied engineering applications, including the application in soft and hard tissue biomechanics. Chicken drumstick ligaments were harvested and used during the experiments. The surface of the ligament was speckled with black paint to allow for correlation to be done. Results show that the stress-strain curve exhibits a bi-linear behavior i.e. a "toe region" and a "linear elastic region". The Young's modulus obtained for the toe region is about 92 MPa and the modulus for the linear elastic region is about 230 MPa. The results are within the values for mammalian anterior cruciate ligaments of 150-300 MPa.

Fractal Dimensionality of Pore and Grain Volume of a Siliciclastic Marine Sand

NASA Astrophysics Data System (ADS)

Reed, A. H.; Pandey, R. B.; Lavoie, D. L.

Three-dimensional (3D) spatial distributions of pore and grain volumes were determined from high-resolution computer tomography (CT) images of resin-impregnated marine sands. Using a linear gradient extrapolation method, cubic three-dimensional samples were constructed from two-dimensional CT images. Image porosity (0.37) was found to be consistent with the estimate of porosity by water weight loss technique (0.36). Scaling of the pore volume (Vp) with the linear size (L), V~LD provides the fractal dimensionalities of the pore volume (D=2.74+/-0.02) and grain volume (D=2.90+/-0.02) typical for sedimentary materials.

Development of a Linearized Unsteady Euler Analysis with Application to Wake/Blade-Row Interactions

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Chuang, H. Andrew

1999-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide a comprehensive and efficient unsteady aerodynamic analysis for predicting the aeroacoustic and aeroelastic responses of axial-flow turbomachinery blading. The mathematical models needed to describe nonlinear and linearized, inviscid, unsteady flows through a blade row operating within a cylindrical annular duct are presented in this report. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to far-field eigen analyses, is also described. The linearized aerodynamic and numerical models have been implemented into the three-dimensional unsteady flow code, LINFLUX. This code is applied herein to predict unsteady subsonic flows driven by wake or vortical excitations. The intent is to validate the LINFLUX analysis via numerical results for simple benchmark unsteady flows and to demonstrate this analysis via application to a realistic wake/blade-row interaction. Detailed numerical results for a three-dimensional version of the 10th Standard Cascade and a fan exit guide vane indicate that LINFLUX is becoming a reliable and useful unsteady aerodynamic prediction capability that can be applied, in the future, to assess the three-dimensional flow physics important to blade-row, aeroacoustic and aeroelastic responses.

A 2D nonlinear multiring model for blood flow in large elastic arteries

NASA Astrophysics Data System (ADS)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

Fabrication of a biomimetic elastic intervertebral disk scaffold using additive manufacturing.

PubMed

Whatley, Benjamin R; Kuo, Jonathan; Shuai, Cijun; Damon, Brooke J; Wen, Xuejun

2011-03-01

A custom-designed three-dimensional additive manufacturing device was developed to fabricate scaffolds for intervertebral disk (IVD) regeneration. This technique integrated a computer with a device capable of 3D movement allowing for precise motion and control over the polymer scaffold resolution. IVD scaffold structures were designed using computer-aided design to resemble the natural IVD structure. Degradable polyurethane (PU) was used as an elastic scaffold construct to mimic the elastic nature of the native IVD tissue and was deposited at a controlled rate using ultra-fine micropipettes connected to a syringe pump. The elastic PU was extruded directly onto a collecting substrate placed on a freezing stage. The three-dimensional movement of the computer-controlled device combined with the freezing stage enabled precise control of polymer deposition using extrusion. The addition of the freezing stage increased the polymer solution viscosity and hardened the polymer solution as it was extruded out of the micropipette tip. This technique created scaffolds with excellent control over macro- and micro-structure to influence cell behavior, specifically for cell adhesion, proliferation, and alignment. Concentric lamellae were printed at a high resolution to mimic the native shape and structure of the IVD. Seeded cells aligned along the concentric lamellae and acquired cell morphology similar to native tissue in the outer portion of the IVD. The fabricated scaffolds exhibited elastic behavior during compressive and shear testing, proving that the scaffolds could support loads with proper fatigue resistance without permanent deformation. Additionally, the mechanical properties of the scaffolds were comparable to those of native IVD tissue.

From local to global measurements of nonclassical nonlinear elastic effects in geomaterials

DOE PAGES

Lott, Martin; Remillieux, Marcel C.; Le Bas, Pierre-Yves; ...

2016-09-07

Here, the equivalence between local and global measures of nonclassical nonlinear elasticity is established in a slender resonant bar. Nonlinear effects are first measured globally using nonlinear resonance ultrasound spectroscopy (NRUS), which monitors the relative shift of the resonance frequency as a function of the maximum dynamic strain in the sample. Subsequently, nonlinear effects are measured locally at various positions along the sample using dynamic acousto elasticity testing (DAET). Finally, after correcting analytically the DAET data for three-dimensional strain effects and integrating numerically these corrected data along the length of the sample, the NRUS global measures are retrieved almost exactly.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Critical Nucleation Length for Accelerating Frictional Slip

NASA Astrophysics Data System (ADS)

Aldam, Michael; Weikamp, Marc; Spatschek, Robert; Brener, Efim A.; Bouchbinder, Eran

2017-11-01

The spontaneous nucleation of accelerating slip along slowly driven frictional interfaces is central to a broad range of geophysical, physical, and engineering systems, with particularly far-reaching implications for earthquake physics. A common approach to this problem associates nucleation with an instability of an expanding creep patch upon surpassing a critical length Lc. The critical nucleation length Lc is conventionally obtained from a spring-block linear stability analysis extended to interfaces separating elastically deformable bodies using model-dependent fracture mechanics estimates. We propose an alternative approach in which the critical nucleation length is obtained from a related linear stability analysis of homogeneous sliding along interfaces separating elastically deformable bodies. For elastically identical half-spaces and rate-and-state friction, the two approaches are shown to yield Lc that features the same scaling structure, but with substantially different numerical prefactors, resulting in a significantly larger Lc in our approach. The proposed approach is also shown to be naturally applicable to finite-size systems and bimaterial interfaces, for which various analytic results are derived. To quantitatively test the proposed approach, we performed inertial Finite-Element-Method calculations for a finite-size two-dimensional elastically deformable body in rate-and-state frictional contact with a rigid body under sideway loading. We show that the theoretically predicted Lc and its finite-size dependence are in reasonably good quantitative agreement with the full numerical solutions, lending support to the proposed approach. These results offer a theoretical framework for predicting rapid slip nucleation along frictional interfaces.

The method of lines in three dimensional fracture mechanics

NASA Technical Reports Server (NTRS)

Gyekenyesi, J.; Berke, L.

1980-01-01

A review of recent developments in the calculation of design parameters for fracture mechanics by the method of lines (MOL) is presented. Three dimensional elastic and elasto-plastic formulations are examined and results from previous and current research activities are reported. The application of MOL to the appropriate partial differential equations of equilibrium leads to coupled sets of simultaneous ordinary differential equations. Solutions of these equations are obtained by the Peano-Baker and by the recurrance relations methods. The advantages and limitations of both solution methods from the computational standpoint are summarized.

Optical conductivity of three and two dimensional topological nodal-line semimetals

NASA Astrophysics Data System (ADS)

Barati, Shahin; Abedinpour, Saeed H.

2017-10-01

The peculiar shape of the Fermi surface of topological nodal-line semimetals at low carrier concentrations results in their unusual optical and transport properties. We analytically investigate the linear optical responses of three- and two-dimensional nodal-line semimetals using the Kubo formula. The optical conductivity of a three-dimensional nodal-line semimetal is anisotropic. Along the axial direction (i.e., the direction perpendicular to the nodal-ring plane), the Drude weight has a linear dependence on the chemical potential at both low and high carrier dopings. For the radial direction (i.e., the direction parallel to the nodal-ring plane), this dependence changes from linear into quadratic in the transition from low into high carrier concentration. The interband contribution into optical conductivity is also anisotropic. In particular, at large frequencies, it saturates to a constant value for the axial direction and linearly increases with frequency along the radial direction. In two-dimensional nodal-line semimetals, no interband optical transition could be induced and the only contribution to the optical conductivity arises from the intraband excitations. The corresponding Drude weight is independent of the carrier density at low carrier concentrations and linearly increases with chemical potential at high carrier doping.

Linearized compressible-flow theory for sonic flight speeds

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard; Spreiter, John R

1950-01-01

The partial differential equation for the perturbation velocity potential is examined for free-stream Mach numbers close to and equal to one. It is found that, under the assumptions of linearized theory, solutions can be found consistent with the theory for lifting-surface problems both in stationary three-dimensional flow and in unsteady two-dimensional flow. Several examples are solved including a three dimensional swept-back wing and two dimensional harmonically-oscillating wing, both for a free stream Mach number equal to one. Momentum relations for the evaluation of wave and vortex drag are also discussed. (author)

Variations in lithospheric thickness on Venus

NASA Technical Reports Server (NTRS)

Johnson, C. L.; Sandwell, David T.

1992-01-01

Recent analyses of Magellan data have indicated many regions exhibiting topograhic flexure. On Venus, flexure is associated predominantly with coronae and the chasmata with Aphrodite Terra. Modeling of these flexural signatures allows the elastic and mechanical thickness of the lithosphere to be estimated. In areas where the lithosphere is flexed beyond its elastic limit the saturation moment provides information on the strength of the lithosphere. Modeling of 12 flexural features on Venus has indicated lithospheric thicknesses comparable with terrestrial values. This has important implications for the venusian heat budget. Flexure of a thin elastic plate due simultaneously to a line load on a continuous plate and a bending moment applied to the end of a broken plate is considered. The mean radius and regional topographic gradient are also included in the model. Features with a large radius of curvature were selected so that a two-dimensional approximation could be used. Comparisons with an axisymmetric model were made for some features to check the validity of the two-dimensional assumption. The best-fit elastic thickness was found for each profile crossing a given flexural feature. In addition, the surface stress and bending moment at the first zero crossing of each profile were also calculated. Flexural amplitudes and elastic thicknesses obtained for 12 features vary significantly. Three examples of the model fitting procedures are discussed.

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1996-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic response characteristics of axial-flow turbomachinery blading. The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. In addition, a numerical model for linearized inviscid unsteady flow, which is based upon an existing nonlinear, implicit, wave-split, finite volume analysis, is described. These aerodynamic and numerical models have been implemented into an unsteady flow code, called LINFLUX. A preliminary version of the LINFLUX code is applied herein to selected, benchmark three-dimensional, subsonic, unsteady flows, to illustrate its current capabilities and to uncover existing problems and deficiencies. The numerical results indicate that good progress has been made toward developing a reliable and useful three-dimensional prediction capability. However, some problems, associated with the implementation of an unsteady displacement field and numerical errors near solid boundaries, still exist. Also, accurate far-field conditions must be incorporated into the FINFLUX analysis, so that this analysis can be applied to unsteady flows driven be external aerodynamic excitations.

Elastic, Optoelectronic and Thermoelectric Properties of the Lead-Free Halide Semiconductors Cs2AgBi X 6 ( X = Cl, Br): Ab Initio Investigation

NASA Astrophysics Data System (ADS)

Guechi, N.; Bouhemadou, A.; Bin-Omran, S.; Bourzami, A.; Louail, L.

2018-02-01

We report a detailed investigation of the elastic moduli, electronic band structure, density of states, chemical bonding, electron and hole effective masses, optical response functions and thermoelectric properties of the lead-free halide double perovskites Cs2AgBiCl6 and Cs2AgBiBr6 using the full potential linearized augmented plane wave (FP-LAPW) method with the generalized gradient approximation (GGA-PBEsol) and the Tran-Blaha modified Becke-Johnson (TB-mBJ) potential. Because of the presence of heavy elements in the studied compounds, we include the spin-orbit coupling (SOC) effect. Our calculated structural parameters agree very well with the available experimental and theoretical findings. Single-crystal and polycrystalline elastic constants are predicted using the total-energy versus strain approach. Three-dimensional representations of the crystallographic direction dependence on the shear modulus, Young's modulus and Poisson's ratio demonstrate a noticeable elastic anisotropy. The TB-mBJ potential with SOC yields an indirect band gap of 2.44 (1.93) eV for Cs2AgBiCl6 (Cs2AgBiBr6), in good agreement with the existing experimental data. The chemical bonding features are probed via density of states and valence electron density distribution calculations. Optical response functions were predicted from the calculated band structure. Both of the investigated compounds have a significant absorption coefficient (˜ 25 × 104 {cm}^{ - 1} ) in the visible range of sunlight. The thermoelectric properties of the title compounds were investigated using the FP-LAPW approach in combination with the semi-classical Boltzmann transport theory. The Cs2AgBiCl6 and Cs2AgBiBr6 compounds have a large thermopower S, which makes them potential candidates for thermoelectric applications.

Elastic Response of Crimped Collagen Fibrils

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Doehring, Todd C.

2005-01-01

A physiologic constitutive expression is presented in algorithmic format for the elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils have a three-dimensional structure at the micrometer scale that we approximate as a helical spring. The symmetry of this waveform allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendineae

Local elasticity map and plasticity in a model Lennard-Jones glass.

PubMed

Tsamados, Michel; Tanguy, Anne; Goldenberg, Chay; Barrat, Jean-Louis

2009-08-01

In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

Compositions and methods for direct capture of organic materials from process streams

DOEpatents

Lin, YuPo J.; Brotzman, Richard W.; Snyder, Seth W.

2016-08-09

A particulate magnetic nanostructured solid sorbent (MNSS) material is described herein. The particles of the MNSS comprise a plurality of tethered nanoparticles. The nanoparticles are tethered together by substantially linear hydrocarbon chains, a poly(alkylene oxide) chains, or a combination thereof connecting the nanoparticles in a three-dimensional elastic network with the nanoparticles as junctions of the network having junction functionality of about 2.1 to about 6. The surfaces of at least some of the nanoparticles comprise a polymerized siloxane bearing at least one sorption-aiding substituent selected from a hydrophilic group and a lipophilic group. The plurality of nanoparticles is made up of superparamagnetic nanoparticles or a combination of superparamagnetic and non-magnetic nanoparticles. The individual superparamagnetic nanoparticles comprise a passivating metal oxide coating around a core comprising at least one nanocrystalline metal or alloy having ferromagnetic or ferrimagnetic properties.

Internal strain estimation for quantification of human heel pad elastic modulus: A phantom study.

PubMed

Holst, Karen; Liebgott, Hervé; Wilhjelm, Jens E; Nikolov, Svetoslav; Torp-Pedersen, Søren T; Delachartre, Philippe; Jensen, Jørgen A

2013-02-01

Shock absorption is the most important function of the human heel pad. However, changes in heel pad elasticity, as seen in e.g. long-distance runners, diabetes patients, and victims of Falanga torture are affecting this function, often in a painful manner. Assessment of heel pad elasticity is usually based on one or a few strain measurements obtained by an external load-deformation system. The aim of this study was to develop a technique for quantitative measurements of heel pad elastic modulus based on several internal strain measures from within the heel pad by use of ultrasound images. Nine heel phantoms were manufactured featuring a combination of three heel pad stiffnesses and three heel pad thicknesses to model the normal human variation. Each phantom was tested in an indentation system comprising a 7MHz linear array ultrasound transducer, working as the indentor, and a connected load cell. Load-compression data and ultrasound B-mode images were simultaneously acquired in 19 compression steps of 0.1mm each. The internal tissue displacement was for each step calculated by a phase-based cross-correlation technique and internal strain maps were derived from these displacement maps. Elastic moduli were found from the resulting stress-strain curves. The elastic moduli made it possible to distinguish eight of nine phantoms from each other according to the manufactured stiffness and showed very little dependence of the thickness. Mean elastic moduli for the three soft, the three medium, and the three hard phantoms were 89kPa, 153kPa, and 168kPa, respectively. The combination of ultrasound images and force measurements provided an effective way of assessing the elastic properties of the heel pad due to the internal strain estimation. Copyright © 2012 Elsevier B.V. All rights reserved.

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.

Damage in fatigue: A new outlook

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

Miller, K.J.

1995-12-01

This paper concentrates on the difficulties produced by linear elastic fracture mechanics (LEFM) and how recent research has removed many of these difficulties thereby permitting the design engineer to have a much improved basis for solving complex problems of engineering plant subjected to cyclic loading. This paper intends to show that: (1) In polycrystalline materials the period of initiation is in reality, zero and fatigue lifetime is entirely composed of crack propagation. (2) The fatigue limit of a metal, component or structure is related to whether or not a crack can propagate. (3) Elastic Fracture Mechanics is only a beginningmore » in the science of, and application of, fracture mechanics. (4) Fatigue Damage is current crack length and the rate of damage accumulation is the rate of crack growth. (5) Only two basic forms of crack extension occur when any combination of the three loading mode mechanisms (Modes 1, 2, and 3) are applied, namely Stage 1 (shear crack growth) and Stage 2 (tensile crack growth). (6) Three fundamentally different fatigue crack growth thresholds exist. (7) The fatigue resistance of a metal is predominantly concerned with a crack changing its crack-growth direction, ie from Stage 1 to Stage 2, or vice versa. (8) Notches fall into two clearly defined categories; sharp notches where failure is related to the mechanical threshold condition, and shallow notches where failure is related to the material threshold condition. (9) Complex three-dimensional cyclic stress systems should be evaluated with respect to the possible Stage 1 and Stage 2 crack growth planes. (10) Barriers to fatigue crack growth can have origins in the microstructure (eg: grain boundaries) and in the mechanical state (eg: other crack systems). (11) The removal of a fatigue limit by a corrosive environment can be evaluated by the interface conditions between the Elastic-Plastic Fracture Mechanics (EPFM) and Microstructural Fracture Mechanics (MFM) regimes.« less

Finite Element Modeling of Elastic Volume Changes in Fluid Inclusions: Comparison with Experiment

NASA Astrophysics Data System (ADS)

Burnley, P. C.; Bruhn, D.; Schmidt, C.

2003-12-01

Inclusions within mineral grains in rocks of all types are widely studied because they contain information about either the environment of formation of the mineral grain or conditions since. Understanding the mechanics of the inclusion-host system caused by differences in thermal expansion and compressibility is often essential for interpreting measurements made on the inclusion. We are studying the mechanics of inclusions by comparing elastic volume changes and deformation of synthetic pure water inclusions in quartz with finite element models of the individual inclusions. Synthetic fluid inclusions are ideal for such a study because the mechanical boundary conditions as well as the resulting deformation are either known or can be determined from the homogenization temperature and equation of state of the fluid. The experiments for this study were conducted using a hydrothermal diamond anvil cell with water as the pressure medium. The homogenization temperature of the inclusions was used to determine the inclusion volume at various confining pressures. The confining pressure was obtained from the homogenization or the ice I liquidus temperature of the pressure medium. After the experiment the homogenization temperature of the inclusion at 1 atm confining pressure was re-determined to confirm that the deformation of the inclusions was completely elastic. The inclusion shape for each model was determined from optical photomicrographs. The thickness of the synthetic fluid inclusions is consistently about 1 micron. We used a commercially available engineering package, MSC MARC/Mentat, to create and analyze two-dimensional and three-dimensional finite element models of the inclusions. The inclusions are assumed to have at least one mirror plane (parallel to the plane of the photograph) permitting a portion of the inclusion to be modeled. We assume a linear elastic response for the quartz host and have used both isotropic and anisotropic elastic moduli. Within the uncertainties associated with the inclusion's cross sectional shape and orientation within the quartz, the 3D models can reproduce the observed elastic volume changes for each loading condition. We also observe that sheet-like inclusions experience greater elastic volume changes than do elongate inclusion. For elongate inclusions, the length to thickness ratio has no measurable effect on the compressibility of the inclusion. This is consistent with systematics observed in our 2D axisymmetric models of prolate ellipsoids and cylinders terminated by cones. For these inclusions, the compressibility of the inclusion is highly dependent on its aspect ratio below about 5:1 and only slightly dependent on the aspect ration above 10:1. Ongoing work is focusing on improving the 3D characterization of the inclusions and on refining the estimates of stress in the quartz host.

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

NASA Astrophysics Data System (ADS)

Yi, Dake; Wang, TzuChiang

2018-06-01

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J( z), the stress intensity factor K( z) and the tri-axial stress constraint level T z ( z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J( z) and T z ( z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

Concurrent optimization of material spatial distribution and material anisotropy repartition for two-dimensional structures

NASA Astrophysics Data System (ADS)

Ranaivomiarana, Narindra; Irisarri, François-Xavier; Bettebghor, Dimitri; Desmorat, Boris

2018-04-01

An optimization methodology to find concurrently material spatial distribution and material anisotropy repartition is proposed for orthotropic, linear and elastic two-dimensional membrane structures. The shape of the structure is parameterized by a density variable that determines the presence or absence of material. The polar method is used to parameterize a general orthotropic material by its elasticity tensor invariants by change of frame. A global structural stiffness maximization problem written as a compliance minimization problem is treated, and a volume constraint is applied. The compliance minimization can be put into a double minimization of complementary energy. An extension of the alternate directions algorithm is proposed to solve the double minimization problem. The algorithm iterates between local minimizations in each element of the structure and global minimizations. Thanks to the polar method, the local minimizations are solved explicitly providing analytical solutions. The global minimizations are performed with finite element calculations. The method is shown to be straightforward and efficient. Concurrent optimization of density and anisotropy distribution of a cantilever beam and a bridge are presented.

Topology and boundary shape optimization as an integrated design tool

NASA Technical Reports Server (NTRS)

Bendsoe, Martin Philip; Rodrigues, Helder Carrico

1990-01-01

The optimal topology of a two dimensional linear elastic body can be computed by regarding the body as a domain of the plane with a high density of material. Such an optimal topology can then be used as the basis for a shape optimization method that computes the optimal form of the boundary curves of the body. This results in an efficient and reliable design tool, which can be implemented via common FEM mesh generator and CAD type input-output facilities.

Development of a nonlinear unsteady transonic flow theory

NASA Technical Reports Server (NTRS)

Stahara, S. S.; Spreiter, J. R.

1973-01-01

A nonlinear, unsteady, small-disturbance theory capable of predicting inviscid transonic flows about aerodynamic configurations undergoing both rigid body and elastic oscillations was developed. The theory is based on the concept of dividing the flow into steady and unsteady components and then solving, by method of local linearization, the coupled differential equation for unsteady surface pressure distribution. The equations, valid at all frequencies, were derived for two-dimensional flows, numerical results, were obtained for two classses of airfoils and two types of oscillatory motions.

Linear-Elastic 2D and 3D Finite Element Contact Analysis of a Hole Containing a Circular Insert in a Fatigue Test Coupon

DTIC Science & Technology

2015-07-01

circular hole in an aluminium plate fitted with a titanium fastener that were computed using two-dimensional finite element contact analysis. By...used to validate the contact stress distributions associated with a circular hole in an aluminium plate fitted with a titanium fastener that were...fatigue life and aircraft structural integrity management of RAAF airframes. An aluminium coupon has been previously designed in support of the

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

PubMed

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

Elasticity, slowness, thermal conductivity and the anisotropies in the Mn3Cu1-xGexN compounds

NASA Astrophysics Data System (ADS)

Li, Guan-Nan; Chen, Zhi-Qian; Lu, Yu-Ming; Hu, Meng; Jiao, Li-Na; Zhao, Hao-Ting

2018-03-01

We perform the first-principles to systematically investigate the elastic properties, minimum thermal conductivity and anisotropy of the negative thermal expansion compounds Mn3Cu1-xGexN. The elastic constant, bulk modulus, shear modulus, Young’s modulus and Poisson ratio are calculated for all the compounds. The results of the elastic constant indicate that all the compounds are mechanically stable and the doped Ge can adjust the ductile character of the compounds. According to the values of the percent ratio of the elastic anisotropy AB, AE and AG, shear anisotropic factors A1, A2 and A3, all the Mn3Cu1-xGexN compounds are elastic anisotropy. The three-dimensional diagrams of elastic moduli in space also show that all the compounds are elastic anisotropy. In addition, the acoustic wave speed, slowness, minimum thermal conductivity and Debye temperature are also calculated. When the ratio of content for Cu and Ge arrived to 1:1, the compound has the lowest thermal conductivity and the highest Debye temperature.

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.

A three-dimensional collagen-fiber network model of the extracellular matrix for the simulation of the mechanical behaviors and micro structures.

PubMed

Dong, Shoubin; Huang, Zetao; Tang, Liqun; Zhang, Xiaoyang; Zhang, Yongrou; Jiang, Yi

2017-07-01

The extracellular matrix (ECM) provides structural and biochemical support to cells and tissues, which is a critical factor for modulating cell dynamic behavior and intercellular communication. In order to further understand the mechanisms of the interactive relationship between cell and the ECM, we developed a three-dimensional (3D) collagen-fiber network model to simulate the micro structure and mechanical behaviors of the ECM and studied the stress-strain relationship as well as the deformation of the ECM under tension. In the model, the collagen-fiber network consists of abundant random distributed collagen fibers and some crosslinks, in which each fiber is modeled as an elastic beam and a crosslink is modeled as a linear spring with tensile limit, it means crosslinks will fail while the tensile forces exceed the limit of spring. With the given parameters of the beam and the spring, the simulated tensile stress-strain relation of the ECM highly matches the experimental results including damaged and failed behaviors. Moreover, by applying the maximal inscribed sphere method, we measured the size distribution of pores in the fiber network and learned the variation of the distribution with deformation. We also defined the alignment of the collagen-fibers to depict the orientation of fibers in the ECM quantitatively. By the study of changes of the alignment and the damaged crosslinks against the tensile strain, this paper reveals the comprehensive mechanisms of four stages of 'toe', 'linear', 'damage' and 'failure' in the tensile stress-strain relation of the ECM which can provide further insight in the study of cell-ECM interaction.

A spectral-Tchebychev solution for three-dimensional dynamics of curved beams under mixed boundary conditions

NASA Astrophysics Data System (ADS)

Bediz, Bekir; Aksoy, Serdar

2018-01-01

This paper presents the application of the spectral-Tchebychev (ST) technique for solution of three-dimensional dynamics of curved beams/structures having variable and arbitrary cross-section under mixed boundary conditions. To accurately capture the vibrational behavior of curved structures, a three-dimensional (3D) solution approach is required since these structures generally exhibit coupled motions. In this study, the integral boundary value problem (IBVP) governing the dynamics of the curved structures is found using extended Hamilton's principle where the strain energy is expressed using 3D linear elasticity equation. To solve the IBVP numerically, the 3D spectral Tchebychev (3D-ST) approach is used. To evaluate the integral and derivative operations defined by the IBVP and to render the complex geometry into an equivalent straight beam with rectangular cross-section, a series of coordinate transformations are applied. To validate and assess the performance of the presented solution approach, two case studies are performed: (i) curved beam with rectangular cross-section, (ii) curved and pretwisted beam with airfoil cross-section. In both cases, the results (natural frequencies and mode shapes) are also found using a finite element (FE) solution approach. It is shown that the difference in predicted natural frequencies are less than 1%, and the mode shapes are in excellent agreement based on the modal assurance criteria (MAC) analyses; however, the presented spectral-Tchebychev solution approach significantly reduces the computational burden. Therefore, it can be concluded that the presented solution approach can capture the 3D vibrational behavior of curved beams as accurately as an FE solution, but for a fraction of the computational cost.

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.

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.

Residual stresses and their effects on deformation

NASA Astrophysics Data System (ADS)

Davis, L. C.; Allison, J. E.

1993-11-01

Residual stresses induced by thermal expansion mismatch in metal-matrix composites are studied by three-dimensional (3-D) elastic-plastic finite element analyses. Typically, the stress-free state is 150 to 300 K above room temperature. The coefficient of thermal expansion of the matrix is 3 to 5 times larger than that of the ceramic inclusion, resulting in compressive stresses of order 200 MPa in the inclusions. Both compressive and tensile stresses can be found in the matrix. Since the stress may exceed the matrix yield strength near the particles, plastic flow occurs. The authors find a significant influence of this flow on the elastic and plastic properties of the composite. The calculated residual strains in TiC particles due to thermal expansion mismatch and external loads compare well with recent neutron diffraction experiments (Bourke et al.) The present work is the first reported three-dimensional analysis of spherical inclusions in different arrays (simple cubic (sc) and face-centered cubic (fcc)) that permit a study of particle interactions.

Nanoscale mapping of the three-dimensional deformation field within commercial nanodiamonds

DOE PAGES

Maqbool, Muhammad Salman; Hoxley, David; Phillips, Nicholas W.; ...

2017-02-21

Here, the unique properties of nanodiamonds make them suitable for use in a wide range of applications, including as biomarkers for cellular tracking in vivo at the molecular level. The sustained fluorescence of nanodiamonds containing nitrogen-vacancy (N-V) centres is related to their internal structure and strain state. Theoretical studies predict that the location of the N-V centre and the nanodiamonds' residual elastic strain state have a major influence on their photoluminescence properties. However, to date there have been no direct measurements made of their spatially resolved deformation fields owing to the challenges that such measurements present. Here we apply themore » recently developed technique of Bragg coherent diffractive imaging (BCDI) to map the three-dimensional deformation field within a single nanodiamond of approximately 0.5 µm diameter. The results indicate that there are high levels of residual elastic strain present in the nanodiamond which could have a critical influence on its optical and electronic properties.« less

Nanoscale mapping of the three-dimensional deformation field within commercial nanodiamonds

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

Maqbool, Muhammad Salman; Hoxley, David; Phillips, Nicholas W.

2017-01-01

The unique properties of nanodiamonds make them suitable for use in a wide range of applications, including as biomarkers for cellular tracking in vivo at the molecular level. The sustained fluorescence of nanodiamonds containing nitrogen-vacancy (N-V) centres is related to their internal structure and strain state. Theoretical studies predict that the location of the N-V centre and the nanodiamonds' residual elastic strain state have a major influence on their photoluminescence properties. However, to date there have been no direct measurements made of their spatially resolved deformation fields owing to the challenges that such measurements present. Here we apply the recentlymore » developed technique of Bragg coherent diffractive imaging (BCDI) to map the three-dimensional deformation field within a single nanodiamond of approximately 0.5 µm diameter. The results indicate that there are high levels of residual elastic strain present in the nanodiamond which could have a critical influence on its optical and electronic properties.« less

Three-dimensional protonic conductivity in porous organic cage solids.

PubMed

Liu, Ming; Chen, Linjiang; Lewis, Scott; Chong, Samantha Y; Little, Marc A; Hasell, Tom; Aldous, Iain M; Brown, Craig M; Smith, Martin W; Morrison, Carole A; Hardwick, Laurence J; Cooper, Andrew I

2016-09-13

Proton conduction is a fundamental process in biology and in devices such as proton exchange membrane fuel cells. To maximize proton conduction, three-dimensional conduction pathways are preferred over one-dimensional pathways, which prevent conduction in two dimensions. Many crystalline porous solids to date show one-dimensional proton conduction. Here we report porous molecular cages with proton conductivities (up to 10(-3) S cm(-1) at high relative humidity) that compete with extended metal-organic frameworks. The structure of the organic cage imposes a conduction pathway that is necessarily three-dimensional. The cage molecules also promote proton transfer by confining the water molecules while being sufficiently flexible to allow hydrogen bond reorganization. The proton conduction is explained at the molecular level through a combination of proton conductivity measurements, crystallography, molecular simulations and quasi-elastic neutron scattering. These results provide a starting point for high-temperature, anhydrous proton conductors through inclusion of guests other than water in the cage pores.

Three-dimensional protonic conductivity in porous organic cage solids

NASA Astrophysics Data System (ADS)

Liu, Ming; Chen, Linjiang; Lewis, Scott; Chong, Samantha Y.; Little, Marc A.; Hasell, Tom; Aldous, Iain M.; Brown, Craig M.; Smith, Martin W.; Morrison, Carole A.; Hardwick, Laurence J.; Cooper, Andrew I.

2016-09-01

Proton conduction is a fundamental process in biology and in devices such as proton exchange membrane fuel cells. To maximize proton conduction, three-dimensional conduction pathways are preferred over one-dimensional pathways, which prevent conduction in two dimensions. Many crystalline porous solids to date show one-dimensional proton conduction. Here we report porous molecular cages with proton conductivities (up to 10-3 S cm-1 at high relative humidity) that compete with extended metal-organic frameworks. The structure of the organic cage imposes a conduction pathway that is necessarily three-dimensional. The cage molecules also promote proton transfer by confining the water molecules while being sufficiently flexible to allow hydrogen bond reorganization. The proton conduction is explained at the molecular level through a combination of proton conductivity measurements, crystallography, molecular simulations and quasi-elastic neutron scattering. These results provide a starting point for high-temperature, anhydrous proton conductors through inclusion of guests other than water in the cage pores.

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

NASA Astrophysics Data System (ADS)

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

2004-07-01

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

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

PubMed

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

Nonlinear Equations of Motion for Cantilever Rotor Blades in Hover with Pitch Link Flexibility, Twist, Precone, Droop, Sweep, Torque Offset, and Blade Root Offset

NASA Technical Reports Server (NTRS)

Hodges, D. H.

1976-01-01

Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.

Oscillation of satellite droplets in an Oldroyd-B viscoelastic liquid jet

NASA Astrophysics Data System (ADS)

Li, Fang; Yin, Xie-Yuan; Yin, Xie-Zhen

2017-01-01

A one-dimensional numerical simulation is carried out to study the oscillation characteristics of satellite droplets in the beads-on-a-string structure of an Oldroyd-B viscoelastic liquid jet. The oscillation of satellite droplets is compared with the linear oscillation of a single viscoelastic droplet. It is found that, contrary to the predictions of linear theory, the period of oscillation of satellite droplets decreases with time, despite the increase in droplet volume. The mechanism may lie in the existence of the filament, which exerts an extra resistance on droplets. On the other hand, the oscillation of droplets does not influence very much the thinning of the filament. The influence of the axial wave number, viscosity, and elasticity on the oscillation of satellite droplets is examined. Increasing the wave number may result in the decrease in the period and the increase in the decay rate of oscillation, while increasing viscosity may lead to the increase in both the period and the decay rate of oscillation. Elasticity is shown to suppress the oscillation at large wave numbers, but its influence is limited at small wave numbers.

Seismic Design of a Single Bored Tunnel: Longitudinal Deformations and Seismic Joints

NASA Astrophysics Data System (ADS)

Oh, J.; Moon, T.

2018-03-01

The large diameter bored tunnel passing through rock and alluvial deposits subjected to seismic loading is analyzed for estimating longitudinal deformations and member forces on the segmental tunnel liners. The project site has challenges including high hydrostatic pressure, variable ground profile and high seismic loading. To ensure the safety of segmental tunnel liner from the seismic demands, the performance-based two-level design earthquake approach, Functional Evaluation Earthquake and Safety Evaluation Earthquake, has been adopted. The longitudinal tunnel and ground response seismic analyses are performed using a three-dimensional quasi-static linear elastic and nonlinear elastic discrete beam-spring elements to represent segmental liner and ground spring, respectively. Three components (longitudinal, transverse and vertical) of free-field ground displacement-time histories evaluated from site response analyses considering wave passage effects have been applied at the end support of the strain-compatible ground springs. The result of the longitudinal seismic analyses suggests that seismic joint for the mitigation measure requiring the design deflection capacity of 5-7.5 cm is to be furnished at the transition zone between hard and soft ground condition where the maximum member forces on the segmental liner (i.e., axial, shear forces and bending moments) are induced. The paper illustrates how detailed numerical analyses can be practically applied to evaluate the axial and curvature deformations along the tunnel alignment under difficult ground conditions and to provide the seismic joints at proper locations to effectively reduce the seismic demands below the allowable levels.

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.

Three dimensional microstructural network of elastin, collagen, and cells in Achilles tendons.

PubMed

Pang, Xin; Wu, Jian-Ping; Allison, Garry T; Xu, Jiake; Rubenson, Jonas; Zheng, Ming-Hao; Lloyd, David G; Gardiner, Bruce; Wang, Allan; Kirk, Thomas Brett

2017-06-01

Similar to most biological tissues, the biomechanical, and functional characteristics of the Achilles tendon are closely related to its composition and microstructure. It is commonly reported that type I collagen is the predominant component of tendons and is mainly responsible for the tissue's function. Although elastin has been found in varying proportions in other connective tissues, previous studies report that tendons contain very small quantities of elastin. However, the morphology and the microstructural relationship among the elastic fibres, collagen, and cells in tendon tissue have not been well examined. We hypothesize the elastic fibres, as another fibrillar component in the extracellular matrix, have a unique role in mechanical function and microstructural arrangement in Achilles tendons. It has been shown that elastic fibres present a close connection with the tenocytes. The close relationship of the three components has been revealed as a distinct, integrated and complex microstructural network. Notably, a "spiral" structure within fibril bundles in Achilles tendons was observed in some samples in specialized regions. This study substantiates the hierarchical system of the spatial microstructure of tendon, including the mapping of collagen, elastin and tenocytes, with 3-dimensional confocal images. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:1203-1214, 2017. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

Cortical bone fracture analysis using XFEM - case study.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2017-04-01

We aim to achieve an accurate simulation of human cortical bone fracture using the extended finite element method within a commercial finite element software abaqus. A two-dimensional unit cell model of cortical bone is built based on a microscopy image of the mid-diaphysis of tibia of a 70-year-old human male donor. Each phase of this model, an interstitial bone, a cement line, and an osteon, are considered linear elastic and isotropic with material properties obtained by nanoindentation, taken from literature. The effect of using fracture analysis methods (cohesive segment approach versus linear elastic fracture mechanics approach), finite element type, and boundary conditions (traction, displacement, and mixed) on cortical bone crack initiation and propagation are studied. In this study cohesive segment damage evolution for a traction separation law based on energy and displacement is used. In addition, effects of the increment size and mesh density on analysis results are investigated. We find that both cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can effectively simulate cortical bone fracture. Mesh density and simulation increment size can influence analysis results when employing either approach, and using finer mesh and/or smaller increment size does not always provide more accurate results. Both approaches provide close but not identical results, and crack propagation speed is found to be slower when using the cohesive segment approach. Also, using reduced integration elements along with the cohesive segment approach decreases crack propagation speed compared with using full integration elements. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

[Finite element analysis of the stress distribution of two-piece post crown with different adhesives ].

PubMed

He, Lihui; Liu, Lijie; Gao, Bei; Gao, Shang; Chen, Yifu; Zhihui, Liu

2013-08-01

To establish three-dimensional finite element model of two-piece post crown to the mandibular first molar residual roots, and analyze the stress distribution characteristic to the residual roots with different adhesives, so as to get the best combination under different conditions. The complete mandibular first molar in vitro was selected, the crown was removed along the cemento-enamel junction, then the residual roots were scanned by CT. CT images were imported into a reverse engineering software, and the three-dimensional finite element model of the mandibular first molar residual roots was reconstructed. Titanium two-piece post crown of the mandibular first molar residual roots was produced, then was scanned by CT. The model was reconstructed and assembled by MIMICS. The stress distribution of the root canal and root section under the vertical load and lateral load with different bonding systems were analyzed. Three-dimensional finite element model of two-piece post crown to the mandibular first molar residual roots was established. With the increasing of elastic modulus of the adhesives, the maximum stress within the root canal was also increasing. Elastic modulus of zinc phosphate was the biggest, so the stress within the root canal was the biggest; elastic modulus of Superbond C&B was the smallest, so the stress within the root canal was the smallest. Lateral loading stress was much larger than the vertical load. Under vertical load, the load on the root section was even with different bonding systems. Under lateral load, the maximum stress was much larger than the vertical load. The stress on the root section was minimum using zinc phosphate binder, and the stress on the root section was maximum using Superbond C&B. In two-piece post crown restorations, there is significant difference between different adhesives on tooth protection. When the tooth structure of the root canal orifices is weak, in order to avoid the occurrence of splitting, the larger elastic modulus bonding system is the first choice, such as zinc phosphate binder. When the resistance form of the root canal orifices is good enough but the root is too weak, it is suggested that the smaller elastic modulus bonding system is the first choice, such as Superbond C&B.

Lump Solitons in Surface Tension Dominated Flows

NASA Astrophysics Data System (ADS)

Milewski, Paul; Berger, Kurt

1999-11-01

The Kadomtsev-Petviashvilli I equation (KPI) which models small-amplitude, weakly three-dimensional surface-tension dominated long waves is integrable and allows for algebraically decaying lump solitary waves. It is not known (theoretically or numerically) whether the full free-surface Euler equations support such solutions. We consider an intermediate model, the generalised Benney-Luke equation (gBL) which is isotropic (not weakly three-dimensional) and contains KPI as a limit. We show numerically that: 1. gBL supports lump solitary waves; 2. These waves collide elastically and are stable; 3. They are generated by resonant flow over an obstacle.

Study of guided modes in three-dimensional composites

NASA Astrophysics Data System (ADS)

Baste, S.; Gerard, A.

The propagation of elastic waves in a three-dimensional carbon-carbon composite is modeled with a mixed variational method, using the Bloch or Floquet theories and the Hellinger-Reissner function for two independent fields. The model of the equivalent homogeneous material only exists below a cut-off frequency of about 600 kHz. The existence below the cut-off frequency of two guided waves can account for the presence of a slow guided wave on either side of the cut-off frequency. Optical modes are generated at low frequencies, and can attain high velocites (rapid guided modes of 15,000 m/sec).

Numerical investigation of the effects of compressibility on the flutter of a cantilevered plate in an inviscid, subsonic, open flow

NASA Astrophysics Data System (ADS)

Colera, Manuel; Pérez-Saborid, Miguel

2018-06-01

We have carried out a numerical study of the influence of the upstream Mach number on the flutter of a two-dimensional, cantilevered, flexible plate subject to a subsonic, inviscid, open flow. We have assumed a linear elastic model for the plate and that the fluid flow is governed by the linearized potential theory. The fluid equations are solved with a novel frequency-domain, finite differences method to obtain the generalized aerodynamic forces as a function of the plate displacements. Then, these generalized forces are coupled to the equation of motion of the plate and an eigenvalue analysis is performed to find the flutter point. The obtained results are in good agreement with those of related theoretical and experimental studies found in the literature. To the best of our knowledge, the analysis performed here is the first self-consistent, parametric study of the influence of the compressibility on the flutter point of a two-dimensional cantilevered plate in subsonic flow.

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

Equations of motion of slung load systems with results for dual lift

NASA Technical Reports Server (NTRS)

Cicolani, Luigi S.; Kanning, Gerd

1990-01-01

General simulation equations are derived for the rigid body motion of slung load systems. These systems are viewed as consisting of several rigid bodies connected by straight-line cables or links. The suspension can be assumed to be elastic or inelastic, both cases being of interest in simulation and control studies. Equations for the general system are obtained via D'Alembert's principle and the introduction of generalized velocity coordinates. Three forms are obtained. Two of these generalize previous case-specific results for single helicopter systems with elastic or inelastic suspensions. The third is a new formulation for inelastic suspensions. It is derived from the elastic suspension equations by choosing the generalized coordinates so as to separate motion due to cable stretching from motion with invariant cable lengths. The result is computationally more efficient than the conventional formulation, and is readily integrated with the elastic suspension formulation and readily applied to the complex dual lift and multilift systems. Equations are derived for dual lift systems. Three proposed suspension arrangements can be integrated in a single equation set. The equations are given in terms of the natural vectors and matrices of three-dimensional rigid body mechanics and are tractable for both analysis and programming.

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard

1950-01-01

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.

A Three-Dimensional Computational Model of Collagen Network Mechanics

PubMed Central

Lee, Byoungkoo; Zhou, Xin; Riching, Kristin; Eliceiri, Kevin W.; Keely, Patricia J.; Guelcher, Scott A.; Weaver, Alissa M.; Jiang, Yi

2014-01-01

Extracellular matrix (ECM) strongly influences cellular behaviors, including cell proliferation, adhesion, and particularly migration. In cancer, the rigidity of the stromal collagen environment is thought to control tumor aggressiveness, and collagen alignment has been linked to tumor cell invasion. While the mechanical properties of collagen at both the single fiber scale and the bulk gel scale are quite well studied, how the fiber network responds to local stress or deformation, both structurally and mechanically, is poorly understood. This intermediate scale knowledge is important to understanding cell-ECM interactions and is the focus of this study. We have developed a three-dimensional elastic collagen fiber network model (bead-and-spring model) and studied fiber network behaviors for various biophysical conditions: collagen density, crosslinker strength, crosslinker density, and fiber orientation (random vs. prealigned). We found the best-fit crosslinker parameter values using shear simulation tests in a small strain region. Using this calibrated collagen model, we simulated both shear and tensile tests in a large linear strain region for different network geometry conditions. The results suggest that network geometry is a key determinant of the mechanical properties of the fiber network. We further demonstrated how the fiber network structure and mechanics evolves with a local formation, mimicking the effect of pulling by a pseudopod during cell migration. Our computational fiber network model is a step toward a full biomechanical model of cellular behaviors in various ECM conditions. PMID:25386649

Stress relaxation study of fillers for directly compressed tablets

PubMed Central

Rehula, M.; Adamek, R.; Spacek, V.

2012-01-01

It is possible to assess viscoelastic properties of materials by means of the stress relaxation test. This method records the decrease in pressing power in a tablet at its constant height. The cited method was used to evaluate the time-dependent deformation for six various materials: microcrystalline cellulose, cellulose powder, hydroxypropyl methylcellulose, mannitol, lactose monohydrate, and hydrogen phosphate monohydrate. The decrease in pressing powering of a tablet during a 180 s period was described mathematically by the parameters of three exponential equations, where the whole course of the stress relaxation is divided into three individual processes (instant elastic deformation, retarded elastic deformation and permanent plastic deformation). Three values of the moduli of plasticity and elasticity were calculated for each compound. The values of elastic parameters ATi have a strong relationship with bulk density. The plastic parameters PTi represent particle tendency to form bonds. The values of plasticity in the third process PT3 ranged from 400 to 600 MPas. Mannitol had higher plasticity and lactose monohydrate on the contrary reduced plasticity. A linear relation exists between AT3 and PT3 for the third process. No similar interpretation of moduli calculated on the basis of three exponential equations has been realized yet. PMID:24850972

Effect of kinesiotaping, non-elastic taping and bracing on segmental foot kinematics during drop landing in healthy subjects and subjects with chronic ankle instability.

PubMed

Kuni, B; Mussler, J; Kalkum, E; Schmitt, H; Wolf, S I

2016-09-01

To evaluate the effects of kinesiotape, non-elastic tape, and soft brace on segmental foot kinematics during drop landing in subjects with chronic ankle instability and healthy subjects. Controlled study with repeated measurements. Three-dimensional motion analysis laboratory. Twenty participants with chronic ankle instability and 20 healthy subjects. The subjects performed drop landings with 17 retroreflective markers on the foot and lower leg in four conditions: barefoot, with kinesiotape, with non-elastic tape and with a soft brace. Ranges of motion of foot segments using a foot measurement method. In participants with chronic ankle instability, midfoot movement in the frontal plane (inclination of the medial arch) was reduced significantly by non-elastic taping, but kinesiotaping and bracing had no effect. In healthy subjects, both non-elastic taping and bracing reduced that movement. In both groups, non-elastic taping and bracing reduced rearfoot excursion in inversion/eversion significantly, which indicates a stabilisation effect. No such effect was found with kinesiotaping. All three methods reduced maximum plantar flexion significantly. Non-elastic taping stabilised the midfoot best in patients with chronic ankle instability, while kinesiotaping did not influence foot kinematics other than to stabilise the rearfoot in the sagittal plane. ClinicalTrials.gov NCT01810471. Copyright © 2015 Chartered Society of Physiotherapy. Published by Elsevier Ltd. All rights reserved.

Turbofan Volume Dynamics Model for Investigations of Aero-Propulso-Servo-Elastic Effects in a Supersonic Commercial Transport

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George; Lemon, Kimberly A.

2010-01-01

A turbofan simulation has been developed for use in aero-propulso-servo-elastic coupling studies, on supersonic vehicles. A one-dimensional lumped volume approach is used whereby each component (fan, high-pressure compressor, combustor, etc.) is represented as a single volume using characteristic performance maps and conservation equations for continuity, momentum and energy. The simulation is developed in the MATLAB/SIMULINK (The MathWorks, Inc.) environment in order to facilitate controls development, and ease of integration with a future aero-servo-elastic vehicle model being developed at NASA Langley. The complete simulation demonstrated steady state results that closely match a proposed engine suitable for a supersonic business jet at the cruise condition. Preliminary investigation of the transient simulation revealed expected trends for fuel flow disturbances as well as upstream pressure disturbances. A framework for system identification enables development of linear models for controller design. Utilizing this framework, a transfer function modeling an upstream pressure disturbance s impacts on the engine speed is developed as an illustrative case of the system identification. This work will eventually enable an overall vehicle aero-propulso-servo-elastic model

Analytic Intermodel Consistent Modeling of Volumetric Human Lung Dynamics.

PubMed

Ilegbusi, Olusegun; Seyfi, Behnaz; Neylon, John; Santhanam, Anand P

2015-10-01

Human lung undergoes breathing-induced deformation in the form of inhalation and exhalation. Modeling the dynamics is numerically complicated by the lack of information on lung elastic behavior and fluid-structure interactions between air and the tissue. A mathematical method is developed to integrate deformation results from a deformable image registration (DIR) and physics-based modeling approaches in order to represent consistent volumetric lung dynamics. The computational fluid dynamics (CFD) simulation assumes the lung is a poro-elastic medium with spatially distributed elastic property. Simulation is performed on a 3D lung geometry reconstructed from four-dimensional computed tomography (4DCT) dataset of a human subject. The heterogeneous Young's modulus (YM) is estimated from a linear elastic deformation model with the same lung geometry and 4D lung DIR. The deformation obtained from the CFD is then coupled with the displacement obtained from the 4D lung DIR by means of the Tikhonov regularization (TR) algorithm. The numerical results include 4DCT registration, CFD, and optimal displacement data which collectively provide consistent estimate of the volumetric lung dynamics. The fusion method is validated by comparing the optimal displacement with the results obtained from the 4DCT registration.

Three-dimensional modelling of slope stability using the Local Factor of Safety concept

NASA Astrophysics Data System (ADS)

Moradi, Shirin; Huisman, Sander; Beck, Martin; Vereecken, Harry; Class, Holger

2017-04-01

Slope stability is governed by coupled hydrological and mechanical processes. The slope stability depends on the effective stress, which in turn depends on the weight of the soil and the matrix potential. Therefore, changes in water content and matrix potential associated with infiltration will affect slope stability. Most available models describing these coupled hydro-mechanical processes either rely on a one- or two-dimensional representation of hydrological and mechanical properties and processes, which obviously is a strong simplification in many applications. Therefore, the aim of this work is to develop a three-dimensional hydro-mechanical model that is able to capture the effect of spatial and temporal variability of both mechanical and hydrological parameters on slope stability. For this, we rely on DuMux, which is a free and open-source simulator for flow and transport processes in porous media that facilitates coupling of different model approaches and offers flexibility for model development. We use the Richards equation to model unsaturated water flow. The simulated water content and matrix potential distribution is used to calculate the effective stress. We only consider linear elasticity and solve for statically admissible fields of stress and displacement without invoking failure or the redistribution of post-failure stress or displacement. The Local Factor of Safety concept is used to evaluate slope stability in order to overcome some of the main limitations of commonly used methods based on limit equilibrium considerations. In a first step, we compared our model implementation with a 2D benchmark model that was implemented in COMSOL Multiphysics. In a second step, we present in-silico experiments with the newly developed 3D model to show the effect of slope morphology, spatial variability in hydraulic and mechanical material properties, and spatially variable soil depth on simulated slope stability. It is expected that this improved physically-based three-dimensional hydro-mechanical model is able to provide more reliable slope instability predictions in more complex situations.

Transient simulation of hydropower station with consideration of three-dimensional unsteady flow in turbine

NASA Astrophysics Data System (ADS)

Huang, W. D.; Fan, H. G.; Chen, N. X.

2012-11-01

To study the interaction between the transient flow in pipe and the unsteady turbulent flow in turbine, a coupled model of the transient flow in the pipe and three-dimensional unsteady flow in the turbine is developed based on the method of characteristics and the fluid governing equation in the accelerated rotational relative coordinate. The load-rejection process under the closing of guide vanes of the hydraulic power plant is simulated by the coupled method, the traditional transient simulation method and traditional three-dimensional unsteady flow calculation method respectively and the results are compared. The pressure, unit flux and rotation speed calculated by three methods show a similar change trend. However, because the elastic water hammer in the pipe and the pressure fluctuation in the turbine have been considered in the coupled method, the increase of pressure at spiral inlet is higher and the pressure fluctuation in turbine is stronger.

Nonlinear Dynamic Modeling of a Supersonic Commercial Transport Turbo-Machinery Propulsion System for Aero-Propulso-Servo-Elasticity Research

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George; Carlson, Jan-Renee; Woolwine, Kyle

2015-01-01

This paper covers the development of an integrated nonlinear dynamic model for a variable cycle turbofan engine, supersonic inlet, and convergent-divergent nozzle that can be integrated with an aeroelastic vehicle model to create an overall Aero-Propulso-Servo-Elastic (APSE) modeling tool. The primary focus of this study is to provide a means to capture relevant thrust dynamics of a full supersonic propulsion system by using relatively simple quasi-one dimensional computational fluid dynamics (CFD) methods that will allow for accurate control algorithm development and capture the key aspects of the thrust to feed into an APSE model. Previously, propulsion system component models have been developed and are used for this study of the fully integrated propulsion system. An overview of the methodology is presented for the modeling of each propulsion component, with a focus on its associated coupling for the overall model. To conduct APSE studies the de- scribed dynamic propulsion system model is integrated into a high fidelity CFD model of the full vehicle capable of conducting aero-elastic studies. Dynamic thrust analysis for the quasi-one dimensional dynamic propulsion system model is presented along with an initial three dimensional flow field model of the engine integrated into a supersonic commercial transport.

Nonlinear Dynamic Modeling of a Supersonic Commercial Transport Turbo-Machinery Propulsion System for Aero-Propulso-Servo-Elasticity Research

NASA Technical Reports Server (NTRS)

Connolly, Joe; Carlson, Jan-Renee; Kopasakis, George; Woolwine, Kyle

2015-01-01

This paper covers the development of an integrated nonlinear dynamic model for a variable cycle turbofan engine, supersonic inlet, and convergent-divergent nozzle that can be integrated with an aeroelastic vehicle model to create an overall Aero-Propulso-Servo-Elastic (APSE) modeling tool. The primary focus of this study is to provide a means to capture relevant thrust dynamics of a full supersonic propulsion system by using relatively simple quasi-one dimensional computational fluid dynamics (CFD) methods that will allow for accurate control algorithm development and capture the key aspects of the thrust to feed into an APSE model. Previously, propulsion system component models have been developed and are used for this study of the fully integrated propulsion system. An overview of the methodology is presented for the modeling of each propulsion component, with a focus on its associated coupling for the overall model. To conduct APSE studies the described dynamic propulsion system model is integrated into a high fidelity CFD model of the full vehicle capable of conducting aero-elastic studies. Dynamic thrust analysis for the quasi-one dimensional dynamic propulsion system model is presented along with an initial three dimensional flow field model of the engine integrated into a supersonic commercial transport.

Elastic model for crimped collagen fibrils

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Doehring, Todd C.

2005-01-01

A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendinece.

Three-dimensional formulation of dislocation climb

NASA Astrophysics Data System (ADS)

Gu, Yejun; Xiang, Yang; Quek, Siu Sin; Srolovitz, David J.

2015-10-01

We derive a Green's function formulation for the climb of curved dislocations and multiple dislocations in three-dimensions. In this new dislocation climb formulation, the dislocation climb velocity is determined from the Peach-Koehler force on dislocations through vacancy diffusion in a non-local manner. The long-range contribution to the dislocation climb velocity is associated with vacancy diffusion rather than from the climb component of the well-known, long-range elastic effects captured in the Peach-Koehler force. Both long-range effects are important in determining the climb velocity of dislocations. Analytical and numerical examples show that the widely used local climb formula, based on straight infinite dislocations, is not generally applicable, except for a small set of special cases. We also present a numerical discretization method of this Green's function formulation appropriate for implementation in discrete dislocation dynamics (DDD) simulations. In DDD implementations, the long-range Peach-Koehler force is calculated as is commonly done, then a linear system is solved for the climb velocity using these forces. This is also done within the same order of computational cost as existing discrete dislocation dynamics methods.

Aeroelastic loads prediction for an arrow wing. Task 3: Evaluation of the Boeing three-dimensional leading-edge vortex code

NASA Technical Reports Server (NTRS)

Manro, M. E.

1983-01-01

Two separated flow computer programs and a semiempirical method for incorporating the experimentally measured separated flow effects into a linear aeroelastic analysis were evaluated. The three dimensional leading edge vortex (LEV) code is evaluated. This code is an improved panel method for three dimensional inviscid flow over a wing with leading edge vortex separation. The governing equations are the linear flow differential equation with nonlinear boundary conditions. The solution is iterative; the position as well as the strength of the vortex is determined. Cases for both full and partial span vortices were executed. The predicted pressures are good and adequately reflect changes in configuration.

Three-dimensional analysis of surface crack-Hertzian stress field interaction

NASA Technical Reports Server (NTRS)

Ballarini, R.; Hsu, Y.

1989-01-01

The results are presented of a stress intensity factor analysis of semicircular surface cracks in the inner raceway of an engine bearing. The loading consists of a moving spherical Hertzian contact load and an axial stress due to rotation and shrink fit. A 3-D linear elastic Boundary Element Method code was developed to perform the stress analysis. The element library includes linear and quadratic isoparametric surface elements. Singular quarter point elements were employed to capture the square root displacement variation and the inverse square root stress singularity along the crack front. The program also possesses the capability to separate the whole domain into two subregions. This procedure enables one to solve nonsymmetric fracture mechanics problems without having to separate the crack surfaces a priori. A wide range of configuration parameters was investigated. The ratio of crack depth to bearing thickness was varied from one-sixtieth to one-fifth for several different locations of the Hertzian load. The stress intensity factors for several crack inclinations were also investigated. The results demonstrate the efficiency and accuracy of the Boundary Element Method. Moreover, the results can provide the basis for crack growth calculations and fatigue life prediction.

Inverse methods for 3D quantitative optical coherence elasticity imaging (Conference Presentation)

NASA Astrophysics Data System (ADS)

Dong, Li; Wijesinghe, Philip; Hugenberg, Nicholas; Sampson, David D.; Munro, Peter R. T.; Kennedy, Brendan F.; Oberai, Assad A.

2017-02-01

In elastography, quantitative elastograms are desirable as they are system and operator independent. Such quantification also facilitates more accurate diagnosis, longitudinal studies and studies performed across multiple sites. In optical elastography (compression, surface-wave or shear-wave), quantitative elastograms are typically obtained by assuming some form of homogeneity. This simplifies data processing at the expense of smearing sharp transitions in elastic properties, and/or introducing artifacts in these regions. Recently, we proposed an inverse problem-based approach to compression OCE that does not assume homogeneity, and overcomes the drawbacks described above. In this approach, the difference between the measured and predicted displacement field is minimized by seeking the optimal distribution of elastic parameters. The predicted displacements and recovered elastic parameters together satisfy the constraint of the equations of equilibrium. This approach, which has been applied in two spatial dimensions assuming plane strain, has yielded accurate material property distributions. Here, we describe the extension of the inverse problem approach to three dimensions. In addition to the advantage of visualizing elastic properties in three dimensions, this extension eliminates the plane strain assumption and is therefore closer to the true physical state. It does, however, incur greater computational costs. We address this challenge through a modified adjoint problem, spatially adaptive grid resolution, and three-dimensional decomposition techniques. Through these techniques the inverse problem is solved on a typical desktop machine within a wall clock time of 20 hours. We present the details of the method and quantitative elasticity images of phantoms and tissue samples.

Reaction-Infiltration Instabilities in Fractured and Porous Rocks

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

Ladd, Anthony

In this project we are developing a multiscale analysis of the evolution of fracture permeability, using numerical simulations and linear stability analysis. Our simulations include fully three-dimensional simulations of the fracture topography, fluid flow, and reactant transport, two-dimensional simulations based on aperture models, and linear stability analysis.

A Glimpse in the Third Dimension for Electrical Resistivity Profiles

NASA Astrophysics Data System (ADS)

Robbins, A. R.; Plattner, A.

2017-12-01

We present an electrode layout strategy designed to enhance the popular two-dimensional electrical resistivity profile. Offsetting electrodes from the traditional linear layout and using 3-D inversion software allows for mapping the three-dimensional electrical resistivity close to the profile plane. We established a series of synthetic tests using simulated data generated from chosen resistivity distributions with a three-dimensional target feature. All inversions and simulations were conducted using freely-available ERT software, BERT and E4D. Synthetic results demonstrate the effectiveness of the offset electrode approach, whereas the linear layout failed to resolve the three-dimensional character of our subsurface feature. A field survey using trench backfill as a known resistivity contrast confirmed our synthetic tests. As we show, 3-D inversions of linear layouts for starting models without previously known structure are futile ventures because they generate symmetric resistivity solutions with respect to the profile plane. This is a consequence of the layout's inherent symmetrical sensitivity patterns. An offset electrode layout is not subject to the same limitation, as the collective measurements do not share a common sensitivity symmetry. For practitioners, this approach presents a low-cost improvement of a traditional geophysical method which is simple to use yet may provide critical information about the three dimensional structure of the subsurface close to the profile.

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.

Three-dimensional elastic wave analysis of the October 2, 2004 tremor at Mount St. Helens, Washington.

NASA Astrophysics Data System (ADS)

Denlinger, R. P.

2006-12-01

On October 2, 2004, three component, broad-frequency band seismometers as far as 250 km away from Mount St. Helens volcano detected a prominent low-frequency resonance associated with the onset of eruptive volcanic activity. The energy is dominantly in the 0.5 to 10 Hz range. Since gas emissions were low, I investigate a gas-free tremor mechanism generated by sudden extension of a pressurized, cylindrical, visco- elastic magma conduit beneath the mountain as it forces its way through a brittle crust. The concept is that rapid faulting of the crust around and above the magma results in a sudden drop in resistance and, consequently, a concurrent extension of the magma in the magma column at a rate greater than magma can resupply the column. The result is a rapid pressure drop in the magma, causing the column to oscillate and radiate elastic energy into the surrounding crust. The full wavefield generated by this physical mechanism is analyzed using the finite volume method of Leveque (2002), with the approximation outlined in Langseth and Leveque (2000) for hyperbolic conservation laws. In this method, the three-dimensional equations of elasticity are written as a first order set of conservation equations, with a solution vector composed of 3 velocity components and 6 stress components. The eigenvectors of the jacobian matrices of these conservation equations are used in a fourth-order Taylors series expansion of the solution vector around a small increment in time. This method is robust, allows waves to cleanly propagate off of a finite computational grid, and includes surface and interface waves. The method also allows for extremely large contrasts in elastic moduli across internal boundaries in the grid, necessary to accommodate the large variations in rigidity between a hot, visco-elastic magma at depth and the Earth's crust. Analyzing the October 2, 2004 tremor observed at Johnson Ridge Observatory, 9 km north of the mountain, for pressure drop in a 10 km long conduit, I obtain 0.3 +/- .05 MPa, which is consistent with elastic analysis of crustal deformation around the mountain during this time period. Langseth, J.O., and R.J. LeVeque, 2000, A wave propagation method for 3D hyperbolic conservation laws, J. Comp. Phys., 165, 126-166. Leveque, R.J., 2002, Finite volume methods for hyperbolic problems, Cambridge U. Press, 558 p.

Instrument for the application of controlled mechanical loads to tissues in sterile culture

DOEpatents

Lintilhac, Phillip M.; Vesecky, Thompson B.

1995-01-01

Apparatus and methods are disclosed facilitating the application of forces and measurement of dimensions of a test subject. In one arrangement the test subject is coupled to a forcing frame and controlled forces applied thereto by a series of guideways and sliders. The sliders, which contact the test subject are in force transmitting relation to a forcing frame. Tension, compression and bending forces can be applied to the test subject. Force applied to the test subject is measured and controlled. A dimensional characteristic of the test subject, such as growth, is measured by a linear variable differential transformer. The growth measurement data can be used to control the force applied. Substantially uniaxial stretching is achieved by placing the test subject on an elastic membrane stretched by an arrangement of members securing the elastic member to the forcing frame.

The three-dimensional evolution of a plane mixing layer. Part 1: The Kelvin-Helmholtz roll-up

NASA Technical Reports Server (NTRS)

Rogers, Michael M.; Moser, Robert D.

1991-01-01

The Kelvin Helmholtz roll up of three dimensional, temporally evolving, plane mixing layers were simulated numerically. All simulations were begun from a few low wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity profile. The spanwise disturbance wavelength was taken to be less than or equal to the streamwise wavelength associated with the Kelvin Helmholtz roll up. A standard set of clean structures develop in most of the simulations. The spanwise vorticity rolls up into a corrugated spanwise roller, with vortex stretching creating strong spanwise vorticity in a cup shaped region at the vends of the roller. Predominantly streamwise rib vortices develop in the braid region between the rollers. For sufficiently strong initial three dimensional disturbances, these ribs collapse into compact axisymmetric vortices. The rib vortex lines connect to neighboring ribs and are kinked in the opposite direction of the roller vortex lines. Because of this, these two sets of vortex lines remain distinct. For certain initial conditions, persistent ribs do not develop. In such cases the development of significant three dimensionality is delayed. When the initial three dimensional disturbance energy is about equal to, or less than, the two dimensional fundamental disturbance energy, the evolution of the three dimensional disturbance is nearly linear (with respect to the mean and the two dimensional disturbances), at least until the first Kelvin Helmholtz roll up is completed.

Solitons interaction and integrability for a (2+1)-dimensional variable-coefficient Broer-Kaup system in water waves

NASA Astrophysics Data System (ADS)

Zhao, Xue-Hui; Tian, Bo; Guo, Yong-Jiang; Li, Hui-Min

2018-03-01

Under investigation in this paper is a (2+1)-dimensional variable-coefficient Broer-Kaup system in water waves. Via the symbolic computation, Bell polynomials and Hirota method, the Bäcklund transformation, Lax pair, bilinear forms, one- and two-soliton solutions are derived. Propagation and interaction for the solitons are illustrated: Amplitudes and shapes of the one soliton keep invariant during the propagation, which implies that the transport of the energy is stable for the (2+1)-dimensional water waves; and inelastic interactions between the two solitons are discussed. Elastic interactions between the two parabolic-, cubic- and periodic-type solitons are displayed, where the solitonic amplitudes and shapes remain unchanged except for certain phase shifts. However, inelastically, amplitudes of the two solitons have a linear superposition after each interaction which is called as a soliton resonance phenomenon.

Imaging of downward-looking linear array SAR using three-dimensional spatial smoothing MUSIC algorithm

NASA Astrophysics Data System (ADS)

Zhang, Siqian; Kuang, Gangyao

2014-10-01

In this paper, a novel three-dimensional imaging algorithm of downward-looking linear array SAR is presented. To improve the resolution, multiple signal classification (MUSIC) algorithm has been used. However, since the scattering centers are always correlated in real SAR system, the estimated covariance matrix becomes singular. To address the problem, a three-dimensional spatial smoothing method is proposed in this paper to restore the singular covariance matrix to a full-rank one. The three-dimensional signal matrix can be divided into a set of orthogonal three-dimensional subspaces. The main idea of the method is based on extracting the array correlation matrix as the average of all correlation matrices from the subspaces. In addition, the spectral height of the peaks contains no information with regard to the scattering intensity of the different scattering centers, thus it is difficulty to reconstruct the backscattering information. The least square strategy is used to estimate the amplitude of the scattering center in this paper. The above results of the theoretical analysis are verified by 3-D scene simulations and experiments on real data.

Advanced development of BEM for elastic and inelastic dynamic analysis of solids

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Ahmad, S.; Wang, H. C.

1989-01-01

Direct Boundary Element formulations and their numerical implementation for periodic and transient elastic as well as inelastic transient dynamic analyses of two-dimensional, axisymmetric and three-dimensional solids are presented. The inelastic formulation is based on an initial stress approach and is the first of its kind in the field of Boundary Element Methods. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution, and the divergence theorem, together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of the small displacement theory of elastoplasticity. The dynamic (periodic, transient as well as nonlinear transient) formulations have been applied to a range of problems. The numerical formulations presented here are included in the BEST3D and GPBEST systems.

Optimization of the dynamic behavior of strongly nonlinear heterogeneous materials

NASA Astrophysics Data System (ADS)

Herbold, Eric B.

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

Folding and faulting of an elastic continuum

NASA Astrophysics Data System (ADS)

Bigoni, Davide; Gourgiotis, Panos A.

2016-03-01

Folding is a process in which bending is localized at sharp edges separated by almost undeformed elements. This process is rarely encountered in Nature, although some exceptions can be found in unusual layered rock formations (called `chevrons') and seashell patterns (for instance Lopha cristagalli). In mechanics, the bending of a three-dimensional elastic solid is common (for example, in bulk wave propagation), but folding is usually not achieved. In this article, the route leading to folding is shown for an elastic solid obeying the couple-stress theory with an extreme anisotropy. This result is obtained with a perturbation technique, which involves the derivation of new two-dimensional Green's functions for applied concentrated force and moment. While the former perturbation reveals folding, the latter shows that a material in an extreme anisotropic state is also prone to a faulting instability, in which a displacement step of finite size emerges. Another failure mechanism, namely the formation of dilation/compaction bands, is also highlighted. Finally, a geophysical application to the mechanics of chevron formation shows how the proposed approach may explain the formation of natural structures.

Folding and faulting of an elastic continuum

PubMed Central

Gourgiotis, Panos A.

2016-01-01

Folding is a process in which bending is localized at sharp edges separated by almost undeformed elements. This process is rarely encountered in Nature, although some exceptions can be found in unusual layered rock formations (called ‘chevrons’) and seashell patterns (for instance Lopha cristagalli). In mechanics, the bending of a three-dimensional elastic solid is common (for example, in bulk wave propagation), but folding is usually not achieved. In this article, the route leading to folding is shown for an elastic solid obeying the couple-stress theory with an extreme anisotropy. This result is obtained with a perturbation technique, which involves the derivation of new two-dimensional Green's functions for applied concentrated force and moment. While the former perturbation reveals folding, the latter shows that a material in an extreme anisotropic state is also prone to a faulting instability, in which a displacement step of finite size emerges. Another failure mechanism, namely the formation of dilation/compaction bands, is also highlighted. Finally, a geophysical application to the mechanics of chevron formation shows how the proposed approach may explain the formation of natural structures. PMID:27118925

StructMap: Elastic Distance Analysis of Electron Microscopy Maps for Studying Conformational Changes.

PubMed

Sanchez Sorzano, Carlos Oscar; Alvarez-Cabrera, Ana Lucia; Kazemi, Mohsen; Carazo, Jose María; Jonić, Slavica

2016-04-26

Single-particle electron microscopy (EM) has been shown to be very powerful for studying structures and associated conformational changes of macromolecular complexes. In the context of analyzing conformational changes of complexes, distinct EM density maps obtained by image analysis and three-dimensional (3D) reconstruction are usually analyzed in 3D for interpretation of structural differences. However, graphic visualization of these differences based on a quantitative analysis of elastic transformations (deformations) among density maps has not been done yet due to a lack of appropriate methods. Here, we present an approach that allows such visualization. This approach is based on statistical analysis of distances among elastically aligned pairs of EM maps (one map is deformed to fit the other map), and results in visualizing EM maps as points in a lower-dimensional distance space. The distances among points in the new space can be analyzed in terms of clusters or trajectories of points related to potential conformational changes. The results of the method are shown with synthetic and experimental EM maps at different resolutions. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Pinning by rare defects and effective mobility for elastic interfaces in high dimensions

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Démery, Vincent; Rosso, Alberto

2018-06-01

The existence of a depinning transition for a high dimensional interface in a weakly disordered medium is controversial. Following Larkin arguments and a perturbative expansion, one expects a linear response with a renormalized mobility . In this paper, we compare these predictions with the exact solution of a fully connected model, which displays a finite critical force . At small disorder, we unveil an intermediary linear regime for characterized by the renormalized mobility . Our results suggest that in high dimension the critical force is always finite and determined by the effect of rare impurities that is missed by the perturbative expansion. However, the perturbative expansion correctly describes an intermediate regime that should be visible at small disorder.

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

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.

Singularity-free dislocation dynamics with strain gradient elasticity

NASA Astrophysics Data System (ADS)

Po, Giacomo; Lazar, Markus; Seif, Dariush; Ghoniem, Nasr

2014-08-01

The singular nature of the elastic fields produced by dislocations presents conceptual challenges and computational difficulties in the implementation of discrete dislocation-based models of plasticity. In the context of classical elasticity, attempts to regularize the elastic fields of discrete dislocations encounter intrinsic difficulties. On the other hand, in gradient elasticity, the issue of singularity can be removed at the outset and smooth elastic fields of dislocations are available. In this work we consider theoretical and numerical aspects of the non-singular theory of discrete dislocation loops in gradient elasticity of Helmholtz type, with interest in its applications to three dimensional dislocation dynamics (DD) simulations. The gradient solution is developed and compared to its singular and non-singular counterparts in classical elasticity using the unified framework of eigenstrain theory. The fundamental equations of curved dislocation theory are given as non-singular line integrals suitable for numerical implementation using fast one-dimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line integral form of the generalized solid angle associated with dislocations having a spread core. The single characteristic length scale of Helmholtz elasticity is determined from independent molecular statics (MS) calculations. The gradient solution is implemented numerically within our variational formulation of DD, with several examples illustrating the viability of the non-singular solution. The displacement field around a dislocation loop is shown to be smooth, and the loop self-energy non-divergent, as expected from atomic configurations of crystalline materials. The loop nucleation energy barrier and its dependence on the applied shear stress are computed and shown to be in good agreement with atomistic calculations. DD simulations of Lome-Cottrell junctions in Al show that the strength of the junction and its configuration are easily obtained, without ad-hoc regularization of the singular fields. Numerical convergence studies related to the implementation of the non-singular theory in DD are presented.

ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code

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

Noble, Charles R.; Anderson, Andrew T.; Barton, Nathan R.

ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.

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.

Asymmetries and three-dimensional features of vestibular cross-coupled stimuli illuminated through modeling

PubMed Central

Holly, Jan E.; Masood, M. Arjumand; Bhandari, Chiran S.

2017-01-01

Head movements during sustained rotation can cause angular cross-coupling which leads to tumbling illusions. Even though angular vectors predict equal magnitude illusions for head movements in opposite directions, the magnitudes of the illusions are often surprisingly asymmetric, such as during leftward versus rightward yaw while horizontal in a centrifuge. This paper presents a comprehensive investigation of the angular-linear stimulus combinations from eight different published papers in which asymmetries were found. Interactions between all angular and linear vectors, including gravity, are taken into account to model the three-dimensional consequences of the stimuli. Three main results followed. First, for every pair of head yaw movements, an asymmetry was found in the stimulus itself when considered in a fully three-dimensional manner, and the direction of the asymmetry matched the subjectively reported magnitude asymmetry. Second, for pitch and roll head movements for which motion sickness was measured, the stimulus was found symmetric in every case except one, and motion sickness generally aligned with other factors such as the existence of a head rest. Third, three-dimensional modeling predicted subjective inconsistency in the direction of perceived rotation when linear and angular components were oppositely-directed, and predicted surplus illusory rotation in the direction of head movement. PMID:27814310

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

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.

Three-dimensional Organotypic Cultures of Vestibular and Auditory Sensory Organs.

PubMed

Gnedeva, Ksenia; Hudspeth, A J; Segil, Neil

2018-06-01

The sensory organs of the inner ear are challenging to study in mammals due to their inaccessibility to experimental manipulation and optical observation. Moreover, although existing culture techniques allow biochemical perturbations, these methods do not provide a means to study the effects of mechanical force and tissue stiffness during development of the inner ear sensory organs. Here we describe a method for three-dimensional organotypic culture of the intact murine utricle and cochlea that overcomes these limitations. The technique for adjustment of a three-dimensional matrix stiffness described here permits manipulation of the elastic force opposing tissue growth. This method can therefore be used to study the role of mechanical forces during inner ear development. Additionally, the cultures permit virus-mediated gene delivery, which can be used for gain- and loss-of-function experiments. This culture method preserves innate hair cells and supporting cells and serves as a potentially superior alternative to the traditional two-dimensional culture of vestibular and auditory sensory organs.

Topology determines force distributions in one-dimensional random spring networks.

PubMed

Heidemann, Knut M; Sageman-Furnas, Andrew O; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F; Wardetzky, Max

2018-02-01

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N,z). Despite the universal properties of such (N,z) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.

Topology determines force distributions in one-dimensional random spring networks

NASA Astrophysics Data System (ADS)

Heidemann, Knut M.; Sageman-Furnas, Andrew O.; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F.; Wardetzky, Max

2018-02-01

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N ,z ) . Despite the universal properties of such (N ,z ) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.

Point force and point electric charge applied to the boundary of three-dimensional anisotropic piezoelectric solid

DOE PAGES

Borovikov, V. A.; Kalinin, S. V.; Khavin, Yu.; ...

2015-08-19

We derive the Green's functions for a three-dimensional semi-infinite fully anisotropic piezoelectric material using the plane wave theory method. The solution gives the complete set of electromechanical fields due to an arbitrarily oriented point force and a point electric charge applied to the boundary of the half-space. Moreover, the solution constitutes generalization of Boussinesq's and Cerruti's problems of elastic isotropy for the anisotropic piezoelectric materials. On the example of piezoceramics PZT-6B, the present results are compared with the previously obtained solution for the special case of transversely isotropic piezoelectric solid subjected to the same boundary condition.

Optical Forging of Graphene into Three-Dimensional Shapes.

PubMed

Johansson, Andreas; Myllyperkiö, Pasi; Koskinen, Pekka; Aumanen, Jukka; Koivistoinen, Juha; Tsai, Hung-Chieh; Chen, Chia-Hao; Chang, Lo-Yueh; Hiltunen, Vesa-Matti; Manninen, Jyrki J; Woon, Wei Yen; Pettersson, Mika

2017-10-11

Atomically thin materials, such as graphene, are the ultimate building blocks for nanoscale devices. But although their synthesis and handling today are routine, all efforts thus far have been restricted to flat natural geometries, since the means to control their three-dimensional (3D) morphology has remained elusive. Here we show that, just as a blacksmith uses a hammer to forge a metal sheet into 3D shapes, a pulsed laser beam can forge a graphene sheet into controlled 3D shapes in the nanoscale. The forging mechanism is based on laser-induced local expansion of graphene, as confirmed by computer simulations using thin sheet elasticity theory.

Nanoindentation study of electrodeposited Ag thin coating: An inverse calculation of anisotropic elastic-plastic properties

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

Cheng, Guang; Sun, Xin; Wang, Yuxin

A new inverse method was proposed to calculate the anisotropic elastic-plastic properties (flow stress) of thin electrodeposited Ag coating utilizing nanoindentation tests, previously reported inverse method for isotropic materials and three-dimensional (3-D) finite element analyses (FEA). Indentation depth was ~4% of coating thickness (~10 μm) to avoid substrate effect and different indentation responses were observed in the longitudinal (L) and the transverse (T) directions. The estimated elastic-plastic properties were obtained in the newly developed inverse method by matching the predicted indentation responses in the L and T directions with experimental measurements considering indentation size effect (ISE). The results were validatedmore » with tensile flow curves measured from free-standing (FS) Ag film. The current method can be utilized to characterize the anisotropic elastic-plastic properties of coatings and to provide the constitutive properties for coating performance evaluations.« less

Stress fields around two pores in an elastic body: exact quadrature domain solutions.

PubMed

Crowdy, Darren

2015-08-08

Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky-Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores.

Elastic moduli of a smectic membrane: a rod-level scaling analysis

NASA Astrophysics Data System (ADS)

Wensink, H. H.; Morales Anda, L.

2018-02-01

Chiral rodlike colloids exposed to strong depletion attraction may self-assemble into chiral membranes whose twisted director field differs from that of a 3D bulk chiral nematic. We formulate a simple microscopic variational theory to determine the elastic moduli of rods assembled into a bidimensional smectic membrane. The approach is based on a simple Onsager-Straley theory for a non-uniform director field that we apply to describe rod twist within the membrane. A microscopic approach enables a detailed estimate of the individual Frank elastic moduli (splay, twist and bend) as well as the twist penetration depth of the smectic membrane in relation to the rod density and shape. We find that the elastic moduli are distinctly different from those of a bulk nematic fluid, with the splay elasticity being much stronger and the curvature elasticity much weaker than for rods assembled in a three-dimensional nematic fluid. We argue that the use of the simplistic one-constant approximation in which all moduli are assumed to be of equal magnitude is not appropriate for modelling the structure-property relation of smectic membranes.

Linear and nonlinear dynamics of isospectral granular chains

NASA Astrophysics Data System (ADS)

Chaunsali, R.; Xu, H.; Yang, J.; Kevrekidis, P. G.

2017-04-01

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.

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.

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.

Graphic kinematics, visual virtual work and elastographics

PubMed Central

Konstantatou, Marina; Athanasopoulos, Georgios; Hannigan, Laura

2017-01-01

In this paper, recent progress in graphic statics is combined with Williot displacement diagrams to create a graphical description of both statics and kinematics for two- and three-dimensional pin-jointed trusses. We begin with reciprocal form and force diagrams. The force diagram is dissected into its component cells which are then translated relative to each other. This defines a displacement diagram which is topologically equivalent to the form diagram (the structure). The various contributions to the overall Virtual Work appear as parallelograms (for two-dimensional trusses) or parallelopipeds (for three-dimensional trusses) that separate the force and the displacement pieces. Structural mechanisms can be identified by translating the force cells such that their shared faces slide across each other without separating. Elastic solutions can be obtained by choosing parallelograms or parallelopipeds of the appropriate aspect ratio. Finally, a new type of ‘elastographic’ diagram—termed a deformed Maxwell–Williot diagram (two-dimensional) or a deformed Rankine–Williot diagram (three-dimensional)—is presented which combines the deflected structure with the forces carried by its members. PMID:28573030

[Three-dimensional finite analysis of the stress in first mandibular molar with composite class I restoration when various mixing ratios of bases were used].

PubMed

Zhou, Lan; Yang, Jin-Bo; Liu, Dan; Liu, Zhan; Chen, Ying; Gao, Bo

2008-06-01

To analyze the possible damage to the remaining tooth and composite restorations when various mixing ratios of bases were used. Testing elastic modulus and poission's ratio of glass-ionomer Vitrebond and self-cured calcium hydroxide Dycal with mixing ratios of 1:1, 3:4, 4:3. Micro-CT was used to scan the first mandibular molar, and the three-dimensional finite element model of the first permanent mandibular molar with class I cavity was established. Analyzing the stress of tooth structure, composite and base cement under physical load when different mixing ratios of base cement were used. The elastic modulus of base cement in various mixing ratios was different, which had the statistic significance. The magnitude and location of stress in restored tooth made no differences when the mixing ratios of Vitrebond and Dycal were changed. The peak stress and spreading area in the model with Dycal was more than that with Vitrebond. Changing the best mixing ratio of base cement can partially influence the mechanistic character, but make no differences on the magnitude and location of stress in restored tooth. During the treatment of deep caries, the base cement of the elastic modulus which is proximal to the dentin and restoration should be chosen to avoid the fracture of tooth or restoration.

Composites from southern pine juvenile wood. Part 2. Durability and dimensional stability

Treesearch

Anton D. Pugel; Eddie W. Price; Chung-Yun Hse

1990-01-01

Southern pine juvenile and mature wood were processed into three composites: flakeboard, particleboard, and fiberboard. The durability of these composites was assessed by subjecting specimens to an ovendry-vacuumpressure-soak (ODVPS) treatment, and then evaluated for modulus of elasticity, modulus of rupture, and internal bond. Overall, juvenile wood composites had...

Cross Flow Effects on Glaze Ice Roughness Formation

NASA Technical Reports Server (NTRS)

Tsao, Jen-Ching

2004-01-01

The present study examines the impact of large-scale cross flow on the creation of ice roughness elements on the leading edge of a swept wing under glaze icing conditions. A three-dimensional triple-deck structure is developed to describe the local interaction of a 3 D air boundary layer with ice sheets and liquid films. A linear stability analysis is presented here. It is found that, as the sweep angle increases, the local icing instabilities enhance and the most linearly unstable modes are strictly three dimensional.

Three-dimensional piezoelectric vibration energy harvester using spiral-shaped beam with triple operating frequencies

NASA Astrophysics Data System (ADS)

Zhao, Nian; Yang, Jin; Yu, Qiangmo; Zhao, Jiangxin; Liu, Jun; Wen, Yumei; Li, Ping

2016-01-01

This work has demonstrated a novel piezoelectric energy harvester without a complex structure and appended component that is capable of scavenging vibration energy from arbitrary directions with multiple resonant frequencies. In this harvester, a spiral-shaped elastic thin beam instead of a traditional thin cantilever beam was adopted to absorb external vibration with arbitrary direction in three-dimensional (3D) spaces owing to its ability to bend flexibly and stretch along arbitrary direction. Furthermore, multiple modes in the elastic thin beam contribute to a possibility to widen the working bandwidth with multiple resonant frequencies. The experimental results show that the harvester was capable of scavenging the vibration energy in 3D arbitrary directions; they also exhibited triple power peaks at about 16 Hz, 21 Hz, and 28 Hz with the powers of 330 μW, 313 μW, and 6 μW, respectively. In addition, human walking and water wave energies were successfully converted into electricity, proving that our harvester was practical to scavenge the time-variant or multi-directional vibration energies in our daily life.

Three-dimensional piezoelectric vibration energy harvester using spiral-shaped beam with triple operating frequencies.

PubMed

Zhao, Nian; Yang, Jin; Yu, Qiangmo; Zhao, Jiangxin; Liu, Jun; Wen, Yumei; Li, Ping

2016-01-01

This work has demonstrated a novel piezoelectric energy harvester without a complex structure and appended component that is capable of scavenging vibration energy from arbitrary directions with multiple resonant frequencies. In this harvester, a spiral-shaped elastic thin beam instead of a traditional thin cantilever beam was adopted to absorb external vibration with arbitrary direction in three-dimensional (3D) spaces owing to its ability to bend flexibly and stretch along arbitrary direction. Furthermore, multiple modes in the elastic thin beam contribute to a possibility to widen the working bandwidth with multiple resonant frequencies. The experimental results show that the harvester was capable of scavenging the vibration energy in 3D arbitrary directions; they also exhibited triple power peaks at about 16 Hz, 21 Hz, and 28 Hz with the powers of 330 μW, 313 μW, and 6 μW, respectively. In addition, human walking and water wave energies were successfully converted into electricity, proving that our harvester was practical to scavenge the time-variant or multi-directional vibration energies in our daily life.

Three-dimensional interaction and movements of various dislocations in anisotropic bicrystals with semicoherent interfaces

NASA Astrophysics Data System (ADS)

Vattré, A.; Pan, E.

2018-07-01

Lattice dislocation interactions with semicoherent interfaces are investigated by means of anisotropic field solutions in metallic homo- and hetero-structures. The present framework is based on the mathematically elegant and computationally powerful Stroh formalism, combining further with the Fourier integral and series transforms, which cover different shapes and dimensions of various extrinsic and intrinsic dislocations. Two-dimensional equi-spaced arrays of straight lattice dislocations and finite arrangements of piled-up dislocations as well as any polygonal and elliptical dislocation loops in three dimensions are considered using a superposition scheme. Self, image and Peach-Koehler forces are derived to compute the equilibrium dislocation positions in pile-ups, including the internal structures and energetics of the interfacial dislocation networks. For illustration, the effects due to the elastic and misfit mismatches are discussed in the pure misfit Au/Cu and heterophase Cu/Nb systems, while discrepancies resulting from the approximation of isotropic elasticity are clearly exhibited. These numerical examples not only feature and enhance the existing works in anisotropic bimaterials, but also promote a novel opportunity of analyzing the equilibrium shapes of planar glide dislocation loops at nanoscale.

Exploring the CAESAR database using dimensionality reduction techniques

NASA Astrophysics Data System (ADS)

Mendoza-Schrock, Olga; Raymer, Michael L.

2012-06-01

The Civilian American and European Surface Anthropometry Resource (CAESAR) database containing over 40 anthropometric measurements on over 4000 humans has been extensively explored for pattern recognition and classification purposes using the raw, original data [1-4]. However, some of the anthropometric variables would be impossible to collect in an uncontrolled environment. Here, we explore the use of dimensionality reduction methods in concert with a variety of classification algorithms for gender classification using only those variables that are readily observable in an uncontrolled environment. Several dimensionality reduction techniques are employed to learn the underlining structure of the data. These techniques include linear projections such as the classical Principal Components Analysis (PCA) and non-linear (manifold learning) techniques, such as Diffusion Maps and the Isomap technique. This paper briefly describes all three techniques, and compares three different classifiers, Naïve Bayes, Adaboost, and Support Vector Machines (SVM), for gender classification in conjunction with each of these three dimensionality reduction approaches.

Analytical modeling of operating characteristics of premixing-prevaporizing fuel-air mixing passages. Volume 1: Analysis and results

NASA Technical Reports Server (NTRS)

Anderson, O. L.; Chiappetta, L. M.; Edwards, D. E.; Mcvey, J. B.

1982-01-01

A model for predicting the distribution of liquid fuel droplets and fuel vapor in premixing-prevaporizing fuel-air mixing passages of the direct injection type is reported. This model consists of three computer programs; a calculation of the two dimensional or axisymmetric air flow field neglecting the effects of fuel; a calculation of the three dimensional fuel droplet trajectories and evaporation rates in a known, moving air flow; a calculation of fuel vapor diffusing into a moving three dimensional air flow with source terms dependent on the droplet evaporation rates. The fuel droplets are treated as individual particle classes each satisfying Newton's law, a heat transfer, and a mass transfer equation. This fuel droplet model treats multicomponent fuels and incorporates the physics required for the treatment of elastic droplet collisions, droplet shattering, droplet coalescence and droplet wall interactions. The vapor diffusion calculation treats three dimensional, gas phase, turbulent diffusion processes. The analysis includes a model for the autoignition of the fuel air mixture based upon the rate of formation of an important intermediate chemical species during the preignition period.

[Elastic registration method to compute deformation functions for mitral valve].

PubMed

Yang, Jinyu; Zhang, Wan; Yin, Ran; Deng, Yuxiao; Wei, Yunfeng; Zeng, Junyi; Wen, Tong; Ding, Lu; Liu, Xiaojian; Li, Yipeng

2014-10-01

Mitral valve disease is one of the most popular heart valve diseases. Precise positioning and displaying of the valve characteristics is necessary for the minimally invasive mitral valve repairing procedures. This paper presents a multi-resolution elastic registration method to compute the deformation functions constructed from cubic B-splines in three dimensional ultrasound images, in which the objective functional to be optimized was generated by maximum likelihood method based on the probabilistic distribution of the ultrasound speckle noise. The algorithm was then applied to register the mitral valve voxels. Numerical results proved the effectiveness of the algorithm.

Modeling spanwise nonuniformity in the cross-sectional analysis of composite beams

NASA Astrophysics Data System (ADS)

Ho, Jimmy Cheng-Chung

Spanwise nonuniformity effects are modeled in the cross-sectional analysis of beam theory. This modeling adheres to an established numerical framework on cross-sectional analysis of uniform beams with arbitrary cross-sections. This framework is based on two concepts: decomposition of the rotation tensor and the variational-asymptotic method. Allowance of arbitrary materials and geometries in the cross-section is from discretization of the warping field by finite elements. By this approach, dimensional reduction from three-dimensional elasticity is performed rigorously and the sectional strain energy is derived to be asymptotically-correct. Elastic stiffness matrices are derived for inputs into the global beam analysis. Recovery relations for the displacement, stress, and strain fields are also derived with care to be consistent with the energy. Spanwise nonuniformity effects appear in the form of pointwise and sectionwise derivatives, which are approximated by finite differences. The formulation also accounts for the effects of spanwise variations in initial twist and/or curvature. A linearly tapered isotropic strip is analyzed to demonstrate spanwise nonuniformity effects on the cross-sectional analysis. The analysis is performed analytically by the variational-asymptotic method. Results from beam theory are validated against solutions from plane stress elasticity. These results demonstrate that spanwise nonuniformity effects become significant as the rate at which the cross-sections vary increases. The modeling of transverse shear modes of deformation is accomplished by transforming the strain energy into generalized Timoshenko form. Approximations in this transformation procedure from previous works, when applied to uniform beams, are identified. The approximations are not used in the present work so as to retain more accuracy. Comparison of present results with those previously published shows that these approximations sometimes change the results measurably and thus are inappropriate. Static and dynamic results, from the global beam analysis, are calculated to show the differences between using stiffness constants from previous works and the present work. As a form of validation of the transformation procedure, calculations from the global beam analysis of initially twisted isotropic beams from using curvilinear coordinate axes featuring twist are shown to be equivalent to calculations using Cartesian coordinates.

New Computer Automated Holo-Photoelastic Method For Measuring Planar Principal Stress Magnitudes And Orientation

NASA Astrophysics Data System (ADS)

Brown, G. M.; Sullivan, J. L.

1987-09-01

A complete experimental determination of the stress and strain fields in an arbitrary deformed structure is generally unavailable. However, for two dimensional elasticity problems, such determinations are possible since in those cases one needs only to solve for three stresses (two normal and one shear). In fact, such determinations have been conducted quite often. By using isochromatic and isoclinic photoelastic data, the shear difference and numerical iteration techniques (1) and the least squares techniques (2) have been successfully used for complete stress field determinations of two dimensional elasticity problems. Though the shear difference technique can be particularly sensitive to cumulative errors resulting from numerical integration, the least squares technique is not affected by this and appears to yield better accuracy. The methods just cited use both experimental data and one or more mechanics conditions(e.g., the equations of equilibrium) to determine the stress field. However, the stress field can also be obtained from experimental data alone for planar elasticity problems, if there is enough of it to solve for the three stresses. For example, the Moire* technique or the combination of isochromatic, isoclinic, and isopachic data (for transparent models) can be used for such determinations. Further, with the marriage of advanced image processing equipment to computers, such analyses using this type of data can be conveniently conducted. It is even possible that such analyses could be more accurate than those using the combined experimental/numerical techniques cited above. The purposes of this report are two fold: i) to describe a single apparatus for obtaining isochromatic, isopachic, and isoclinic results for complete stress field determinations of two dimensional transparent models, and ii) to compare experimental and theoretical stress field values for an antisymmetrically loaded beam obtained using that apparatus.

The relationship between facial 3-D morphometry and the perception of attractiveness in children.

PubMed

Ferrario, V F; Sforza, C; Poggio, C E; Colombo, A; Tartaglia, G

1997-01-01

The aim of this investigation was to determine whether attractive children differ in their three-dimensional facial characteristics from nonattractive children of the same age, race, and sex. The facial characteristics of 36 boys and 44 girls aged 8 to 9 years were investigated. Frontal and profile photographs were analyzed independently by 21 judges, and, for each view, four groups were obtained: attractive boys, nonattractive boys, attractive girls, and nonattractive girls. For each child, the three-dimensional coordinates of 16 standardized soft tissue facial landmarks were automatically collected using an infrared system and used to calculate several three-dimensional angles, linear distances, and linear distance ratios. Mean values were computed in the eight groups, and attractive and nonattractive children were compared within sex and view. Most children received a different esthetic evaluation in the separate frontal and profile assessments; concordance in both attractive and nonattractive groups was only 50%. Moreover, three-dimensional facial morphometry was not able to separate attractive and nonattractive children.

Instrument for the application of controlled mechanical loads to tissues in sterile culture

DOEpatents

Lintilhac, P.M.; Vesecky, T.B.

1995-04-18

Apparatus and methods are disclosed facilitating the application of forces and measurement of dimensions of a test subject. In one arrangement the test subject is coupled to a forcing frame and controlled forces applied thereto by a series of guideways and sliders. The sliders, which contact the test subject are in force transmitting relation to a forcing frame. Tension, compression and bending forces can be applied to the test subject. Force applied to the test subject is measured and controlled. A dimensional characteristic of the test subject, such as growth, is measured by a linear variable differential transformer. The growth measurement data can be used to control the force applied. Substantially uniaxial stretching is achieved by placing the test subject on an elastic membrane stretched by an arrangement of members securing the elastic member to the forcing frame. 8 figs.

Aggregate linear properties of ferroelectric ceramics and polycrystalline thin films: Calculation by the method of effective piezoelectric medium

NASA Astrophysics Data System (ADS)

Pertsev, N. A.; Zembilgotov, A. G.; Waser, R.

1998-08-01

The effective dielectric, piezoelectric, and elastic constants of polycrystalline ferroelectric materials are calculated from single-crystal data by an advanced method of effective medium, which takes into account the piezoelectric interactions between grains in full measure. For bulk BaTiO3 and PbTiO3 polarized ceramics, the dependences of material constants on the remanent polarization are reported. Dielectric and elastic constants are computed also for unpolarized c- and a-textured ferroelectric thin films deposited on cubic or amorphous substrates. It is found that the dielectric properties of BaTiO3 and PbTiO3 polycrystalline thin films strongly depend on the type of crystal texture. The influence of two-dimensional clamping by the substrate on the dielectric and piezoelectric responses of polarized films is described quantitatively and shown to be especially important for the piezoelectric charge coefficient of BaTiO3 films.

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.

Tomography experiment of an integrated circuit specimen using 3 MeV electrons in the transmission electron microscope.

PubMed

Zhang, Hai-Bo; Zhang, Xiang-Liang; Wang, Yong; Takaoka, Akio

2007-01-01

The possibility of utilizing high-energy electron tomography to characterize the micron-scale three dimensional (3D) structures of integrated circuits has been demonstrated experimentally. First, electron transmission through a tilted SiO(2) film was measured with an ultrahigh-voltage electron microscope (ultra-HVEM) and analyzed from the point of view of elastic scattering of electrons, showing that linear attenuation of the logarithmic electron transmission still holds valid for effective specimen thicknesses up to 5 microm under 2 MV accelerating voltages. Electron tomography of a micron-order thick integrated circuit specimen including the Cu/via interconnect was then tried with 3 MeV electrons in the ultra-HVEM. Serial projection images of the specimen tilted at different angles over the range of +/-90 degrees were acquired, and 3D reconstruction was performed with the images by means of the IMOD software package. Consequently, the 3D structures of the Cu lines, via and void, were revealed by cross sections and surface rendering.

3D multiscale crack propagation using the XFEM applied to a gas turbine blade

NASA Astrophysics Data System (ADS)

Holl, Matthias; Rogge, Timo; Loehnert, Stefan; Wriggers, Peter; Rolfes, Raimund

2014-01-01

This work presents a new multiscale technique to investigate advancing cracks in three dimensional space. This fully adaptive multiscale technique is designed to take into account cracks of different length scales efficiently, by enabling fine scale domains locally in regions of interest, i.e. where stress concentrations and high stress gradients occur. Due to crack propagation, these regions change during the simulation process. Cracks are modeled using the extended finite element method, such that an accurate and powerful numerical tool is achieved. Restricting ourselves to linear elastic fracture mechanics, the -integral yields an accurate solution of the stress intensity factors, and with the criterion of maximum hoop stress, a precise direction of growth. If necessary, the on the finest scale computed crack surface is finally transferred to the corresponding scale. In a final step, the model is applied to a quadrature point of a gas turbine blade, to compute crack growth on the microscale of a real structure.

Elastic and viscoelastic effects in rubber/air acoustic band gap structures: A theoretical and experimental study

NASA Astrophysics Data System (ADS)

Merheb, B.; Deymier, P. A.; Jain, M.; Aloshyna-Lesuffleur, M.; Mohanty, S.; Berker, A.; Greger, R. W.

2008-09-01

The transmission of acoustic waves through centimeter-scale elastic and viscoelastic two-dimensional silicone rubber/air phononic crystal structures is investigated theoretically and experimentally. We introduce a finite difference time domain method for two-dimensional elastic and viscoelastic composite structures. Elastic fluid-solid phononic crystals composed of a two-dimensional array of cylindrical air inclusions in a solid rubber matrix, as well as an array of rubber cylinders in an air matrix, are shown to behave similarly to fluid-fluid composite structures. These systems exhibit very wide band gaps in their transmission spectra that extend to frequencies in the audible range of the spectrum. This effect is associated with the very low value of the transverse speed of sound in rubber compared to that of the longitudinal polarization. The difference in transmission between elastic and viscoelastic rubber/air crystals results from attenuation of transmission over a very wide frequency range, leaving only narrow passing bands at very low frequencies. These phononic crystals demonstrate the practical design of elastic or viscoelastic solid rubber/air acoustic band gap sound barriers with small dimensions.

The three-dimensional evolution of a plane mixing layer. Part 2: Pairing and transition to turbulence

NASA Technical Reports Server (NTRS)

Moser, Robert D.; Rogers, Michael M.

1992-01-01

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings was simulated numerically. Initial conditions for all simulations consisted of a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found both to inhibit the growth of infinitesimal three-dimensional disturbances and to trigger the transition to turbulence in highly three dimensional flows. The mechanisms responsible for the growth of three-dimensionality as well as the initial phases of the transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of span wise vorticity, which undergo a secondary roll up. Transition also produces an increase in the degree of scalar mixing, in agreement with experimental observations of mixing transition. Simulations were also conducted to investigate changes in span wise length scale that may occur in response to the change in stream wise length scale during a pairing. The linear mechanism for this process was found to be very slow, requiring roughly three pairings to complete a doubling of the span wise scale. Stronger three-dimensionality can produce more rapid scale changes but is also likely to trigger transition to turbulence. No evidence was found for a change from an organized array of rib vortices at one span wise scale to a similar array at a larger span wise scale.

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.

Elastic Multilayer Bandages for Chronic Venous Insufficiency: Features of Our Technique

PubMed Central

2012-01-01

Objectives: To evaluate the interface pressure (IP) and stiffness of our elastic multilayer bandages (eMLB). Methods: Three medical staff wrapped the legs of 10 healthy volunteers with one to six rolls of elastic bandages. The IP was measured at the medial aspect of the lower leg at the level of transposition of the medial gastrocnemius muscle into the Achilles tendon (level of B1) with the patient supine and then standing, for each number of bandages worn. The static stiffness index (SSI) was calculated as a difference between these IPs. Results: The IPs in the standing position increased linearly for up to five bandages (21.8 ± 7.2, 32.5 ± 6.1, 41.8 ± 8.5, 52.0 ± 10.4, 60.3 ± 11.8, and 66.7 ± 13.4 mmHg, with one to six bandages). SSI also increased linearly for up to five bandages (6.8 ± 5.1, 10.2 ± 4.8, 13.4 ± 7.2, 17.4 ± 8.8, 19.7 ± 9.1, and 20.4 ± 9.4 mmHg, with one to six bandages). No significant technical variation in the IP was observed among the three operators. Conclusions: Our eMLB provided stable, predictable and sufficient IPs and SSIs in healthy volunteers. PMID:23555535

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

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

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

Using an ultrasound elasticity microscope to map three-dimensional strain in a porcine cornea.

PubMed

Hollman, Kyle W; Shtein, Roni M; Tripathy, Sakya; Kim, Kang

2013-08-01

An ultrasound elasticity microscope was used to map 3-D strain volume in an ex vivo porcine cornea to illustrate its ability to measure the mechanical properties of this tissue. Mechanical properties of the cornea play an important role in its function and, therefore, also in ophthalmic diseases such as kerataconus and corneal ectasia. The ultrasound elasticity microscope combines a tightly focused high-frequency transducer with confocal scanning to produce high-quality speckle over the entire volume of tissue. This system and the analysis were able to generate volume maps of compressional strain in all three directions for porcine corneal tissue, more information than any previous study has reported. Strain volume maps indicated features of the cornea and mechanical behavior as expected. These results constitute a step toward better understanding of corneal mechanics and better treatment of corneal diseases. Copyright © 2013 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Two-Dimensional Imaging Velocimetry of Heterogeneous Flow and Brittle Failure in Diamond

NASA Astrophysics Data System (ADS)

Ali, S. J.; Smith, R.; Erskine, D.; Eggert, J.; Celliers, P. M.; Collins, G. W.; Jeanloz, R.

2014-12-01

Understanding the nature and dynamics of heterogeneous flow in diamond subjected to shock compression is important for many fields of research, from inertial confinement fusion to the study of carbon rich planets. Waves propagating through a shocked material can be significantly altered by the various deformation mechanisms present in shocked materials, including anisotropic sound speeds, phase transformations, plastic/inelastic flow and brittle failure. Quantifying the spatial and temporal effects of these deformation mechanisms has been limited by a lack of diagnostics capable of obtaining simultaneous micron resolution spatial measurements and nanosecond resolution time measurements. We have utilized the 2D Janus High Resolution Velocimeter at LLNL to study the time and space dependence of fracture in shock-compressed diamond above the Hugoniot elastic limit. Previous work on the OMEGA laser facility (Rochester) has shown that the free-surface reflectivity of μm-grained diamond samples drops linearly with increasing sample pressure, whereas under the same conditions the reflectivity of nm-grained samples remains unaffected. These disparate observations can be understood by way of better documenting fracture in high-strain compression of diamond. To this end, we have imaged the development and evolution of elastic-wave propagation, plastic-wave propagation and fracture networks in the three primary orientations of single-crystal diamond, as well as in microcrystalline and nanocrystalline diamond, and find that the deformation behavior depends sensitively on the orientation and crystallinity of the diamonds.

Source parameters controlling the generation and propagation of potential local tsunamis along the cascadia margin

USGS Publications Warehouse

Geist, E.; Yoshioka, S.

1996-01-01

The largest uncertainty in assessing hazards from local tsunamis along the Cascadia margin is estimating the possible earthquake source parameters. We investigate which source parameters exert the largest influence on tsunami generation and determine how each parameter affects the amplitude of the local tsunami. The following source parameters were analyzed: (1) type of faulting characteristic of the Cascadia subduction zone, (2) amount of slip during rupture, (3) slip orientation, (4) duration of rupture, (5) physical properties of the accretionary wedge, and (6) influence of secondary faulting. The effect of each of these source parameters on the quasi-static displacement of the ocean floor is determined by using elastic three-dimensional, finite-element models. The propagation of the resulting tsunami is modeled both near the coastline using the two-dimensional (x-t) Peregrine equations that includes the effects of dispersion and near the source using the three-dimensional (x-y-t) linear long-wave equations. The source parameters that have the largest influence on local tsunami excitation are the shallowness of rupture and the amount of slip. In addition, the orientation of slip has a large effect on the directivity of the tsunami, especially for shallow dipping faults, which consequently has a direct influence on the length of coastline inundated by the tsunami. Duration of rupture, physical properties of the accretionary wedge, and secondary faulting all affect the excitation of tsunamis but to a lesser extent than the shallowness of rupture and the amount and orientation of slip. Assessment of the severity of the local tsunami hazard should take into account that relatively large tsunamis can be generated from anomalous 'tsunami earthquakes' that rupture within the accretionary wedge in comparison to interplate thrust earthquakes of similar magnitude. ?? 1996 Kluwer Academic Publishers.

Opening of an interface flaw in a layered elastic half-plane under compressive loading

NASA Technical Reports Server (NTRS)

Kennedy, J. M.; Fichter, W. B.; Goree, J. G.

1984-01-01

A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.

Investigation on Tensile Fatigue Characteristics of Meshed GUM Metal Plates for Bone Graft Applications

NASA Astrophysics Data System (ADS)

Sekiguchi, Koki; He, Jianmei

2017-11-01

GUM Metal has characteristics of lower elasticity rigidity, large elastic deformation, higher strength and biocompatibility etc. When it is used for implant applications, there is still problem like overloading on the natural-bone because of its high rigidity compared with the human bones. Therefore, the purpose of this study is to create more flexible meshed plates for implant applications from the viewpoints of elastic rigidity and volume density. Basic mesh shapes are designed, devised and applied for meshed GUM Metal plates using three dimensional (3D) CAD tools. Experimental evaluation on tensile fatigue characteristics of meshed GUM Metal plate specimens are carried out. Analytical approaches on stress evaluation are also executed through finite element method to obtain the S-N curve for fatigue characteristic evaluation.

Optimum Particle Size for Gold-Catalyzed CO Oxidation

PubMed Central

2018-01-01

The structure sensitivity of gold-catalyzed CO oxidation is presented by analyzing in detail the dependence of CO oxidation rate on particle size. Clusters with less than 14 gold atoms adopt a planar structure, whereas larger ones adopt a three-dimensional structure. The CO and O2 adsorption properties depend strongly on particle structure and size. All of the reaction barriers relevant to CO oxidation display linear scaling relationships with CO and O2 binding strengths as main reactivity descriptors. Planar and three-dimensional gold clusters exhibit different linear scaling relationship due to different surface topologies and different coordination numbers of the surface atoms. On the basis of these linear scaling relationships, first-principles microkinetics simulations were conducted to determine CO oxidation rates and possible rate-determining step of Au particles. Planar Au9 and three-dimensional Au79 clusters present the highest CO oxidation rates for planar and three-dimensional clusters, respectively. The planar Au9 cluster is much more active than the optimum Au79 cluster. A common feature of optimum CO oxidation performance is the intermediate binding strengths of CO and O2, resulting in intermediate coverages of CO, O2, and O. Both these optimum particles present lower performance than maximum Sabatier performance, indicating that there is sufficient room for improvement of gold catalysts for CO oxidation. PMID:29707098

Viscoelastic Taylor-Couette instability as analog of the magnetorotational instability.

PubMed

Bai, Yang; Crumeyrolle, Olivier; Mutabazi, Innocent

2015-09-01

A linear stability analysis and an experimental study of a viscoelastic Taylor-Couette flow corotating in the Keplerian ratio allow us to elucidate the analogy between the viscoelastic instability and the magnetorotational instability (MRI). A generalized Rayleigh criterion allows us to determine the potentially unstable zone to pure-elasticity-driven perturbations. Experiments with a viscoelastic polymer solution yield four modes: one pure-elasticity mode and three elastorotational instability (ERI) modes that represent the MRI-analog modes. The destabilization by the polymer viscosity is evidenced for the ERI modes.

AucPR: an AUC-based approach using penalized regression for disease prediction with high-dimensional omics data.

PubMed

Yu, Wenbao; Park, Taesung

2014-01-01

It is common to get an optimal combination of markers for disease classification and prediction when multiple markers are available. Many approaches based on the area under the receiver operating characteristic curve (AUC) have been proposed. Existing works based on AUC in a high-dimensional context depend mainly on a non-parametric, smooth approximation of AUC, with no work using a parametric AUC-based approach, for high-dimensional data. We propose an AUC-based approach using penalized regression (AucPR), which is a parametric method used for obtaining a linear combination for maximizing the AUC. To obtain the AUC maximizer in a high-dimensional context, we transform a classical parametric AUC maximizer, which is used in a low-dimensional context, into a regression framework and thus, apply the penalization regression approach directly. Two kinds of penalization, lasso and elastic net, are considered. The parametric approach can avoid some of the difficulties of a conventional non-parametric AUC-based approach, such as the lack of an appropriate concave objective function and a prudent choice of the smoothing parameter. We apply the proposed AucPR for gene selection and classification using four real microarray and synthetic data. Through numerical studies, AucPR is shown to perform better than the penalized logistic regression and the nonparametric AUC-based method, in the sense of AUC and sensitivity for a given specificity, particularly when there are many correlated genes. We propose a powerful parametric and easily-implementable linear classifier AucPR, for gene selection and disease prediction for high-dimensional data. AucPR is recommended for its good prediction performance. Beside gene expression microarray data, AucPR can be applied to other types of high-dimensional omics data, such as miRNA and protein data.

Linear and volumetric dimensional changes of injection-molded PMMA denture base resins.

PubMed

El Bahra, Shadi; Ludwig, Klaus; Samran, Abdulaziz; Freitag-Wolf, Sandra; Kern, Matthias

2013-11-01

The aim of this study was to evaluate the linear and volumetric dimensional changes of six denture base resins processed by their corresponding injection-molding systems at 3 time intervals of water storage. Two heat-curing (SR Ivocap Hi Impact and Lucitone 199) and four auto-curing (IvoBase Hybrid, IvoBase Hi Impact, PalaXpress, and Futura Gen) acrylic resins were used with their specific injection-molding technique to fabricate 6 specimens of each material. Linear and volumetric dimensional changes were determined by means of a digital caliper and an electronic hydrostatic balance, respectively, after water storage of 1, 30, or 90 days. Means and standard deviations of linear and volumetric dimensional changes were calculated in percentage (%). Statistical analysis was done using Student's and Welch's t tests with Bonferroni-Holm correction for multiple comparisons (α=0.05). Statistically significant differences in linear dimensional changes between resins were demonstrated at all three time intervals of water immersion (p≤0.05), with exception of the following comparisons which showed no significant difference: IvoBase Hi Impact/SR Ivocap Hi Impact and PalaXpress/Lucitone 199 after 1 day, Futura Gen/PalaXpress and PalaXpress/Lucitone 199 after 30 days, and IvoBase Hybrid/IvoBase Hi Impact after 90 days. Also, statistically significant differences in volumetric dimensional changes between resins were found at all three time intervals of water immersion (p≤0.05), with exception of the comparison between PalaXpress and Futura Gen. Denture base resins (IvoBase Hybrid and IvoBase Hi Impact) processed by the new injection-molding system (IvoBase), revealed superior dimensional precision. Copyright © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Comparing the influence of crestal cortical bone and sinus floor cortical bone in posterior maxilla bi-cortical dental implantation: a three-dimensional finite element analysis.

PubMed

Yan, Xu; Zhang, Xinwen; Chi, Weichao; Ai, Hongjun; Wu, Lin

2015-05-01

This study aimed to compare the influence of alveolar ridge cortical bone and sinus floor cortical bone in sinus areabi-cortical dental implantation by means of 3D finite element analysis. Three-dimensional finite element (FE) models in a posterior maxillary region with sinus membrane and the same height of alveolar ridge of 10 mm were generated according to the anatomical data of the sinus area. They were either with fixed thickness of crestal cortical bone and variable thickness of sinus floor cortical bone or vice versa. Ten models were assumed to be under immediate loading or conventional loading. The standard implant model based on the Nobel Biocare implant system was created via computer-aided design software. All materials were assumed to be isotropic and linearly elastic. An inclined force of 129 N was applied. Von Mises stress mainly concentrated on the surface of crestal cortical bone around the implant neck. For all the models, both the axial and buccolingual resonance frequencies of conventional loading were higher than those of immediate loading; however, the difference is less than 5%. The results showed that bi-cortical implant in sinus area increased the stability of the implant, especially for immediately loading implantation. The thickness of both crestal cortical bone and sinus floor cortical bone influenced implant micromotion and stress distribution; however, crestal cortical bone may be more important than sinus floor cortical bone.

Non-Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

NASA Astrophysics Data System (ADS)

Khatri, Devvrath

A chain of granular particles is one of the most studied examples of highly nonlinear systems deriving its response from the nonlinear Hertzian contact interaction between particles. Interest in these systems derives from their tunable dynamic response, encompassing linear, weakly nonlinear, and strongly nonlinear regimes, controlled by varying the static and dynamic load applied. In chains with a very weak (or zero) static precompression, the system supports the formation and propagation of highly nonlinear solitary waves (HNSWs). The dual-nonlinear interaction between particles (i.e., a power-law type contact potential in compression, and zero strength in tension) combined with discreteness of the system, makes the granular system highly tunable. The propagation properties of these waves, such as traveling pulse width, wave speed, number of separated pulses (single or train of pulses), etc., can be controlled by modifying one or many of the parameters, like the particle's dimension, material properties, static and dynamic force amplitude, the type and duration of the initial excitation applied to the system, and/or the periodicity of the chain. The ability to control the wave properties in such chains has been proposed for several different practical engineering applications. The dynamic properties of these granular chains have been conventionally studied using discrete particle models (DPMs) which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although, this is a good approximation under proper circumstances, it does not capture many features of the three dimensional elastic particles such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes in the contact area, and the collective vibrations of the particles among others. This thesis focuses on the development of a finite element model (FEM) using the commercially available software Abaqus, which takes into account many of these characteristic features. The finite element model discretizes particles by considering them as three-dimensional deformable bodies of revolution and describes the nonlinear dynamic response of one-dimensional granular chains composed of particles with various geometries and orientations. We showed that particles' geometries and orientations provide additional design parameters for controlling the dynamic response of the system, compared to chains composed of spherical particles. We also showed that the tunable and compact nature of these waves can be used to tailor the properties of HNSWs for specific application, such as information carriers for actuation and sensing of mechanical properties and boundary effects of adjoining media in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Using experiments and numerics, we characterized interface dynamics between granular media and adjoining linear elastic media, and found that the coupling produced temporary localization of the incident waves at the boundaries between the two media and their decomposition into reflected waves. We monitored the formation of reflected solitary waves propagating back from the interface and found that their properties are sensitive to the geometric and material properties of the adjoining media. The work done in this research enhances our understanding of the basic physics and tunability of nonlinear granular media, and further establishes a theoretical and numerical foundation in the applications of HNSWs as information carriers.

Should ground-motion records be rotated to fault-normal/parallel or maximum direction for response history analysis of buildings?

USGS Publications Warehouse

Reyes, Juan C.; Kalkan, Erol

2012-01-01

In the United States, regulatory seismic codes (for example, California Building Code) require at least two sets of horizontal ground-motion components for three-dimensional (3D) response history analysis (RHA) of building structures. For sites within 5 kilometers (3.1 miles) of an active fault, these records should be rotated to fault-normal and fault-parallel (FN/FP) directions, and two RHAs should be performed separately—when FN and then FP direction are aligned with transverse direction of the building axes. This approach is assumed to lead to two sets of responses that envelope the range of possible responses over all nonredundant rotation angles. The validity of this assumption is examined here using 3D computer models of single-story structures having symmetric (torsionally stiff) and asymmetric (torsionally flexible) layouts subjected to an ensemble of near-fault ground motions with and without apparent velocity pulses. In this parametric study, the elastic vibration period is varied from 0.2 to 5 seconds, and yield-strength reduction factors, R, are varied from a value that leads to linear-elastic design to 3 and 5. Further validations are performed using 3D computer models of 9-story structures having symmetric and asymmetric layouts subjected to the same ground-motion set. The influence of the ground-motion rotation angle on several engineering demand parameters (EDPs) is examined in both linear-elastic and nonlinear-inelastic domains to form benchmarks for evaluating the use of the FN/FP directions and also the maximum direction (MD). The MD ground motion is a new definition for horizontal ground motions for use in site-specific ground-motion procedures for seismic design according to provisions of the American Society of Civil Engineers/Seismic Engineering Institute (ASCE/SEI) 7-10. The results of this study have important implications for current practice, suggesting that ground motions rotated to MD or FN/FP directions do not necessarily provide the most critical EDPs in nonlinear-inelastic domain; however, they tend to produce larger EDPs than as-recorded (arbitrarily oriented) motions.

Long-Wavelength Elastic Wave Propagation Across Naturally Fractured Rock Masses

NASA Astrophysics Data System (ADS)

Mohd-Nordin, Mohd Mustaqim; Song, Ki-Il; Cho, Gye-Chun; Mohamed, Zainab

2014-03-01

Geophysical site investigation techniques based on elastic waves have been widely used to characterize rock masses. However, characterizing jointed rock masses by using such techniques remains challenging because of a lack of knowledge about elastic wave propagation in multi-jointed rock masses. In this paper, the roughness of naturally fractured rock joint surfaces is estimated by using a three-dimensional (3D) image-processing technique. The classification of the joint roughness coefficient (JRC) is enhanced by introducing the scan line technique. The peak-to-valley height is selected as a key indicator for JRC classification. Long-wavelength P-wave and torsional S-wave propagation across rock masses containing naturally fractured joints are simulated through the quasi-static resonant column (QSRC) test. In general, as the JRC increases, the S-wave velocity increases within the range of stress levels considered in this paper, whereas the P-wave velocity and the damping ratio of the shear wave decrease. In particular, the two-dimensional joint specimen underestimates the S-wave velocity while overestimating the P-wave velocity. This suggests that 3D joint surfaces should be implicated to obtain the reliable elastic wave velocity in jointed rock masses. The contact characteristic and degree of roughness and waviness of the joint surface are identified as a factor influencing P-wave and S-wave propagation in multi-jointed rock masses. The results indicate a need for a better understanding of the sensitivity of contact area alterations to the elastic wave velocity induced by changes in normal stress. This paper's framework can be a reference for future research on elastic wave propagation in naturally multi-jointed rock masses.

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.

Performance of parallel computation using CUDA for solving the one-dimensional elasticity equations

NASA Astrophysics Data System (ADS)

Darmawan, J. B. B.; Mungkasi, S.

2017-01-01

In this paper, we investigate the performance of parallel computation in solving the one-dimensional elasticity equations. Elasticity equations are usually implemented in engineering science. Solving these equations fast and efficiently is desired. Therefore, we propose the use of parallel computation. Our parallel computation uses CUDA of the NVIDIA. Our research results show that parallel computation using CUDA has a great advantage and is powerful when the computation is of large scale.

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.

Software to compute elastostatic Green's functions for sources in 3D homogeneous elastic layers above a (visco)elastic halfspace

NASA Astrophysics Data System (ADS)

Bradley, A. M.; Segall, P.

2012-12-01

We describe software, in development, to calculate elastostatic displacement Green's functions and their derivatives for point and polygonal dislocations in three-dimensional homogeneous elastic layers above an elastic or a viscoelastic halfspace. The steps to calculate a Green's function for a point source at depth zs are as follows. 1. A grid in wavenumber space is chosen. 2. A six-element complex rotated stress-displacement vector x is obtained at each grid point by solving a two-point boundary value problem (2P-BVP). If the halfspace is viscoelastic, the solution is inverse Laplace transformed. 3. For each receiver, x is propagated to the receiver depth zr (often zr = 0) and then, 4, inverse Fourier transformed, with the Fourier component corresponding to the receiver's horizontal position. 5. The six elements are linearly combined into displacements and their derivatives. The dominant work is in step 2. The grid is chosen to represent the wavenumber-space solution with as few points as possible. First, the wavenumber space is transformed to increase sampling density near 0 wavenumber. Second, a tensor-product grid of Chebyshev points of the first kind is constructed in each quadrant of the transformed wavenumber space. Moment-tensor-dependent symmetries further reduce work. The numerical solution of the 2P-BVP problem in step 2 involves solving a linear equation A x = b. Half of the elements of x are of geophysical interest; the subset depends on whether zr ≤ zs. Denote these \\hat x. As wavenumber k increases, \\hat x can become inaccurate in finite precision arithmetic for two reasons: 1. The condition number of A becomes too large. 2. The norm-wise relative error (NWRE) in \\hat x is large even though it is small in x. To address this problem, a number of researchers have used determinants to obtain x. This may be the best approach for 6-dimensional or smaller 2P-BVP, where the combinatorial increase in work is still moderate. But there is an alternative. Let \\bar A be the matrix after scaling its columns to unit infinity norm and \\bar x the scaled x. If \\bar A is well conditioned, as it often is in (visco)elastostatic problems, then using determinants is unnecessary. Multiply each side of A x = b by a propagator matrix to the computation depth zcd prior to storing the matrix in finite precision. zcd is determined by the rule that zr and zcd must be on opposite sides of zs. Let the resulting matrix be A(zcd). Three facts imply that this rule controls the NWRE in \\hat x: 1. Diagonally scaling a matrix changes the accuracy of an element of the solution by about one ULP (unit in the last place). 2. If the NWRE of \\bar x is small, then the largest elements are accurate. 3. zcd controls the magnitude of elements in \\bar x. In step 4, to avoid numerically Fourier transforming the (nearly) non-square-integrable functions that arise when the receiver and source depths are (nearly) the same, a function is divided into an analytical part and a numerical part that goes quickly to 0 as k -> ∞ . Our poster will describe these calculations, present a preliminary interface to a C-language package in development, and show some physical results.

Hierarchic models for laminated plates

NASA Technical Reports Server (NTRS)

Szabo, Barna A.; Actis, Ricardo L.

1991-01-01

The research conducted in the formulation of hierarchic models for laminated plates is described. The work is an extension of the work done for laminated strips. The use of a single parameter, beta, is investigated that represents the degree to which the equilibrium equations of three dimensional elasticity are satisfied. The powers of beta identify members in the hierarchic sequence. Numerical examples that were analyzed with the proposed sequence of models are included. The results obtained for square plates with uniform loading and homogeneous boundary conditions are very encouraging. Several cross-ply and angle-ply laminates were evaluated and the results compared with those of the fully three dimensional model, computed using MSC/PROBE, and with previously reported work on laminated strips.

PAFAC- PLASTIC AND FAILURE ANALYSIS OF COMPOSITES

NASA Technical Reports Server (NTRS)

Bigelow, C. A.

1994-01-01

The increasing number of applications of fiber-reinforced composites in industry demands a detailed understanding of their material properties and behavior. A three-dimensional finite-element computer program called PAFAC (Plastic and Failure Analysis of Composites) has been developed for the elastic-plastic analysis of fiber-reinforced composite materials and structures. The evaluation of stresses and deformations at edges, cut-outs, and joints is essential in understanding the strength and failure for metal-matrix composites since the onset of plastic yielding starts very early in the loading process as compared to the composite's ultimate strength. Such comprehensive analysis can only be achieved by a finite-element program like PAFAC. PAFAC is particularly suited for the analysis of laminated metal-matrix composites. It can model the elastic-plastic behavior of the matrix phase while the fibers remain elastic. Since the PAFAC program uses a three-dimensional element, the program can also model the individual layers of the laminate to account for thickness effects. In PAFAC, the composite is modeled as a continuum reinforced by cylindrical fibers of vanishingly small diameter which occupy a finite volume fraction of the composite. In this way, the essential axial constraint of the phases is retained. Furthermore, the local stress and strain fields are uniform. The PAFAC finite-element solution is obtained using the displacement method. Solution of the nonlinear equilibrium equations is obtained with a Newton-Raphson iteration technique. The elastic-plastic behavior of composites consisting of aligned, continuous elastic filaments and an elastic-plastic matrix is described in terms of the constituent properties, their volume fractions, and mutual constraints between phases indicated by the geometry of the microstructure. The program uses an iterative procedure to determine the overall response of the laminate, then from the overall response determines the stress state in each phase of the composite material. Failure of the fibers or matrix within an element can also be modeled by PAFAC. PAFAC is written in FORTRAN IV for batch execution and has been implemented on a CDC CYBER 170 series computer with a segmented memory requirement of approximately 66K (octal) of 60 bit words. PAFAC was developed in 1982.

ASTROP2-LE: A Mistuned Aeroelastic Analysis System Based on a Two Dimensional Linearized Euler Solver

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Srivastava, R.; Mehmed, Oral

2002-01-01

An aeroelastic analysis system for flutter and forced response analysis of turbomachines based on a two-dimensional linearized unsteady Euler solver has been developed. The ASTROP2 code, an aeroelastic stability analysis program for turbomachinery, was used as a basis for this development. The ASTROP2 code uses strip theory to couple a two dimensional aerodynamic model with a three dimensional structural model. The code was modified to include forced response capability. The formulation was also modified to include aeroelastic analysis with mistuning. A linearized unsteady Euler solver, LINFLX2D is added to model the unsteady aerodynamics in ASTROP2. By calculating the unsteady aerodynamic loads using LINFLX2D, it is possible to include the effects of transonic flow on flutter and forced response in the analysis. The stability is inferred from an eigenvalue analysis. The revised code, ASTROP2-LE for ASTROP2 code using Linearized Euler aerodynamics, is validated by comparing the predictions with those obtained using linear unsteady aerodynamic solutions.

Supercomputer algorithms for efficient linear octree encoding of three-dimensional brain images.

PubMed

Berger, S B; Reis, D J

1995-02-01

We designed and implemented algorithms for three-dimensional (3-D) reconstruction of brain images from serial sections using two important supercomputer architectures, vector and parallel. These architectures were represented by the Cray YMP and Connection Machine CM-2, respectively. The programs operated on linear octree representations of the brain data sets, and achieved 500-800 times acceleration when compared with a conventional laboratory workstation. As the need for higher resolution data sets increases, supercomputer algorithms may offer a means of performing 3-D reconstruction well above current experimental limits.

Acoustic emission from a growing crack

NASA Technical Reports Server (NTRS)

Jacobs, Laurence J.

1989-01-01

An analytical method is being developed to determine the signature of an acoustic emission waveform from a growing crack and the results of this analysis are compared to experimentally obtained values. Within the assumptions of linear elastic fracture mechanics, a two dimensional model is developed to examine a semi-infinite crack that, after propagating with a constant velocity, suddenly stops. The analytical model employs an integral equation method for the analysis of problems of dynamic fracture mechanics. The experimental procedure uses an interferometric apparatus that makes very localized absolute measurements with very high fidelity and without acoustically loading the specimen.

Contact stresses in meshing spur gear teeth: Use of an incremental finite element procedure

NASA Technical Reports Server (NTRS)

Hsieh, Chih-Ming; Huston, Ronald L.; Oswald, Fred B.

1992-01-01

Contact stresses in meshing spur gear teeth are examined. The analysis is based upon an incremental finite element procedure that simultaneously determines the stresses in the contact region between the meshing teeth. The teeth themselves are modeled by two dimensional plain strain elements. Friction effects are included, with the friction forces assumed to obey Coulomb's law. The analysis assumes that the displacements are small and that the tooth materials are linearly elastic. The analysis procedure is validated by comparing its results with those for the classical two contacting semicylinders obtained from the Hertz method. Agreement is excellent.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals.

PubMed

Theocharis, G; Boechler, N; Kevrekidis, P G; Job, S; Porter, Mason A; Daraio, C

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals

NASA Astrophysics Data System (ADS)

Theocharis, G.; Boechler, N.; Kevrekidis, P. G.; Job, S.; Porter, Mason A.; Daraio, C.

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Structural, Electronic and Elastic Properties of Half-Heusler Alloys CrNiZ (Z = Al, Si, Ge and As)

NASA Astrophysics Data System (ADS)

Zitouni, A.; Benstaali, W.; Abbad, A.; Lantri, T.; Bouadjemi, B.; Aziz, Z.

2018-06-01

In the present work, a self-consistent ab-initio calculation using the full- potential linearized augmented plane wave (FP-LAPW) method within the framework of the spin-polarized density functional theory (DFT) was used to study the structural, electronic, magnetic and elastic properties of the half Heusler alloys CrNiZ (Z = Al, Si, Ge and As) in three phases ( α, β and γ phases). The generalized gradient approximation (GGA) described by Perdew-Burke-Ernzerhof (PBE) was used. The results obtained for the spin-polarized band structure and the density of states show a halfmetallic behavior for the four compounds. The elastic constants ( C ij ) show that our compounds are ductile, stiff and anisotropic.

Single-Crystal Elastic Constants of Yttria (Y2O3) Measured to High Temperatures

NASA Technical Reports Server (NTRS)

Sayir, Ali; Palko, James W.; Kriven, Waltraud M.; Sinogeikin, Sergey V.; Bass, Jay D.

2001-01-01

Yttria, or yttrium sesquioxide (Y2O3), has been considered for use in nuclear applications and has gained interest relatively recently for use in infrared optics. Single crystals of yttria have been grown successfully at the NASA Glenn Research Center using a laser-heated float zone technique in a fiber and rod. Such samples allow measurement of the single-crystal elastic properties, and these measurements provide useful property data for the design of components using single crystals. They also yield information as to what degree the elastic properties of yttria ceramics are a result of the intrinsic properties of the yttria crystal in comparison to characteristics that may depend on processing, such as microstructure and intergranular phases, which are common in sintered yttria. The single-crystal elastic moduli are valuable for designing such optical components. In particular, the temperature derivatives of elastic moduli allow the dimensional changes due to heating under physical constraints, as well as acoustic excitation, to be determined. The single-crystal elastic moduli of yttria were measured by Brillouin spectroscopy up to 1200 C. The room-temperature values obtained were C(sub 11) = 223.6 + 0.6 GPa, C(sub 44) = 74.6 + 0.5 GPa, and C(sub 12) = 112.4 + 1.0 GPa. The resulting bulk and (Voigt-Reuss-Hill) shear moduli were K = 149.5 + 1.0 GPa and G(sub VRH) = 66.3 + 0.8 GPa, respectively. Linear least-squares regressions to the variation of bulk and shear moduli with temperature resulted in derivatives of dK/dT = -17 + 2 MPa/C and dG(sub VRH)/dT = -8 + 2 MPa/ C. Elastic anisotropy was found to remain essentially constant over the temperature range studied.

Low-level stretching accelerates cell migration into a gap.

PubMed

Toume, Samer; Gefen, Amit; Weihs, Daphne

2017-08-01

We observed that radially stretching cell monolayers at a low level (3%) increases the rate at which they migrate to close a gap formed by in vitro injury. Wound healing has been shown to accelerate in vivo when deformations are topically applied, for example, by negative pressure wound therapy. However, the direct effect of deformations on cell migration during gap closure is still unknown. Thus, we have evaluated the effect of radially applied, sustained (static) tensile strain on the kinematics of en mass cell migration. Monolayers of murine fibroblasts were cultured on stretchable, linear-elastic substrates that were subjected to different tensile strains, using a custom-designed three-dimensionally printed stretching apparatus. Immediately following stretching, the monolayer was 'wounded' at its centre, and cell migration during gap closure was monitored and quantitatively evaluated. We observed a significant increase in normalised migration rates and a reduction of gap closure time with 3% stretching, relative to unstretched controls or 6% stretch. Interestingly, the initial gap area was linearly correlated with the maximum migration rate, especially when stretching was applied. Therefore, small deformations applied to cell monolayers during gap closure enhance en mass cell migration associated with wound healing and can be used to fine-tune treatment protocols. © 2016 Medicalhelplines.com Inc and John Wiley & Sons Ltd.

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

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

Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less

Bright-dark soliton solutions for the (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger system in a graded-index waveguide

NASA Astrophysics Data System (ADS)

Yuan, Yu-Qiang; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Liu, Lei

2017-04-01

Under investigation in this paper is the (2+1)-dimensional coupled nonlinear Schrödinger (NLS) system with variable coefficients, which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. Through a similarity transformation, we convert that system into a set of the integrable defocusing (1+1)-dimensional coupled NLS equations, and subsequently construct the bright-dark soliton solutions for the original system which are converted from the ones of the latter set. With the graphic analysis, we discuss the soliton propagation and collision with r(t), which is related to the nonlinear, profile and gain/loss coefficients. When r(t) is a constant, one soliton propagates with the amplitude, width and velocity unvaried, while velocity and width of the one soliton can be affected, and two solitons possess the elastic collision; When r(t) is a linear function, velocity and width of the one soliton varies with t increasing, and collision of the two solitons is altered. Besides, bound-state solitons are seen.

A reconstruction algorithm for three-dimensional object-space data using spatial-spectral multiplexing

NASA Astrophysics Data System (ADS)

Wu, Zhejun; Kudenov, Michael W.

2017-05-01

This paper presents a reconstruction algorithm for the Spatial-Spectral Multiplexing (SSM) optical system. The goal of this algorithm is to recover the three-dimensional spatial and spectral information of a scene, given that a one-dimensional spectrometer array is used to sample the pupil of the spatial-spectral modulator. The challenge of the reconstruction is that the non-parametric representation of the three-dimensional spatial and spectral object requires a large number of variables, thus leading to an underdetermined linear system that is hard to uniquely recover. We propose to reparameterize the spectrum using B-spline functions to reduce the number of unknown variables. Our reconstruction algorithm then solves the improved linear system via a least- square optimization of such B-spline coefficients with additional spatial smoothness regularization. The ground truth object and the optical model for the measurement matrix are simulated with both spatial and spectral assumptions according to a realistic field of view. In order to test the robustness of the algorithm, we add Poisson noise to the measurement and test on both two-dimensional and three-dimensional spatial and spectral scenes. Our analysis shows that the root mean square error of the recovered results can be achieved within 5.15%.

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

Glacier crevasses: Observations, models, and mass balance implications

NASA Astrophysics Data System (ADS)

Colgan, William; Rajaram, Harihar; Abdalati, Waleed; McCutchan, Cheryl; Mottram, Ruth; Moussavi, Mahsa S.; Grigsby, Shane

2016-03-01

We review the findings of approximately 60 years of in situ and remote sensing studies of glacier crevasses, as well as the three broad classes of numerical models now employed to simulate crevasse fracture. The relatively new insight that mixed-mode fracture in local stress equilibrium, rather than downstream advection alone, can introduce nontrivial curvature to crevasse geometry may merit the reinterpretation of some key historical observation studies. In the past three decades, there have been tremendous advances in the spatial resolution of satellite imagery, as well as fully automated algorithms capable of tracking crevasse displacements between repeat images. Despite considerable advances in developing fully transient three-dimensional ice flow models over the past two decades, both the zero stress and linear elastic fracture mechanics crevasse models have remained fundamentally unchanged over this time. In the past decade, however, multidimensional and transient formulations of the continuum damage mechanics approach to simulating ice fracture have emerged. The combination of employing damage mechanics to represent slow upstream deterioration of ice strength and fracture mechanics to represent rapid failure at downstream termini holds promise for implementation in large-scale ice sheet models. Finally, given the broad interest in the sea level rise implications of recent and future cryospheric change, we provide a synthesis of 10 mechanisms by which crevasses can influence glacier mass balance.

Temperature Dependence of the Spin-Hall Conductivity of a Two-Dimensional Impure Rashba Electron Gas in the Presence of Electron-Phonon and Electron-Electron Interactions

NASA Astrophysics Data System (ADS)

Yavari, H.; Mokhtari, M.; Bayervand, A.

2015-03-01

Based on Kubo's linear response formalism, temperature dependence of the spin-Hall conductivity of a two-dimensional impure (magnetic and nonmagnetic impurities) Rashba electron gas in the presence of electron-electron and electron-phonon interactions is analyzed theoretically. We will show that the temperature dependence of the spin-Hall conductivity is determined by the relaxation rates due to these interactions. At low temperature, the elastic lifetimes ( and are determined by magnetic and nonmagnetic impurity concentrations which are independent of the temperature, while the inelastic lifetimes ( and related to the electron-electron and electron-phonon interactions, decrease when the temperature increases. We will also show that since the spin-Hall conductivity is sensitive to temperature, we can distinguish the intrinsic and extrinsic contributions.

Three dimensional finite-element analysis of finite-thickness fracture specimens

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1977-01-01

The stress-intensity factors for most of the commonly used fracture specimens (center-crack tension, single and double edge-crack tension, and compact), those that have a through-the-thickness crack, were calculated using a three dimensional finite-element elastic stress analysis. Three-dimensional singularity elements were used around the crack front. The stress intensity factors along the crack front were evaluated by using a force method, developed herein, that requires no prior assumption of either plane stress or plane strain. The calculated stress-intensity factors from the present analysis were compared with those from the literature whenever possible and were generally found to be in good agreement. The stress-intensity factors at the midplane for all specimens analyzed were within 3 percent of the two dimensional plane strain values. The stress intensity factors at the specimen surfaces were considerably lower than at the midplanes. For the center-crack tension specimens with large thickness to crack-length ratios, the stress-intensity factor reached a maximum near the surface of the specimen. In all other specimens considered the maximum stress intensity occurred at the midplane.

Unsteady transonic flows - Introduction, current trends, applications

NASA Technical Reports Server (NTRS)

Yates, E. C., Jr.

1985-01-01

The computational treatment of unsteady transonic flows is discussed, reviewing the historical development and current techniques. The fundamental physical principles are outlined; the governing equations are introduced; three-dimensional linearized and two-dimensional linear-perturbation theories in frequency domain are described in detail; and consideration is given to frequency-domain FEMs and time-domain finite-difference and integral-equation methods. Extensive graphs and diagrams are included.

Asymptotic derivation of nonlocal plate models from three-dimensional stress gradient elasticity

NASA Astrophysics Data System (ADS)

Hache, F.; Challamel, N.; Elishakoff, I.

2018-01-01

This paper deals with the asymptotic derivation of thin and thick nonlocal plate models at different orders from three-dimensional stress gradient elasticity, through the power series expansions of the displacements in the thickness ratio of the plate. Three nonlocal asymptotic approaches are considered: a partial nonlocality following the thickness of the plate, a partial nonlocality following the two directions of the plates and a full nonlocality (following all the directions). The three asymptotic approaches lead at the zeroth order to a nonlocal Kirchhoff-Love plate model, but differ in the expression of the length scale. The nonlocal asymptotic models coincide at this order with the stress gradient Kirchhoff-Love plate model, only when the nonlocality is following the two directions of the plate and expressed through a nabla operator. This asymptotic model also yields the nonlocal truncated Uflyand-Mindlin plate model at the second order. However, the two other asymptotic models lead to equations that differ from the current existing nonlocal engineering models (stress gradient engineering plate models). The natural frequencies for an all-edges simply supported plate are obtained for each model. It shows that the models provide similar results for low orders of frequencies or small thickness ratio or nonlocal lengths. Moreover, only the asymptotic model with a partial nonlocality following the two directions of the plates is consistent with a stress gradient plate model, whatever the geometry of the plate.

A plasma source driven predator-prey like mechanism as a potential cause of spiraling intermittencies in linear plasma devices

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

Reiser, D.; Ohno, N.; Tanaka, H.

2014-03-15

Three-dimensional global drift fluid simulations are carried out to analyze coherent plasma structures appearing in the NAGDIS-II linear device (nagoya divertor plasma Simulator-II). The numerical simulations reproduce several features of the intermittent spiraling structures observed, for instance, statistical properties, rotation frequency, and the frequency of plasma expulsion. The detailed inspection of the three-dimensional plasma dynamics allows to identify the key mechanism behind the formation of these intermittent events. The resistive coupling between electron pressure and parallel electric field in the plasma source region gives rise to a quasilinear predator-prey like dynamics where the axisymmetric mode represents the prey and themore » spiraling structure with low azimuthal mode number represents the predator. This interpretation is confirmed by a reduced one-dimensional quasilinear model derived on the basis of the findings in the full three-dimensional simulations. The dominant dynamics reveals certain similarities to the classical Lotka-Volterra cycle.« less

Mechanical properties of human articular disk and its influence on TMJ loading studied with the finite element method.

PubMed

Tanaka, E; Sasaki, A; Tahmina, K; Yamaguchi, K; Mori, Y; Tanne, K

2001-03-01

The present study was designed to investigate the elastic modulus of human temporomandibular joint (TMJ) disk under tension and its influences on TMJ loading. Seven human TMJ disks served as specimens. Continuous tensile stress was applied to each specimen, and the elastic moduli of human TMJ disks were calculated at 2% strain. Furthermore, using a three-dimensional finite element model of the mandible including the TMJ, changes in the TMJ stresses during clenching were evaluated in association of varying elastic moduli of the articular disk determined by the tensile tests. The elastic moduli at 2% strain varied from 27.1 to 65.2 MPa with a mean of 47.1 MPa. A significant correlation was found between the elastic moduli and age (P < 0.01). On the surface of condyle, compressive stress in the anterior area and tensile stress in the posterior area increased when the elastic moduli of the TMJ disk was varied from 25 to 65 MPa. In the TMJ disk, shear stresses in all the areas became larger with greater stiffness. In conclusion, it is shown that the elastic modulus of human TMJ disk is increased with age and that higher stiffness of the disk exerts substantial influences on mechanical loading for the TMJ structures.

Role of cellular adhesions in tissue dynamics spectroscopy

NASA Astrophysics Data System (ADS)

Merrill, Daniel A.; An, Ran; Turek, John; Nolte, David

2014-02-01

Cellular adhesions play a critical role in cell behavior, and modified expression of cellular adhesion compounds has been linked to various cancers. We tested the role of cellular adhesions in drug response by studying three cellular culture models: three-dimensional tumor spheroids with well-developed cellular adhesions and extracellular matrix (ECM), dense three-dimensional cell pellets with moderate numbers of adhesions, and dilute three-dimensional cell suspensions in agarose having few adhesions. Our technique for measuring the drug response for the spheroids and cell pellets was biodynamic imaging (BDI), and for the suspensions was quasi-elastic light scattering (QELS). We tested several cytoskeletal chemotherapeutic drugs (nocodazole, cytochalasin-D, paclitaxel, and colchicine) on three cancer cell lines chosen from human colorectal adenocarcinoma (HT-29), human pancreatic carcinoma (MIA PaCa-2), and rat osteosarcoma (UMR-106) to exhibit differences in adhesion strength. Comparing tumor spheroid behavior to that of cell suspensions showed shifts in the spectral motion of the cancer tissues that match predictions based on different degrees of cell-cell contacts. The HT-29 cell line, which has the strongest adhesions in the spheroid model, exhibits anomalous behavior in some cases. These results highlight the importance of using three-dimensional tissue models in drug screening with cellular adhesions being a contributory factor in phenotypic differences between the drug responses of tissue and cells.

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

DOE PAGES

Mohamed, Mamdouh S.; Larson, Bennett C.; Tischler, Jonathan Z.; ...

2015-05-18

The statistical properties of the elastic distortion fields of dislocations in deforming crystals are investigated using the method of discrete dislocation dynamics to simulate dislocation structures and dislocation density evolution under tensile loading. Probability distribution functions (PDF) and pair correlation functions (PCF) of the simulated internal elastic strains and lattice rotations are generated for tensile strain levels up to 0.85%. The PDFs of simulated lattice rotation are compared with sub-micrometer resolution three-dimensional X-ray microscopy measurements of rotation magnitudes and deformation length scales in 1.0% and 2.3% compression strained Cu single crystals to explore the linkage between experiment and the theoreticalmore » analysis. The statistical properties of the deformation simulations are analyzed through determinations of the Nye and Kr ner dislocation density tensors. The significance of the magnitudes and the length scales of the elastic strain and the rotation parts of dislocation density tensors are demonstrated, and their relevance to understanding the fundamental aspects of deformation is discussed.« less

Crustal deformation along the San Andreas, California

NASA Technical Reports Server (NTRS)

Li, Victor C.

1992-01-01

The goal is to achieve a better understanding of the regional and local deformation and crustal straining processes in western North America, particularly the effects of the San Andreas and nearby faults on the spatial and temporal crustal deformation behavior. Construction of theoretical models based on the mechanics of coupled elastic plate, viscoelastic foundation and large scale crack mechanics provide a rational basis for the interpretation of seismic and aseismic anomalies and expedite efforts in forecasting the stability of plate boundary deformation. Special focus is placed on the three dimensional time dependent surface deformation due to localized slippage in a elastic layer coupled to a visco-elastic substrate. The numerical analysis is based on a 3-D boundary element technique. Extension to visco-elastic coupling demands the derivation of 3-D time dependent Green's function. This method was applied to analyze the viscoelastic surface displacements due to a dislocated embedded patch. Surface uplift as a function of time and position are obtained. Comparisons between surface uplift for long and short dislocated patches are made.

Dominant phonon polarization conversion across dimensionally mismatched interfaces: Carbon-nanotube-graphene junction

NASA Astrophysics Data System (ADS)

Shi, Jingjing; Lee, Jonghoon; Dong, Yalin; Roy, Ajit; Fisher, Timothy S.; Ruan, Xiulin

2018-04-01

Dimensionally mismatched interfaces are emerging for thermal management applications, but thermal transport physics remains poorly understood. Here we consider the carbon-nanotube-graphene junction, which is a dimensionally mismatched interface between one- and two-dimensional materials and is the building block for carbon-nanotube (CNT)-graphene three-dimensional networks. We predict the transmission function of individual phonon modes using the wave packet method; surprisingly, most incident phonon modes show predominantly polarization conversion behavior. For instance, longitudinal acoustic (LA) polarizations incident from CNTs transmit mainly into flexural transverse (ZA) polarizations in graphene. The frequency stays the same as the incident mode, indicating elastic transmission. Polarization conversion is more significant as the phonon wavelength increases. We attribute such unique phonon polarization conversion behavior to the dimensional mismatch across the interface, and it opens significantly new phonon transport channels as compared to existing theories where polarization conversion is neglected.

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.

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

PubMed

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Three-Dimensional Effects of Crack Closure in Laminated Composite Plates Subjected to Bending Loads

DTIC Science & Technology

1994-06-01

Approved by: •UW. Kwon, Thesis Advisor wathe D.K~elleher, Chairman Department of Mechanical Engineering ii ABSTRACT Fracture is one of the dominant...5 A. OVERVIEW .......................................... 5 B. CONSTITUTIVE EQUATION .............................. 9 1. Isotropic...the elemental nodes. B. CONSTITUTIVE EQUATION The material property matrix [D] is a symmetric matrix which includes elasticity moduli and Poisson’s

Thermophysical and Mechanical Properties of Granite and Its Effects on Borehole Stability in High Temperature and Three-Dimensional Stress

PubMed Central

Bao-lin, Liu; Hai-yan, Zhu; Chuan-liang, Yan; Zhi-jun, Li; Zhi-qiao, Wang

2014-01-01

When exploiting the deep resources, the surrounding rock readily undergoes the hole shrinkage, borehole collapse, and loss of circulation under high temperature and high pressure. A series of experiments were conducted to discuss the compressional wave velocity, triaxial strength, and permeability of granite cored from 3500 meters borehole under high temperature and three-dimensional stress. In light of the coupling of temperature, fluid, and stress, we get the thermo-fluid-solid model and governing equation. ANSYS-APDL was also used to stimulate the temperature influence on elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability. In light of the results, we establish a temperature-fluid-stress model to illustrate the granite's stability. The compressional wave velocity and elastic modulus, decrease as the temperature rises, while poisson ratio and permeability of granite increase. The threshold pressure and temperature are 15 MPa and 200°C, respectively. The temperature affects the fracture pressure more than the collapse pressure, but both parameters rise with the increase of temperature. The coupling of thermo-fluid-solid, greatly impacting the borehole stability, proves to be a good method to analyze similar problems of other formations. PMID:24778592

Thermophysical and mechanical properties of granite and its effects on borehole stability in high temperature and three-dimensional stress.

PubMed

Wang, Yu; Liu, Bao-lin; Zhu, Hai-yan; Yan, Chuan-liang; Li, Zhi-jun; Wang, Zhi-qiao

2014-01-01

When exploiting the deep resources, the surrounding rock readily undergoes the hole shrinkage, borehole collapse, and loss of circulation under high temperature and high pressure. A series of experiments were conducted to discuss the compressional wave velocity, triaxial strength, and permeability of granite cored from 3500 meters borehole under high temperature and three-dimensional stress. In light of the coupling of temperature, fluid, and stress, we get the thermo-fluid-solid model and governing equation. ANSYS-APDL was also used to stimulate the temperature influence on elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability. In light of the results, we establish a temperature-fluid-stress model to illustrate the granite's stability. The compressional wave velocity and elastic modulus, decrease as the temperature rises, while poisson ratio and permeability of granite increase. The threshold pressure and temperature are 15 MPa and 200 °C, respectively. The temperature affects the fracture pressure more than the collapse pressure, but both parameters rise with the increase of temperature. The coupling of thermo-fluid-solid, greatly impacting the borehole stability, proves to be a good method to analyze similar problems of other formations.

Origins of oblique-slip faulting during caldera subsidence

NASA Astrophysics Data System (ADS)

Holohan, Eoghan P.; Walter, Thomas R.; Schöpfer, Martin P. J.; Walsh, John J.; van Wyk de Vries, Benjamin; Troll, Valentin R.

2013-04-01

Although conventionally described as purely dip-slip, faults at caldera volcanoes may have a strike-slip displacement component. Examples occur in the calderas of Olympus Mons (Mars), Miyakejima (Japan), and Dolomieu (La Reunion). To investigate this phenomenon, we use numerical and analog simulations of caldera subsidence caused by magma reservoir deflation. The numerical models constrain mechanical causes of oblique-slip faulting from the three-dimensional stress field in the initial elastic phase of subsidence. The analog experiments directly characterize the development of oblique-slip faulting, especially in the later, non-elastic phases of subsidence. The combined results of both approaches can account for the orientation, mode, and location of oblique-slip faulting at natural calderas. Kinematically, oblique-slip faulting originates to resolve the following: (1) horizontal components of displacement that are directed radially toward the caldera center and (2) horizontal translation arising from off-centered or "asymmetric" subsidence. We informally call these two origins the "camera iris" and "sliding trapdoor" effects, respectively. Our findings emphasize the fundamentally three-dimensional nature of deformation during caldera subsidence. They hence provide an improved basis for analyzing structural, geodetic, and geophysical data from calderas, as well as analogous systems, such as mines and producing hydrocarbon reservoirs.

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).

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.

Linear instability in the wake of an elliptic wing

NASA Astrophysics Data System (ADS)

He, Wei; Tendero, Juan Ángel; Paredes, Pedro; Theofilis, Vassilis

2017-12-01

Linear global instability analysis has been performed in the wake of a low aspect ratio three-dimensional wing of elliptic cross section, constructed with appropriately scaled Eppler E387 airfoils. The flow field over the airfoil and in its wake has been computed by full three-dimensional direct numerical simulation at a chord Reynolds number of Rec=1750 and two angles of attack, {AoA}=0° and 5°. Point-vortex methods have been employed to predict the inviscid counterpart of this flow. The spatial BiGlobal eigenvalue problem governing linear small-amplitude perturbations superposed upon the viscous three-dimensional wake has been solved at several axial locations, and results were used to initialize linear PSE-3D analyses without any simplifying assumptions regarding the form of the trailing vortex system, other than weak dependence of all flow quantities on the axial spatial direction. Two classes of linearly unstable perturbations were identified, namely stronger-amplified symmetric modes and weaker-amplified antisymmetric disturbances, both peaking at the vortex sheet which connects the trailing vortices. The amplitude functions of both classes of modes were documented, and their characteristics were compared with those delivered by local linear stability analysis in the wake near the symmetry plane and in the vicinity of the vortex core. While all linear instability analysis approaches employed have delivered qualitatively consistent predictions, only PSE-3D is free from assumptions regarding the underlying base flow and should thus be employed to obtain quantitative information on amplification rates and amplitude functions in this class of configurations.

Heterogeneous mechanics of the mouse pulmonary arterial network.

PubMed

Lee, Pilhwa; Carlson, Brian E; Chesler, Naomi; Olufsen, Mette S; Qureshi, M Umar; Smith, Nicolas P; Sochi, Taha; Beard, Daniel A

2016-10-01

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.

Linear response approach to active Brownian particles in time-varying activity fields

NASA Astrophysics Data System (ADS)

Merlitz, Holger; Vuijk, Hidde D.; Brader, Joseph; Sharma, Abhinav; Sommer, Jens-Uwe

2018-05-01

In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of non-interacting particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.

Optimal swimming of a sheet.

PubMed

Montenegro-Johnson, Thomas D; Lauga, Eric

2014-06-01

Propulsion at microscopic scales is often achieved through propagating traveling waves along hairlike organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of flagellar propulsion. We derive numerically the large-amplitude wave form of the two-dimensional swimming sheet that yields optimum hydrodynamic efficiency: the ratio of the squared swimming speed to the rate-of-working of the sheet against the fluid. Using the boundary element method, we show that the optimal wave form is a front-back symmetric regularized cusp that is 25% more efficient than the optimal sine wave. This optimal two-dimensional shape is smooth, qualitatively different from the kinked form of Lighthill's optimal three-dimensional flagellum, not predicted by small-amplitude theory, and different from the smooth circular-arc-like shape of active elastic filaments.

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.

Synthesis and Characterization of Three Dimensional Nanostructures Based on Interconnected Carbon Nanomaterials

NASA Astrophysics Data System (ADS)

Koizumi, Ryota

This thesis addresses various types of synthetic methods for novel three dimensional nanomaterials and nanostructures based on interconnected carbon nanomaterials using solution chemistry and chemical vapor deposition (CVD) methods. Carbon nanotube (CNT) spheres with porous and scaffold structures consisting of interconnected CNTs were synthesized by solution chemistry followed by freeze-drying, which have high elasticity under nano-indentation tests. This allows the CNT spheres to be potentially applied to mechanical dampers. CNTs were also grown on two dimensional materials--such as reduced graphene oxide (rGO) and hexagonal boron nitride (h-BN)--by CVD methods, which are chemically interconnected. CNTs on rGO and h-BN interconnected structures performed well as electrodes for supercapacitors. Furthermore, unique interconnected flake structures of alpha-phase molybdenum carbide were developed by a CVD method. The molybdenum carbide can be used for a catalyst of hydrogen evolution reaction activity as well as an electrode for supercapacitors.

Nonlinear theory for laminated and thick plates and shells including the effects of transverse shearing

NASA Technical Reports Server (NTRS)

Stein, M.

1985-01-01

Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensional theory, the displacements are expressed by trigonometric series representation through-the-thickness. The nonlinear strain-displacement relations are expanded into series which contain all first and second degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin.

Stress concentration investigations using NASTRAN

NASA Technical Reports Server (NTRS)

Gillcrist, M. C.; Parnell, L. A.

1986-01-01

Parametic investigations are performed using several two dimensional finite element formulations to determine their suitability for use in predicting extremum stresses in marine propellers. Comparisons are made of two NASTRAN elements (CTRIM6 and CTRAIA2) wherein elasticity properties have been modified to yield plane strain results. The accuracy of the elements is investigated by comparing finite element stress predictions with experimentally determined stresses in two classical cases: (1) tension in a flat plate with a circular hole; and (2) a filleted flat bar subjected to in-plane bending. The CTRIA2 element is found to provide good results. The displacement field from a three dimensional finite element model of a representative marine propeller is used as the boundary condition for the two dimensional plane strain investigations of stresses in the propeller blade and fillet. Stress predictions from the three dimensional analysis are compared with those from the two dimensional models. The validity of the plane strain modifications to the NASTRAN element is checked by comparing the modified CTRIA2 element stress predictions with those of the ABAQUS plane strain element, CPE4.

A design concept of parallel elasticity extracted from biological muscles for engineered actuators.

PubMed

Chen, Jie; Jin, Hongzhe; Iida, Fumiya; Zhao, Jie

2016-08-23

Series elastic actuation that takes inspiration from biological muscle-tendon units has been extensively studied and used to address the challenges (e.g. energy efficiency, robustness) existing in purely stiff robots. However, there also exists another form of passive property in biological actuation, parallel elasticity within muscles themselves, and our knowledge of it is limited: for example, there is still no general design strategy for the elasticity profile. When we look at nature, on the other hand, there seems a universal agreement in biological systems: experimental evidence has suggested that a concave-upward elasticity behaviour is exhibited within the muscles of animals. Seeking to draw possible design clues for elasticity in parallel with actuators, we use a simplified joint model to investigate the mechanisms behind this biologically universal preference of muscles. Actuation of the model is identified from general biological joints and further reduced with a specific focus on muscle elasticity aspects, for the sake of easy implementation. By examining various elasticity scenarios, one without elasticity and three with elasticity of different profiles, we find that parallel elasticity generally exerts contradictory influences on energy efficiency and disturbance rejection, due to the mechanical impedance shift thus caused. The trade-off analysis between them also reveals that concave parallel elasticity is able to achieve a more advantageous balance than linear and convex ones. It is expected that the results could contribute to our further understanding of muscle elasticity and provide a theoretical guideline on how to properly design parallel elasticity behaviours for engineering systems such as artificial actuators and robotic joints.

The dynamics and control of large flexible space structures, 3. Part A: Shape and orientation control of a platform in orbit using point actuators

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Reddy, A. S. S. R.; Krishna, R.; James, P. K.

1980-01-01

The dynamics, attitude, and shape control of a large thin flexible square platform in orbit are studied. Attitude and shape control are assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about three different nominal orientations: (1) the platform following the local vertical with its major surface perpendicular to the orbital plane; (2) the platform following the local horizontal with its major surface normal to the local vertical; and (3) the platform following the local vertical with its major surface perpendicular to the orbit normal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on decoupling, pole placement, and linear optimal control theory. Frequencies and elastic modal shape functions are obtained using a finite element computer algorithm, two different approximate analytical methods, and the results of the three methods compared.

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.

ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2005-01-01

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one-, two- and three-space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obtained for solutions with discontinuities. We also present preliminary results for two-dimensional non-linear systems.

Defects in regular nanosystems and interference spectra at reemission of electromagnetic field attosecond pulses

NASA Astrophysics Data System (ADS)

Matveev, V. I.; Makarov, D. N.

2017-01-01

The effect of defects in nanostructured targets on interference spectra at the reemission of attosecond electromagnetic pulses has been considered. General expressions have been obtained for calculations of spectral distributions for one-, two-, and three-dimensional multiatomic nanosystems consisting of identical complex atoms with defects such as bends, vacancies, and breaks. Changes in interference spectra by a linear chain with several removed atoms (chain with breaks) and by a linear chain with a bend have been calculated as examples allowing a simple analytical representation. Generalization to two- and three-dimensional nanosystems has been developed.

Finite element analysis of plantar fascia under stretch-the relative contribution of windlass mechanism and Achilles tendon force.

PubMed

Cheng, Hsin-Yi Kathy; Lin, Chun-Li; Wang, Hsien-Wen; Chou, Shih-Wei

2008-01-01

Stretching plays an important role in the treatment of plantar fasciitis. Information on the internal stresses/strains of the plantar fascia under stretch is useful in enhancing knowledge on the stretch mechanisms. Although direct measurement can monitor plantar fascia changes, it is invasive and gathers only localized information. The purpose of this paper was to construct a three-dimensional finite element model of the foot to calculate the stretch effects on plantar fascia and monitor its stress/strain distributions and concentrations. A three-dimensional foot model was developed and contained 26 bones with joint cartilages, 67 ligaments and a fan-like solid plantar fascia modeling. All tissues were idealized as linear elastic, homogeneous and isotropic whilst the plantar fascia was assigned as hyperelastic to represent its nonlinearity. The plantar fascia was monitored for its biomechanical responses under various stretch combinations: three toe dorsiflexion angles (windlass effect: 15 degrees , 30 degrees and 45 degrees ) and five Achilles tendon forces (100, 200, 300, 400 and 500N). Our results indicated that the plantar fascia strain increased as the dorsiflexion angles increased, and this phenomenon was enhanced by increasing Achilles tendon force. A stress concentration was found near the medial calcaneal tubercle, and the fascia stress was higher underneath the first foot ray and gradually decreased as it moved toward the fifth ray. The current model recreated the position of the foot when stretch is placed on the plantar fascia. The results provided a general insight into the mechanical and biomechanical aspects of the influences of windlass mechanism and Achilles tendon force on plantar fascia stress and strain distribution. These findings might have practical implications onto plantar fascia stretch approaches, and provide guidelines to its surgical release.

Exact Analytical Solutions for Elastodynamic Impact

DTIC Science & Technology

2015-11-30

corroborated by derivation of exact discrete solutions from recursive equations for the impact problems. 15. SUBJECT TERMS One-dimensional impact; Elastic...wave propagation; Laplace transform; Floor function; Discrete solutions 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...impact Elastic wave propagation Laplace transform Floor function Discrete solutionsWe consider the one-dimensional impact problem in which a semi

A Novel Approach For Ankle Foot Orthosis Developed By Three Dimensional Technologies

NASA Astrophysics Data System (ADS)

Belokar, R. M.; Banga, H. K.; Kumar, R.

2017-12-01

This study presents a novel approach for testing mechanical properties of medical orthosis developed by three dimensional (3D) technologies. A hand-held type 3D laser scanner is used for generating 3D mesh geometry directly from patient’s limb. Subsequently 3D printable orthotic design is produced from crude input model by means of Computer Aided Design (CAD) software. Fused Deposition Modelling (FDM) method in Additive Manufacturing (AM) technologies is used to fabricate the 3D printable Ankle Foot Orthosis (AFO) prototype in order to test the mechanical properties on printout. According to test results, printed Acrylonitrile Butadiene Styrene (ABS) AFO prototype has sufficient elasticity modulus and durability for patient-specific medical device manufactured by the 3D technologies.

A Soft Sensor-Based Three-Dimensional (3-D) Finger Motion Measurement System

PubMed Central

Park, Wookeun; Ro, Kyongkwan; Kim, Suin; Bae, Joonbum

2017-01-01

In this study, a soft sensor-based three-dimensional (3-D) finger motion measurement system is proposed. The sensors, made of the soft material Ecoflex, comprise embedded microchannels filled with a conductive liquid metal (EGaln). The superior elasticity, light weight, and sensitivity of soft sensors allows them to be embedded in environments in which conventional sensors cannot. Complicated finger joints, such as the carpometacarpal (CMC) joint of the thumb are modeled to specify the location of the sensors. Algorithms to decouple the signals from soft sensors are proposed to extract the pure flexion, extension, abduction, and adduction joint angles. The performance of the proposed system and algorithms are verified by comparison with a camera-based motion capture system. PMID:28241414

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Viscoelastic effect on acoustic band gaps in polymer-fluid composites

NASA Astrophysics Data System (ADS)

Merheb, B.; Deymier, P. A.; Muralidharan, K.; Bucay, J.; Jain, M.; Aloshyna-Lesuffleur, M.; Greger, R. W.; Mohanty, S.; Berker, A.

2009-10-01

In this paper, we present a theoretical analysis of the propagation of acoustic waves through elastic and viscoelastic two-dimensional phononic crystal structures. Numerical calculations of transmission spectra are conducted by extending the finite-difference-time-domain method to account for linear viscoelastic materials with time-dependent moduli. We study a phononic crystal constituted of a square array of cylindrical air inclusions in a solid viscoelastic matrix. The elastic properties of the solid are those of a silicone rubber. This system exhibits very wide band gaps in its transmission spectrum that extend to frequencies in the audible range of the spectrum. These gaps are characteristic of fluid matrix/air inclusion systems and result from the very large contrast between the longitudinal and transverse speeds of sound in rubber. By treating the matrix as a viscoelastic medium within the standard linear solid (SLS) model, we demonstrate that viscoelasticity impacts the transmission properties of the rubber/air phononic crystal not only by attenuating the transmitted acoustic waves but also by shifting the passing bands frequencies toward lower values. The ranges of frequencies exhibiting attenuation or frequency shift are determined by the value of the relaxation time in the SLS model. We show that viscoelasticity can be used to decrease the frequency of pass bands (and consequently stop bands) in viscoelastic/air phononic crystals.

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

PubMed Central

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

2016-01-01

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

Numerical investigation of the vortex-induced vibration of an elastically mounted circular cylinder at high Reynolds number (Re = 104) and low mass ratio using the RANS code.

PubMed

Khan, Niaz Bahadur; Ibrahim, Zainah; Nguyen, Linh Tuan The; Javed, Muhammad Faisal; Jameel, Mohammed

2017-01-01

This study numerically investigates the vortex-induced vibration (VIV) of an elastically mounted rigid cylinder by using Reynolds-averaged Navier-Stokes (RANS) equations with computational fluid dynamic (CFD) tools. CFD analysis is performed for a fixed-cylinder case with Reynolds number (Re) = 104 and for a cylinder that is free to oscillate in the transverse direction and possesses a low mass-damping ratio and Re = 104. Previously, similar studies have been performed with 3-dimensional and comparatively expensive turbulent models. In the current study, the capability and accuracy of the RANS model are validated, and the results of this model are compared with those of detached eddy simulation, direct numerical simulation, and large eddy simulation models. All three response branches and the maximum amplitude are well captured. The 2-dimensional case with the RANS shear-stress transport k-w model, which involves minimal computational cost, is reliable and appropriate for analyzing the characteristics of VIV.

Landmark-based elastic registration using approximating thin-plate splines.

PubMed

Rohr, K; Stiehl, H S; Sprengel, R; Buzug, T M; Weese, J; Kuhn, M H

2001-06-01

We consider elastic image registration based on a set of corresponding anatomical point landmarks and approximating thin-plate splines. This approach is an extension of the original interpolating thin-plate spline approach and allows to take into account landmark localization errors. The extension is important for clinical applications since landmark extraction is always prone to error. Our approach is based on a minimizing functional and can cope with isotropic as well as anisotropic landmark errors. In particular, in the latter case it is possible to include different types of landmarks, e.g., unique point landmarks as well as arbitrary edge points. Also, the scheme is general with respect to the image dimension and the order of smoothness of the underlying functional. Optimal affine transformations as well as interpolating thin-plate splines are special cases of this scheme. To localize landmarks we use a semi-automatic approach which is based on three-dimensional (3-D) differential operators. Experimental results are presented for two-dimensional as well as 3-D tomographic images of the human brain.

Acoustic resonances in cylinder bundles oscillating in a compressibile fluid

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

Lin, W.H.; Raptis, A.C.

1984-12-01

This paper deals with an analytical study on acoustic resonances of elastic oscillations of a group of parallel, circular, thin cylinders in an unbounded volume of barotropic, compressible, inviscid fluid. The perturbed motion of the fluid is assumed due entirely to the flexural oscillations of the cylinders. The motion of the fluid disturbances is first formulated in a three-dimensional wave form and then casted into a two-dimensional Helmholtz equation for the harmonic motion in time and in axial space. The acoustic motion in the fluid and the elastic motion in the cylinders are solved simultaneously. Acoustic resonances were approximately determinedmore » from the secular (eigenvalue) equation by the method of successive iteration with the use of digital computers for a given set of the fluid properties and the cylinders' geometry and properties. Effects of the flexural wavenumber and the configuration of and the spacing between the cylinders on the acoustic resonances were thoroughly investigated.« less

A three dimensional Dirichlet-to-Neumann map for surface waves over topography

NASA Astrophysics Data System (ADS)

Nachbin, Andre; Andrade, David

2016-11-01

We consider three dimensional surface water waves in the potential theory regime. The bottom topography can have a quite general profile. In the case of linear waves the Dirichlet-to-Neumann operator is formulated in a matrix decomposition form. Computational simulations illustrate the performance of the method. Two dimensional periodic bottom variations are considered in both the Bragg resonance regime as well as the rapidly varying (homogenized) regime. In the three-dimensional case we use the Luneburg lens-shaped submerged mound, which promotes the focusing of the underlying rays. FAPERJ Cientistas do Nosso Estado Grant 102917/2011 and ANP/PRH-32.

Statistical properties of a folded elastic rod

NASA Astrophysics Data System (ADS)

Bayart, Elsa; Deboeuf, Stéphanie; Boué, Laurent; Corson, Francis; Boudaoud, Arezki; Adda-Bedia, Mokhtar

2010-03-01

A large variety of elastic structures naturally seem to be confined into environments too small to accommodate them; the geometry of folded structures span a wide range of length-scales. The elastic properties of these confined systems are further constrained by self-avoidance as well as by the dimensionality of both structures and container. To mimic crumpled paper, we devised an experimental setup to study the packing of a dimensional elastic object in 2D geometries: an elastic rod is folded at the center of a circular Hele-Shaw cell by a centripetal force. The initial configuration of the rod and the acceleration of the rotating disk allow to span different final folded configurations while the final rotation speed controls the packing intensity. Using image analysis we measure geometrical and mechanical properties of the folded configurations, focusing on length, curvature and energy distributions.

A panning DLT procedure for three-dimensional videography.

PubMed

Yu, B; Koh, T J; Hay, J G

1993-06-01

The direct linear transformation (DLT) method [Abdel-Aziz and Karara, APS Symposium on Photogrammetry. American Society of Photogrammetry, Falls Church, VA (1971)] is widely used in biomechanics to obtain three-dimensional space coordinates from film and video records. This method has some major shortcomings when used to analyze events which take place over large areas. To overcome these shortcomings, a three-dimensional data collection method based on the DLT method, and making use of panning cameras, was developed. Several small single control volumes were combined to construct a large total control volume. For each single control volume, a regression equation (calibration equation) is developed to express each of the 11 DLT parameters as a function of camera orientation, so that the DLT parameters can then be estimated from arbitrary camera orientations. Once the DLT parameters are known for at least two cameras, and the associated two-dimensional film or video coordinates of the event are obtained, the desired three-dimensional space coordinates can be computed. In a laboratory test, five single control volumes (in a total control volume of 24.40 x 2.44 x 2.44 m3) were used to test the effect of the position of the single control volume on the accuracy of the computed three dimensional space coordinates. Linear and quadratic calibration equations were used to test the effect of the order of the equation on the accuracy of the computed three dimensional space coordinates. For four of the five single control volumes tested, the mean resultant errors associated with the use of the linear calibration equation were significantly larger than those associated with the use of the quadratic calibration equation. The position of the single control volume had no significant effect on the mean resultant errors in computed three dimensional coordinates when the quadratic calibration equation was used. Under the same data collection conditions, the mean resultant errors in the computed three dimensional coordinates associated with the panning and stationary DLT methods were 17 and 22 mm, respectively. The major advantages of the panning DLT method lie in the large image sizes obtained and in the ease with which the data can be collected. The method also has potential for use in a wide variety of contexts. The major shortcoming of the method is the large amount of digitizing necessary to calibrate the total control volume. Adaptations of the method to reduce the amount of digitizing required are being explored.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

NASA Astrophysics Data System (ADS)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

[My hybrid carrier of clinical pathologist].

PubMed

Honda, Takayuki

2011-03-01

In this review, I showed a brief summary of my carrier in multiple special fields (clinical pathologist, anatomical pathologist of lung, respiratory physician and infection control doctor), my studies and my own view of laboratory medicine. We chiefly study pathology of the lung, especially about type II pneumocytes. Type II pneumocytes had abundant surface coat on the apical surface containing a specific carbohydrate structure of Thomsen-Friedenreich (TF) antigen. TF antigen is a marker of type II pneumocytes beyond animal species, and can be used for evaluating activity of various interstitial pneumonia as type II pneumocyte index (number/lmm alveolar length). Three dimensional views generated from thick sections of ordinary processed paraffin blocks showed new information of normal and abnormal lung morphology. Type II pneumocytes linearly located along the elastic fibers forming framework of polygonal alveoli, and in usual interstitial pneumonia, destruction of these elastic fibers were observed. In Japan, roles of a clinical pathologist are not definite as a radiologist, and clinical laboratory in a hospital is recognized as a section only performing blood and chemical tests. Evaluation of the data and participation in diagnosis were not requested. In future, medical doctors devote themselves to treat patients, and clinical pathologists and laboratory technicians have to help the doctors in diagnostic process. Routine tests (blood and urine) are most frequently performed in clinical medicine, but the data are not adequately used. Therefore, a system is necessary for interpreting routine tests and reporting them to other medical staffs.

System and method for investigating sub-surface features and 3D imaging of non-linear property, compressional velocity VP, shear velocity VS and velocity ratio VP/VS of a rock formation

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

Vu, Cung Khac; Skelt, Christopher; Nihei, Kurt

A system and a method for generating a three-dimensional image of a rock formation, compressional velocity VP, shear velocity VS and velocity ratio VP/VS of a rock formation are provided. A first acoustic signal includes a first plurality of pulses. A second acoustic signal from a second source includes a second plurality of pulses. A detected signal returning to the borehole includes a signal generated by a non-linear mixing process from the first and second acoustic signals in a non-linear mixing zone within an intersection volume. The received signal is processed to extract the signal over noise and/or signals resultingmore » from linear interaction and the three dimensional image of is generated.« less

An exact solution of the van der Waals interaction between two ground-state hydrogen atoms

NASA Astrophysics Data System (ADS)

Koga, Toshikatsu; Matsumoto, Shinya

1985-06-01

A momentum space treatment shows that perturbation equations for the H(1s)-H(1s) van der Waals interaction can be exactly solved in their Schrödinger forms without invoking any variational methods. Using the Fock transformation, which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere, we solve the third order integral-type perturbation equation with respect to the reciprocal of the internuclear distance R. An exact third order wave function is found as a linear combination of infinite number of four-dimensional spherical harmonics. The result allows us to evaluate the exact dispersion energy E6R-6, which is completely determined by the first three coefficients of the above linear combination.

Hydrogels with tunable stress relaxation regulate stem cell fate and activity

NASA Astrophysics Data System (ADS)

Chaudhuri, Ovijit; Gu, Luo; Klumpers, Darinka; Darnell, Max; Bencherif, Sidi A.; Weaver, James C.; Huebsch, Nathaniel; Lee, Hong-Pyo; Lippens, Evi; Duda, Georg N.; Mooney, David J.

2016-03-01

Natural extracellular matrices (ECMs) are viscoelastic and exhibit stress relaxation. However, hydrogels used as synthetic ECMs for three-dimensional (3D) culture are typically elastic. Here, we report a materials approach to tune the rate of stress relaxation of hydrogels for 3D culture, independently of the hydrogel's initial elastic modulus, degradation, and cell-adhesion-ligand density. We find that cell spreading, proliferation, and osteogenic differentiation of mesenchymal stem cells (MSCs) are all enhanced in cells cultured in gels with faster relaxation. Strikingly, MSCs form a mineralized, collagen-1-rich matrix similar to bone in rapidly relaxing hydrogels with an initial elastic modulus of 17 kPa. We also show that the effects of stress relaxation are mediated by adhesion-ligand binding, actomyosin contractility and mechanical clustering of adhesion ligands. Our findings highlight stress relaxation as a key characteristic of cell-ECM interactions and as an important design parameter of biomaterials for cell culture.

Microtubules soften due to cross-sectional flattening

DOE PAGES

Memet, Edvin; Hilitsk, Feodor; Morris, Margaret A.; ...

2018-06-01

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasing deformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effectmore » in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.« less

Microtubules soften due to cross-sectional flattening

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

Memet, Edvin; Hilitsk, Feodor; Morris, Margaret A.

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasing deformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effectmore » in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.« less

Ultralight nanofibre-assembled cellular aerogels with superelasticity and multifunctionality.

PubMed

Si, Yang; Yu, Jianyong; Tang, Xiaomin; Ge, Jianlong; Ding, Bin

2014-12-16

Three-dimensional nanofibrous aerogels (NFAs) that are both highly compressible and resilient would have broad technological implications for areas ranging from electrical devices and bioengineering to damping materials; however, creating such NFAs has proven extremely challenging. Here we report a novel strategy to create fibrous, isotropically bonded elastic reconstructed (FIBER) NFAs with a hierarchical cellular structure and superelasticity by combining electrospun nanofibres and the fibrous freeze-shaping technique. Our approach causes the intrinsically lamellar deposited electrospun nanofibres to assemble into elastic bulk aerogels with tunable densities and desirable shapes on a large scale. The resulting FIBER NFAs exhibit densities of >0.12 mg cm(-3), rapid recovery from deformation, efficient energy absorption and multifunctionality in terms of the combination of thermal insulation, sound absorption, emulsion separation and elasticity-responsive electric conduction. The successful synthesis of such fascinating materials may provide new insights into the design and development of multifunctional NFAs for various applications.

Three-dimensional elasticity solution of an infinite plate with a circular hole

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. The problem was originally solved by Alblas. The reasons for reconsidering it are to develop a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. The problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Various stress components are tabulated as functions of a/h, z/h, r/a, and nu, a and 2h being the radius of the hole and the plate thickness and nu, the Poisson's ratio. The significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses is discussed.

An ultrasonic method for determination of elastic moduli, density, attenuation and thickness of a polymer coating on a stiff plate.

PubMed

Lavrentyev, A I; Rokhlin, S I

2001-04-01

An ultrasonic method proposed by us for determination of the complete set of acoustical and geometrical properties of a thin isotropic layer between semispaces (J. Acoust. Soc. Am. 102 (1997) 3467) is extended to determination of the properties of a coating on a thin plate. The method allows simultaneous determination of the coating thickness, density, elastic moduli and attenuation (longitudinal and shear) from normal and oblique incidence reflection (transmission) frequency spectra. Reflection (transmission) from the coated plate is represented as a function of six nondimensional parameters of the coating which are determined from two experimentally measured spectra: one at normal and one at oblique incidence. The introduction of the set of nondimensional parameters allows one to transform the reconstruction process from one search in a six-dimensional space to two searches in three-dimensional spaces (one search for normal incidence and one for oblique). Thickness, density, and longitudinal and shear elastic moduli of the coating are calculated from the nondimensional parameters determined. The sensitivity of the method to individual properties and its stability against experimental noise are studied and the inversion algorithm is accordingly optimized. An example of the method and experimental measurement for comparison is given for a polypropylene coating on a steel foil.

Summary of Research Report

NASA Technical Reports Server (NTRS)

Elishakoff, Isaac

1998-01-01

Ten papers, published in various publications, on buckling, and the effects of imperfections on various structures are presented. These papers are: (1) Buckling mode localization in elastic plates due to misplacement in the stiffner location; (2) On vibrational imperfection sensitivity on Augusti's model structure in the vicinity of a non-linear static state; (3) Imperfection sensitivity due to elastic moduli in the Roorda Koiter frame; (4) Buckling mode localization in a multi-span periodic structure with a disorder in a single span; (5) Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling; (6) Derivation of multi-dimensional ellipsoidal convex model for experimental data; (7) Passive control of buckling deformation via Anderson localization phenomenon; (8)Effect of the thickness and initial im perfection on buckling on composite cylindrical shells: asymptotic analysis and numerical results by BOSOR4 and PANDA2; (9) Worst case estimation of homology design by convex analysis; (10) Buckling of structures with uncertain imperfections - Personal perspective.

The Constitutive Modeling of Thin Films with Randon Material Wrinkles

NASA Technical Reports Server (NTRS)

Murphey, Thomas W.; Mikulas, Martin M.

2001-01-01

Material wrinkles drastically alter the structural constitutive properties of thin films. Normally linear elastic materials, when wrinkled, become highly nonlinear and initially inelastic. Stiffness' reduced by 99% and negative Poisson's ratios are typically observed. This paper presents an effective continuum constitutive model for the elastic effects of material wrinkles in thin films. The model considers general two-dimensional stress and strain states (simultaneous bi-axial and shear stress/strain) and neglects out of plane bending. The constitutive model is derived from a traditional mechanics analysis of an idealized physical model of random material wrinkles. Model parameters are the directly measurable wrinkle characteristics of amplitude and wavelength. For these reasons, the equations are mechanistic and deterministic. The model is compared with bi-axial tensile test data for wrinkled Kaptong(Registered Trademark) HN and is shown to deterministically predict strain as a function of stress with an average RMS error of 22%. On average, fitting the model to test data yields an RMS error of 1.2%

Symmetrical or Non-Symmetrical Debonds at Fiber-Matrix Interfaces: A Study by BEM and Finite Fracture Mechanics on Elastic Interfaces

NASA Astrophysics Data System (ADS)

Muñoz-Reja, Mar; Távara, Luis; Mantič, Vladislav

A recently proposed criterion is used to study the behavior of debonds produced at a fiber-matrix interface. The criterion is based on the Linear Elastic-(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Special attention is given to the discussion about the symmetry of the debond onset and growth in an isolated single fiber specimen under uniaxial transverse tension. A common composite material system, glass fiber-epoxy matrix, is considered. The present methodology uses a two-dimensional (2D) Boundary Element Method (BEM) code to carry out the analysis of interface failure. The present results show that a non-symmetrical interface crack configuration (debonds at one side only) is produced by a lower critical remote load than the symmetrical case (debonds at both sides). Thus, the non-symmetrical solution is the preferred one, which agrees with the experimental evidences found in the literature.

Two-dimensional strain gradient damage modeling: a variational approach

NASA Astrophysics Data System (ADS)

Placidi, Luca; Misra, Anil; Barchiesi, Emilio

2018-06-01

In this paper, we formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage. The failure is defined as the condition in which the damage parameter reaches 1, at least in one point of the domain. The quasi-static approximation is done, i.e., the kinetic energy is assumed to be negligible. In order to deal with dissipation, a damage dissipation term is considered in the deformation energy functional. The key goal of this paper is to apply a non-standard variational procedure to exploit the damage irreversibility argument. As a result, we derive not only the equilibrium equations but, notably, also the Karush-Kuhn-Tucker conditions. Finally, numerical simulations for exemplary problems are discussed as some constitutive parameters are varying, with the inclusion of a mesh-independence evidence. Element-free Galerkin method and moving least square shape functions have been employed.

Filamentary structures that self-organize due to adhesion

NASA Astrophysics Data System (ADS)

Sengab, A.; Picu, R. C.

2018-03-01

We study the self-organization of random collections of elastic filaments that interact adhesively. The evolution from an initial fully random quasi-two-dimensional state is controlled by filament elasticity, adhesion and interfilament friction, and excluded volume. Three outcomes are possible: the system may remain locked in the initial state, may organize into isolated fiber bundles, or may form a stable, connected network of bundles. The range of system parameters leading to each of these states is identified. The network of bundles is subisostatic and is stabilized by prestressed triangular features forming at bundle-to-bundle nodes, similar to the situation in foams. Interfiber friction promotes locking and expands the parametric range of nonevolving systems.

Coherent transmission of an ultrasonic shock wave through a multiple scattering medium.

PubMed

Viard, Nicolas; Giammarinaro, Bruno; Derode, Arnaud; Barrière, Christophe

2013-08-01

We report measurements of the transmitted coherent (ensemble-averaged) wave resulting from the interaction of an ultrasonic shock wave with a two-dimensional random medium. Despite multiple scattering, the coherent waveform clearly shows the steepening that is typical of nonlinear harmonic generation. This is taken advantage of to measure the elastic mean free path and group velocity over a broad frequency range (2-15 MHz) in only one experiment. Experimental results are found to be in good agreement with a linear theoretical model taking into account spatial correlations between scatterers. These results show that nonlinearity and multiple scattering are both present, yet uncoupled.

Fault slip and seismic moment of the 1700 Cascadia earthquake inferred from Japanese tsunami descriptions

USGS Publications Warehouse

Satake, K.; Wang, K.; Atwater, B.F.

2003-01-01

The 1700 Cascadia earthquake attained moment magnitude 9 according to new estimates based on effects of its tsunami in Japan, computed coseismic seafloor deformation for hypothetical ruptures in Cascadia, and tsunami modeling in the Pacific Ocean. Reports of damage and flooding show that the 1700 Casscadia tsunami reached 1-5 m heights at seven shoreline sites in Japan. Three sets of estimated heights express uncertainty about location and depth of reported flooding, landward decline in tsunami heights from shorelines, and post-1700 land-level changes. We compare each set with tsunami heights computed from six Cascadia sources. Each source is vertical seafloor displacement calculated with a three-dimensional elastic dislocation model, for three sources the rupture extends the 1100 km length of the subduction zone and differs in width and shallow dip; for the other sources, ruptures of ordinary width extend 360-670 km. To compute tsunami waveforms, we use a linear long-wave approximation with a finite difference method, and we employ modern bathymetry with nearshore grid spacing as small as 0.4 km. The various combinations of Japanese tsunami heights and Cascadia sources give seismic moment of 1-9 ?? 1022 N m, equivalent to moment magnitude 8.7-9.2. This range excludes several unquantified uncertainties. The most likely earthquake, of moment magnitude 9.0, has 19 m of coseismic slip on an offshore, full-slip zone 1100 km long with linearly decreasing slip on a downdip partial-slip zone. The shorter rupture models require up to 40 m offshore slip and predict land-level changes inconsistent with coastal paleoseismological evidence. Copyright 2003 by the American Geophysical Union.

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.

Effects of Laboratory Disinfecting Agents on Dimensional Stability of Three Commercially Available Heat-Cured Denture Acrylic Resins in India: An In-Vitro Study

PubMed Central

Jujare, Ravikanth Haridas; Varghese, Rana Kalappattil; Singh, Vishwa Deepak; Gaurav, Amit

2016-01-01

Introduction Dental professionals are exposed to a wide variety of microorganisms which calls for use of effective infection control procedures in the dental office and laboratories that can prevent cross-contamination that could extend to dentists, dental office staff, dental technicians as well as patients. This concern has led to a renewed interest in denture sterilization and disinfection. Heat polymerized dentures exhibit dimensional change during disinfection procedure. Aim The purpose of this study was to determine the influence of different types of widely used laboratory disinfecting agents on the dimensional stability of heat-cured denture acrylic resins and to compare the dimensional stability of three commercially available heat-cured denture acrylic resins in India. Materials and Methods Twelve specimens of uniform dimension each of three different brands namely Stellon, Trevalon and Acralyn-H were prepared using circular metal disc. Chemical disinfectants namely 2% alkaline glutaraldehyde, 1% povidone-iodine, 0.5% sodium hypochlorite and water as control group were used. Diameter of each specimen was measured before immersion and after immersion with time interval of 1 hour and 12 hours. The data was evaluated statistically using one way analysis of variance. Results All the specimens in three disinfectants and in water exhibited very small amount of linear expansion. Among three disinfectants, specimens in 2% alkaline glutaraldehyde exhibited least(0.005mm) and water showed highest (0.009mm) amount of dimensional change. Among resins, Trevalon showed least (0.067mm) and Acralyn-H exhibited highest (0.110mm) amount of dimensional change. Conclusion Although, all the specimens of three different brands of heat-cured denture acrylic resins exhibited increase in linear dimensional change in all the disinfectants and water, they were found to be statistically insignificant. PMID:27134996

Improving the estimate of the effective elastic modulus derived from three-point bending tests of long bones.

PubMed

Kourtis, Lampros C; Carter, Dennis R; Beaupre, Gary S

2014-08-01

Three-point bending tests are often used to determine the apparent or effective elastic modulus of long bones. The use of beam theory equations to interpret such tests can result in a substantial underestimation of the true effective modulus. In this study three-dimensional, nonlinear finite element analysis is used to quantify the errors inherent in beam theory and to create plots that can be used to correct the elastic modulus calculated from beam theory. Correction plots are generated for long bones representative of a variety of species commonly used in research studies. For a long bone with dimensions comparable to the mouse femur, the majority of the error in the effective elastic modulus results from deformations to the bone cross section that are not accounted for in the equations from beam theory. In some cases, the effective modulus calculated from beam theory can be less than one-third of the true effective modulus. Errors are larger: (1) for bones having short spans relative to bone length; (2) for bones with thin vs. thick cortices relative to periosteal diameter; and (3) when using a small radius or "knife-edge" geometry for the center loading ram and the outer supports in the three-point testing system. The use of these correction plots will enable researchers to compare results for long bones from different animal strains and to compare results obtained using testing systems that differ with regard to length between the outer supports and the radius used for the loading ram and outer supports.

β-connectin studies by small-angle x-ray scattering and single-molecule force spectroscopy by atomic force microscopy

NASA Astrophysics Data System (ADS)

Marchetti, S.; Sbrana, F.; Toscano, A.; Fratini, E.; Carlà, M.; Vassalli, M.; Tiribilli, B.; Pacini, A.; Gambi, C. M. C.

2011-05-01

The three-dimensional structure and the mechanical properties of a β-connectin fragment from human cardiac muscle, belonging to the I band, from I27 to I34, were investigated by small-angle x-ray scattering (SAXS) and single-molecule force spectroscopy (SMFS). This molecule presents an entropic elasticity behavior, associated to globular domain unfolding, that has been widely studied in the last 10 years. In addition, atomic force microscopy based SMFS experiments suggest that this molecule has an additional elastic regime, for low forces, probably associated to tertiary structure remodeling. From a structural point of view, this behavior is a mark of the fact that the eight domains in the I27-I34 fragment are not independent and they organize in solution, assuming a well-defined three-dimensional structure. This hypothesis has been confirmed by SAXS scattering, both on a diluted and a concentrated sample. Two different models were used to fit the SAXS curves: one assuming a globular shape and one corresponding to an elongated conformation, both coupled with a Coulomb repulsion potential to take into account the protein-protein interaction. Due to the predominance of the structure factor, the effective shape of the protein in solution could not be clearly disclosed. By performing SMFS by atomic force microscopy, mechanical unfolding properties were investigated. Typical sawtooth profiles were obtained and the rupture force of each unfolding domain was estimated. By fitting a wormlike chain model to each peak of the sawtooth profile, the entropic elasticity of octamer was described.

Reconfigurable interactions and three-dimensional patterning of colloidal particles and defects in lamellar soft media

PubMed Central

Trivedi, Rahul P.; Klevets, Ivan I.; Senyuk, Bohdan; Lee, Taewoo; Smalyukh, Ivan I.

2012-01-01

Colloidal systems find important applications ranging from fabrication of photonic crystals to direct probing of phenomena typically encountered in atomic crystals and glasses. New applications—such as nanoantennas, plasmonic sensors, and nanocircuits—pose a challenge of achieving sparse colloidal assemblies with tunable interparticle separations that can be controlled at will. We demonstrate reconfigurable multiscale interactions and assembly of colloids mediated by defects in cholesteric liquid crystals that are probed by means of laser manipulation and three-dimensional imaging. We find that colloids attract via distance-independent elastic interactions when pinned to the ends of cholesteric oily streaks, line defects at which one or more layers are interrupted. However, dislocations and oily streaks can also be optically manipulated to induce kinks, allowing one to lock them into the desired configurations that are stabilized by elastic energy barriers for structural transformation of the particle-connecting defects. Under the influence of elastic energy landscape due to these defects, sublamellar-sized colloids self-assemble into structures mimicking the cores of dislocations and oily streaks. Interactions between these defect-embedded colloids can be varied from attractive to repulsive by optically introducing dislocation kinks. The reconfigurable nature of defect–particle interactions allows for patterning of defects by manipulation of colloids and, in turn, patterning of particles by these defects, thus achieving desired colloidal configurations on scales ranging from the size of defect core to the sample size. This defect-colloidal sculpturing may be extended to other lamellar media, providing the means for optically guided self-assembly of mesoscopic composites with predesigned properties. PMID:22411822

An experimental and three-dimensional computational study on the aerodynamic contribution to the passive pitching motion of flapping wings in hovering flies.

PubMed

Ishihara, D; Horie, T; Niho, T

2014-11-07

The relative importance of the wing's inertial and aerodynamic forces is the key to revealing how the kinematical characteristics of the passive pitching motion of insect flapping wings are generated, which is still unclear irrespective of its importance in the design of insect-like micro air vehicles. Therefore, we investigate three species of flies in order to reveal this, using a novel fluid-structure interaction analysis that consists of a dynamically scaled experiment and a three-dimensional finite element analysis. In the experiment, the dynamic similarity between the lumped torsional flexibility model as a first approximation of the dipteran wing and the actual insect is measured by the Reynolds number Re, the Strouhal number St, the mass ratio M, and the Cauchy number Ch. In the computation, the three-dimension is important in order to simulate the stable leading edge vortex and lift force in the present Re regime over 254. The drawback of the present experiment is the difficulty in satisfying the condition of M due to the limitation of available solid materials. The novelty of the present analysis is to complement this drawback using the computation. We analyze the following two cases: (a) The equilibrium between the wing's elastic and fluid forces is dynamically similar to that of the actual insect, while the wing's inertial force can be ignored. (b) All forces are dynamically similar to those of the actual insect. From the comparison between the results of cases (a) and (b), we evaluate the contributions of the equilibrium between the aerodynamic and the wing's elastic forces and the wing's inertial force to the passive pitching motion as 80-90% and 10-20%, respectively. It follows from these results that the dipteran passive pitching motion will be based on the equilibrium between the wing's elastic and aerodynamic forces, while it will be enhanced by the wing's inertial force.

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.

Reconstruction of three-dimensional ultrasound images based on cyclic Savitzky-Golay filters

NASA Astrophysics Data System (ADS)

Toonkum, Pollakrit; Suwanwela, Nijasri C.; Chinrungrueng, Chedsada

2011-01-01

We present a new algorithm for reconstructing a three-dimensional (3-D) ultrasound image from a series of two-dimensional B-scan ultrasound slices acquired in the mechanical linear scanning framework. Unlike most existing 3-D ultrasound reconstruction algorithms, which have been developed and evaluated in the freehand scanning framework, the new algorithm has been designed to capitalize the regularity pattern of the mechanical linear scanning, where all the B-scan slices are precisely parallel and evenly spaced. The new reconstruction algorithm, referred to as the cyclic Savitzky-Golay (CSG) reconstruction filter, is an improvement on the original Savitzky-Golay filter in two respects: First, it is extended to accept a 3-D array of data as the filter input instead of a one-dimensional data sequence. Second, it incorporates the cyclic indicator function in its least-squares objective function so that the CSG algorithm can simultaneously perform both smoothing and interpolating tasks. The performance of the CSG reconstruction filter compared to that of most existing reconstruction algorithms in generating a 3-D synthetic test image and a clinical 3-D carotid artery bifurcation in the mechanical linear scanning framework are also reported.

Effect of the crown design and interface lute parameters on the stress-state of a machined crown-tooth system: a finite element analysis.

PubMed

Shahrbaf, Shirin; vanNoort, Richard; Mirzakouchaki, Behnam; Ghassemieh, Elaheh; Martin, Nicolas

2013-08-01

The effect of preparation design and the physical properties of the interface lute on the restored machined ceramic crown-tooth complex are poorly understood. The aim of this work was to determine, by means of three-dimensional finite element analysis (3D FEA) the effect of the tooth preparation design and the elastic modulus of the cement on the stress state of the cemented machined ceramic crown-tooth complex. The three-dimensional structure of human premolar teeth, restored with adhesively cemented machined ceramic crowns, was digitized with a micro-CT scanner. An accurate, high resolution, digital replica model of a restored tooth was created. Two preparation designs, with different occlusal morphologies, were modeled with cements of 3 different elastic moduli. Interactive medical image processing software (mimics and professional CAD modeling software) was used to create sophisticated digital models that included the supporting structures; periodontal ligament and alveolar bone. The generated models were imported into an FEA software program (hypermesh version 10.0, Altair Engineering Inc.) with all degrees of freedom constrained at the outer surface of the supporting cortical bone of the crown-tooth complex. Five different elastic moduli values were given to the adhesive cement interface 1.8GPa, 4GPa, 8GPa, 18.3GPa and 40GPa; the four lower values are representative of currently used cementing lutes and 40GPa is set as an extreme high value. The stress distribution under simulated applied loads was determined. The preparation design demonstrated an effect on the stress state of the restored tooth system. The cement elastic modulus affected the stress state in the cement and dentin structures but not in the crown, the pulp, the periodontal ligament or the cancellous and cortical bone. The results of this study suggest that both the choice of the preparation design and the cement elastic modulus can affect the stress state within the restored crown-tooth complex. Copyright © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Synergistic effects from graphene and carbon nanotubes endow ordered hierarchical structure foams with a combination of compressibility, super-elasticity and stability and potential application as pressure sensors

NASA Astrophysics Data System (ADS)

Kuang, Jun; Dai, Zhaohe; Liu, Luqi; Yang, Zhou; Jin, Ming; Zhang, Zhong

2015-05-01

Nanostructured carbon material based three-dimensional porous architectures have been increasingly developed for various applications, e.g. sensors, elastomer conductors, and energy storage devices. Maintaining architectures with good mechanical performance, including elasticity, load-bearing capacity, fatigue resistance and mechanical stability, is prerequisite for realizing these functions. Though graphene and CNT offer opportunities as nanoscale building blocks, it still remains a great challenge to achieve good mechanical performance in their microarchitectures because of the need to precisely control the structure at different scales. Herein, we fabricate a hierarchical honeycomb-like structured hybrid foam based on both graphene and CNT. The resulting materials possess excellent properties of combined high specific strength, elasticity and mechanical stability, which cannot be achieved in neat CNT and graphene foams. The improved mechanical properties are attributed to the synergistic-effect-induced highly organized, multi-scaled hierarchical architectures. Moreover, with their excellent electrical conductivity, we demonstrated that the hybrid foams could be used as pressure sensors in the fields related to artificial skin.Nanostructured carbon material based three-dimensional porous architectures have been increasingly developed for various applications, e.g. sensors, elastomer conductors, and energy storage devices. Maintaining architectures with good mechanical performance, including elasticity, load-bearing capacity, fatigue resistance and mechanical stability, is prerequisite for realizing these functions. Though graphene and CNT offer opportunities as nanoscale building blocks, it still remains a great challenge to achieve good mechanical performance in their microarchitectures because of the need to precisely control the structure at different scales. Herein, we fabricate a hierarchical honeycomb-like structured hybrid foam based on both graphene and CNT. The resulting materials possess excellent properties of combined high specific strength, elasticity and mechanical stability, which cannot be achieved in neat CNT and graphene foams. The improved mechanical properties are attributed to the synergistic-effect-induced highly organized, multi-scaled hierarchical architectures. Moreover, with their excellent electrical conductivity, we demonstrated that the hybrid foams could be used as pressure sensors in the fields related to artificial skin. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr00841g

Anomalous elasticity, fluctuations and disorder in elastic membranes

NASA Astrophysics Data System (ADS)

Le Doussal, Pierre; Radzihovsky, Leo

2018-05-01

Motivated by freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters (Le Doussal and Radzihovsky, 1992; 1993). The experimental realization atom-thin graphene sheets (Novoselov et al., 2004) have driven a resurgence in this fascinating subject, making our dated predictions and their detailed derivations timely. To this end we analyze the statistical mechanics of a generalized D-dimensional elastic "membrane" embedded in d dimensions using a self-consistent screening approximation (SCSA), that has proved to be unprecedentedly accurate in this system, exact in three complementary limits: (i) d → ∞, (ii) D → 4, and (iii) D = d. Focusing on the critical "flat" phase, for a homogeneous two-dimensional (D = 2) membrane embedded in three dimensions (d = 3), we predict its universal roughness exponent ζ = 0 . 590, length-scale dependent elastic moduli exponents η = 0 . 821 and ηu = 0 . 358, and an anomalous Poisson ratio, σ = - 1 / 3. In the presence of random uncorrelated heterogeneity the membrane exhibits a glassy wrinkled ground state, characterized by ζ‧ = 0 . 775 ,η‧ = 0 . 449, ηu‧ = 1 . 101 and a Poisson ratio σ‧ = - 1 / 3. Motivated by a number of physical realizations (charged impurities, disclinations and dislocations) we also study power-law correlated quenched disorder that leads to a variety of distinct glassy wrinkled phases. Finally, neglecting self-avoiding interaction we demonstrate that at high temperature a "phantom" sheet undergoes a continuous crumpling transition, characterized by a radius of gyration exponent, ν = 0 . 732 and η = 0 . 535. Many of these universal predictions have received considerable support from simulations. We hope that this detailed presentation of the SCSA theory will be useful to further theoretical developments and corresponding experimental investigations on freely suspended graphene.

Nonlinear analysis for the response and failure of compression-loaded angle-ply laminates with a hole

NASA Technical Reports Server (NTRS)

Mathison, Steven R.; Herakovich, Carl T.; Pindera, Marek-Jerzy; Shuart, Mark J.

1987-01-01

The objective was to determine the effect of nonlinear material behavior on the response and failure of unnotched and notched angle-ply laminates under uniaxial compressive loading. The endochronic theory was chosen as the constitutive theory to model the AS4/3502 graphite-epoxy material system. Three-dimensional finite element analysis incorporating the endochronic theory was used to determine the stresses and strains in the laminates. An incremental/iterative initial strain algorithm was used in the finite element program. To increase computational efficiency, a 180 deg rotational symmetry relationship was utilized and the finite element program was vectorized to run on a supercomputer. Laminate response was compared to experimentation revealing excellent agreement for both the unnotched and notched angle-ply laminates. Predicted stresses in the region of the hole were examined and are presented, comparing linear elastic analysis to the inelastic endochronic theory analysis. A failure analysis of the unnotched and notched laminates was performed using the quadratic tensor polynomial. Predicted fracture loads compared well with experimentation for the unnotched laminates, but were very conservative in comparison with experiments for the notched laminates.

Wave propagation in magneto-electro-elastic multilayered plates with nonlocal effect

NASA Astrophysics Data System (ADS)

Chen, Jiangyi; Guo, Junhong; Pan, Ernian

2017-07-01

In this paper, analytical solutions for propagation of time-harmonic waves in three-dimensional, transversely isotropic, magnetoelectroelastic and multilayered plates with nonlocal effect are derived. We first convert the time-harmonic wave problem into a linear eigenvalue system, from which we obtain the general solutions of the extended displacements and stresses. The solutions are then employed to derive the propagator matrix which connects the field variables at the upper and lower interfaces of each layer. Making use of the continuity conditions of the physical quantities across the interface, the global propagator relation is assembled by propagating the solutions in each layer from the bottom to the top of the layered plate. From the global propagator matrix, the dispersion equation is obtained by imposing the traction-free boundary conditions on both the top and bottom surfaces of the layered plate. Dispersion curves and mode shapes in layered plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to show the influence of the nonlocal parameter, stacking sequence, as well as the orientation of incident wave on the time-harmonic field response.

Selective buckling via states of self-stress in topological metamaterials

PubMed Central

Paulose, Jayson; Meeussen, Anne S.; Vitelli, Vincenzo

2015-01-01

States of self-stress—tensions and compressions of structural elements that result in zero net forces—play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self-stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely hinged joints, they leave a distinct signature in the nonlinear buckling behavior of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices. PMID:26056303

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.

Magnetic Resonance Poroelastography: An Algorithm for Estimating the Mechanical Properties of Fluid-Saturated Soft Tissues

PubMed Central

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

2010-01-01

Magnetic Resonance Poroelastography (MRPE) is introduced as an alternative to single-phase model-based elastographic reconstruction methods. A three-dimensional (3D) finite element poroelastic inversion algorithm was developed to recover the mechanical properties of fluid-saturated tissues. The performance of this algorithm was assessed through a variety of numerical experiments, using synthetic data to probe its stability and sensitivity to the relevant model parameters. Preliminary results suggest the algorithm is robust in the presence of noise and capable of producing accurate assessments of the underlying mechanical properties in simulated phantoms. Further, a 3D time-harmonic motion field was recorded for a poroelastic phantom containing a single cylindrical inclusion and used to assess the feasibility of MRPE image reconstruction from experimental data. The elastograms obtained from the proposed poroelastic algorithm demonstrate significant improvement over linearly elastic MRE images generated using the same data. In addition, MRPE offers the opportunity to estimate the time-harmonic pressure field resulting from tissue excitation, highlighting the potential for its application in the diagnosis and monitoring of disease processes associated with changes in interstitial pressure. PMID:20199912

Size dependent nanomechanics of coil spring shaped polymer nanowires

NASA Astrophysics Data System (ADS)

Ushiba, Shota; Masui, Kyoko; Taguchi, Natsuo; Hamano, Tomoki; Kawata, Satoshi; Shoji, Satoru

2015-11-01

Direct laser writing (DLW) via two-photon polymerization (TPP) has been established as a powerful technique for fabrication and integration of nanoscale components, as it enables the production of three dimensional (3D) micro/nano objects. This technique has indeed led to numerous applications, including micro- and nanoelectromechanical systems (MEMS/NEMS), metamaterials, mechanical metamaterials, and photonic crystals. However, as the feature sizes decrease, an urgent demand has emerged to uncover the mechanics of nanosized polymer materials. Here, we fabricate coil spring shaped polymer nanowires using DLW via two-photon polymerization. We find that even the nanocoil springs follow a linear-response against applied forces, following Hooke’s law, as revealed by compression tests using an atomic force microscope. Further, the elasticity of the polymer material is found to become significantly greater as the wire radius is decreased from 550 to 350 nm. Polarized Raman spectroscopy measurements show that polymer chains are aligned in nanowires along the axis, which may be responsible for the size dependence. Our findings provide insight into the nanomechanics of polymer materials fabricated by DLW, which leads to further applications based on nanosized polymer materials.

Size dependent nanomechanics of coil spring shaped polymer nanowires.

PubMed

Ushiba, Shota; Masui, Kyoko; Taguchi, Natsuo; Hamano, Tomoki; Kawata, Satoshi; Shoji, Satoru

2015-11-27

Direct laser writing (DLW) via two-photon polymerization (TPP) has been established as a powerful technique for fabrication and integration of nanoscale components, as it enables the production of three dimensional (3D) micro/nano objects. This technique has indeed led to numerous applications, including micro- and nanoelectromechanical systems (MEMS/NEMS), metamaterials, mechanical metamaterials, and photonic crystals. However, as the feature sizes decrease, an urgent demand has emerged to uncover the mechanics of nanosized polymer materials. Here, we fabricate coil spring shaped polymer nanowires using DLW via two-photon polymerization. We find that even the nanocoil springs follow a linear-response against applied forces, following Hooke's law, as revealed by compression tests using an atomic force microscope. Further, the elasticity of the polymer material is found to become significantly greater as the wire radius is decreased from 550 to 350 nm. Polarized Raman spectroscopy measurements show that polymer chains are aligned in nanowires along the axis, which may be responsible for the size dependence. Our findings provide insight into the nanomechanics of polymer materials fabricated by DLW, which leads to further applications based on nanosized polymer materials.

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.

Characteristics of the First Longitudinal-Fourth Bending Mode Linear Ultrasonic Motors

NASA Astrophysics Data System (ADS)

Park, Taegone; Kim, Beomjin; Kim, Myong-Ho; Uchino, Kenji

2002-11-01

Linear ultrasonic motors using a combination of the first longitudinal mode and the fourth bending mode were designed and fabricated. The driving characteristics of the motors, which were composed of a straight metal bar bonded with piezoelectric ceramic vibrators as a driving element, were measured. Unimorph and bimorph ceramic vibrators were attached on three kinds of metal bars for constructing the stators of the linear motors. As results, motors made with the bimorph ceramic vibrators had higher velocity than motors of the unimorph vibrators. As a metal bar for stator, magnesium alloy, which has lower elastic coefficient than aluminum alloy, was better for the motors.

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.

Extension-torsion coupling behavior of advanced composite tilt-rotor blades

NASA Technical Reports Server (NTRS)

Kosmatka, J. B.

1989-01-01

An analytic model was developed to study the extension-bend-twist coupling behavior of an advanced composite helicopter or tilt-rotor blade. The outer surface of the blade is defined by rotating an arbitrary cross section about an initial twist axis. The cross section can be nonhomogeneous and composed of generally anisotropic materials. The model is developed based upon a three dimensional elasticity approach that is recast as a coupled two-dimensional boundary value problem defined in a curvilinear coordinate system. Displacement solutions are written in terms of known functions that represent extension, bending, and twisting and unknown functions for local cross section deformations. The unknown local deformation functions are determined by applying the principle of minimum potential energy to the discretized two-dimensional cross section. This is an application of the Ritz method, where the trial function family is the displacement field associated with a finite element (8-node isoparametric quadrilaterals) representation of the section. A computer program was written where the cross section is discretized into 8-node quadrilateral subregions. Initially the program was verified using previously published results (both three-dimensional elasticity and technical beam theory) for pretwisted isotropic bars with an elliptical cross section. In addition, solid and thin-wall multi-cell NACA-0012 airfoil sections were analyzed to illustrate the pronounced effects that pretwist, initial twist axis location, and spar location has on coupled behavior. Currently, a series of advanced composite airfoils are being modeled in order to assess how the use of laminated composite materials interacts with pretwist to alter the coupling behavior of the blade. These studies will investigate the use of different ply angle orientations and the use of symmetric versus unsymmetric laminates.

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.

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert

2018-07-01

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

Groundwater withdrawal in the Central Valley, California: implications for San Andreas Fault stressing and lithosphere rheology

NASA Astrophysics Data System (ADS)

Lundgren, P.; Liu, Z.; Ali, S. T.; Farr, T.; Faunt, C. C.

2016-12-01

Anthropogenic perturbations to crustal loading due to groundwater pumping are increasingly recognized as causing changes in nearby fault stresses. We present preliminary analysis of crustal unloading in the Central Valley (CV), California, for the period 2006-2010 to infer Coulomb stress changes on the central San Andreas Fault (CSAF), lithospheric rheology, and system memory due to more than a century of groundwater withdrawal in the southern CV. We use data-driven unloading estimates to drive three-dimensional (3-D) finite element method models and compare model vertical surface deformation rates with observed GPS uplift rates outside the CV. Groundwater level changes are observed through well water elevation changes and through the resultant surface deformation (subsidence) by interferometric synthetic aperture radar (InSAR) and through broader scale changes in gravity from the GRACE satellite time variable gravity data [Famiglietti et al., 2011] that constrain the overall water volume changes. Combining InSAR with well-water data we are able to estimate the aquifer skeletal elastic and inelastic response and through a linear inversion derive the water volume (load) changes across the Central Valley and compare them with GRACE-inferred groundwater changes. Preliminary 3-D finite element method modeling that considers elastic and viscosity structure in the lithosphere gives three interesting results: 1) elastic models poorly fit the uplift rates near the SAF; 2) viscoelastic models that simulate different unloading histories show the past history of groundwater unloading has significant residual uplift rates and fault stress changes; 3) Coulomb stress change varies from inhibited on the locked (Carrizo) section to promoted on the creeping section of the SAF north of Parkfield. Thus, 3D models that account for lithosphere rheology, loading history viscous relaxation, have significant implications for longer-term time-dependent deformation, stress perturbation, and earthquake hazard on the nearby faults. Reference: Famiglietti, J. S., M. Lo, S. L. Ho, J. Bethune, K. J. Anderson, T. H. Syed, S. C. Swenson, C. R. de Linage, and M. Rodell, 2011, Satellites measure recent rates of groundwater depletion in California's Central Valley, Geophys. Res. Lett., 38, L03403, doi:10.1029/2010GL046442.

Modeling drop impacts on inclined flowing soap films

NASA Astrophysics Data System (ADS)

Basu, Saikat; Yawar, Ali; Concha, Andres; Bandi, Mahesh

2015-11-01

Small drops impinging on soap films flowing at an angle primarily exhibit three fundamental regimes of post-impact dynamics: (a) the drop bounces off the film surface, (b) it coalesces with the downstream flow, and (c) it pierces through the film. During impact, the drop deforms along with a simultaneous, almost elastic deformation of the film transverse to the stream direction. Hence, the governing dynamics for this interaction present the rare opportunity to explore the in-tandem effects of elasticity and hydrodynamics alike. In this talk, we outline the analytical framework to study the drop impact dynamics. The model assumes a deformable drop and a deformable three-dimensional soap film and invokes a parametric study to qualify the three mentioned impact types. The physical parameters include the impact angle, drop impact speed, and the diameters of the drop prior to and during impact when it deforms and spreads out. Our model system offers a path towards optimization of interactions between a spray and a flowing liquid.

Three dimensional radiative flow of magnetite-nanofluid with homogeneous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Rashid, Madiha; Alsaedi, Ahmed

2018-03-01

Present communication deals with the effects of homogeneous-heterogeneous reactions in flow of nanofluid by non-linear stretching sheet. Water based nanofluid containing magnetite nanoparticles is considered. Non-linear radiation and non-uniform heat sink/source effects are examined. Non-linear differential systems are computed by Optimal homotopy analysis method (OHAM). Convergent solutions of nonlinear systems are established. The optimal data of auxiliary variables is obtained. Impact of several non-dimensional parameters for velocity components, temperature and concentration fields are examined. Graphs are plotted for analysis of surface drag force and heat transfer rate.

An efficient closed-form solution for acoustic emission source location in three-dimensional structures

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

Li, Xibing; Dong, Longjun, E-mail: csudlj@163.com; Australian Centre for Geomechanics, The University of Western Australia, Crawley, 6009

This paper presents an efficient closed-form solution (ECS) for acoustic emission(AE) source location in three-dimensional structures using time difference of arrival (TDOA) measurements from N receivers, N ≥ 6. The nonlinear location equations of TDOA are simplified to linear equations. The unique analytical solution of AE sources for unknown velocity system is obtained by solving the linear equations. The proposed ECS method successfully solved the problems of location errors resulting from measured deviations of velocity as well as the existence and multiplicity of solutions induced by calculations of square roots in existed close-form methods.

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

NASA Astrophysics Data System (ADS)

Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu

2017-03-01

To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Tangle-Free Mesh Motion for Ablation Simulations

NASA Technical Reports Server (NTRS)

Droba, Justin

2016-01-01

Problems involving mesh motion-which should not be mistakenly associated with moving mesh methods, a class of adaptive mesh redistribution techniques-are of critical importance in numerical simulations of the thermal response of melting and ablative materials. Ablation is the process by which material vaporizes or otherwise erodes due to strong heating. Accurate modeling of such materials is of the utmost importance in design of passive thermal protection systems ("heatshields") for spacecraft, the layer of the vehicle that ensures survival of crew and craft during re-entry. In an explicit mesh motion approach, a complete thermal solve is first performed. Afterwards, the thermal response is used to determine surface recession rates. These values are then used to generate boundary conditions for an a posteriori correction designed to update the location of the mesh nodes. Most often, linear elastic or biharmonic equations are used to model this material response, traditionally in a finite element framework so that complex geometries can be simulated. A simple scheme for moving the boundary nodes involves receding along the surface normals. However, for all but the simplest problem geometries, evolution in time following such a scheme will eventually bring the mesh to intersect and "tangle" with itself, inducing failure. This presentation demonstrates a comprehensive and sophisticated scheme that analyzes the local geometry of each node with help from user-provided clues to eliminate the tangle and enable simulations on a wide-class of difficult problem geometries. The method developed is demonstrated for linear elastic equations but is general enough that it may be adapted to other modeling equations. The presentation will explicate the inner workings of the tangle-free mesh motion algorithm for both two and three-dimensional meshes. It will show abstract examples of the method's success, including a verification problem that demonstrates its accuracy and correctness. The focus of the presentation will be on the algorithm; specifics on how the techniques may be used in spacecraft design will be not discussed.

Theoretical study of phonon dispersion, elastic, mechanical and thermodynamic properties of barium chalcogenides

NASA Astrophysics Data System (ADS)

Musari, A. A.; Orukombo, S. A.

2018-03-01

Barium chalcogenides are known for their high-technological importance and great scientific interest. Detailed studies of their elastic, mechanical, dynamical and thermodynamic properties were carried out using density functional theory and plane-wave pseudo potential method within the generalized gradient approximation. The optimized lattice constants were in good agreement when compared with experimental data. The independent elastic constants, calculated from a linear fit of the computed stress-strain function, were used to determine the Young’s modulus (E), bulk modulus (B), shear modulus (G), Poisson’s ratio (σ) and Zener’s anisotropy factor (A). Also, the Debye temperature and sound velocities for barium chalcogenides were estimated from the three independent elastic constants. The calculations of phonon dispersion showed that there are no negative frequencies throughout the Brillouin zone. Hence barium chalcogenides have dynamically stable NaCl-type crystal structure. Finally, their thermodynamic properties were calculated in the temperature range of 0-1000 K and their constant-volume specific heat capacities at room-temperature were reported.

Second order Method for Solving 3D Elasticity Equations with Complex Interfaces

PubMed Central

Wang, Bao; Xia, Kelin; Wei, Guo-Wei

2015-01-01

Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The solution of three dimensional (3D) elasticity interface problems is significantly more difficult than that of elliptic counterparts due to the coupled vector components and cross derivatives in the governing elasticity equation. This work introduces the matched interface and boundary (MIB) method for solving 3D elasticity interface problems. The proposed MIB elasticity interface scheme utilizes fictitious values on irregular grid points near the material interface to replace function values in the discretization so that the elasticity equation can be discretized using the standard finite difference schemes as if there were no material interface. The interface jump conditions are rigorously enforced on the intersecting points between the interface and the mesh lines. Such an enforcement determines the fictitious values. A number of new techniques has been developed to construct efficient MIB elasticity interface schemes for dealing with cross derivative in coupled governing equations. The proposed method is extensively validated over both weak and strong discontinuity of the solution, both piecewise constant and position-dependent material parameters, both smooth and nonsmooth interface geometries, and both small and large contrasts in the Poisson’s ratio and shear modulus across the interface. Numerical experiments indicate that the present MIB method is of second order convergence in both L∞ and L2 error norms for handling arbitrarily complex interfaces, including biomolecular surfaces. To our best knowledge, this is the first elasticity interface method that is able to deliver the second convergence for the molecular surfaces of proteins.. PMID:25914422

An Easy Way to One-Dimensional Elastic Collisions

ERIC Educational Resources Information Center

Sztrajman, Jorge; Sztrajman, Alejandro

2017-01-01

The aim of this paper is to propose a method for solving head-on elastic collisions, without algebraic complications, to emphasize the use of the fundamental conservations laws. Head-on elastic collisions are treated in many physics textbooks as examples of conservation of momentum and kinetic energy.

Probabilistic finite elements for transient analysis in nonlinear continua

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

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.

Competing effects of particle and medium inertia on particle diffusion in viscoelastic materials, and their ramifications for passive microrheology.

PubMed

Indei, Tsutomu; Schieber, Jay D; Córdoba, Andrés

2012-04-01

We analyze the appropriate form for the generalized Stokes-Einstein relation (GSER) for viscoelastic solids and fluids when bead inertia and medium inertia are taken into account, which we call the inertial GSER. It was previously shown for Maxwell fluids that the Basset (or Boussinesq) force arising from medium inertia can act purely dissipatively at high frequencies, where elasticity of the medium is dominant. In order to elucidate the cause of this counterintuitive result, we consider Brownian motion in a purely elastic solid where ordinary Stokes-type dissipation is not possible. The fluctuation-dissipation theorem requires the presence of a dissipative mechanism for the particle to experience fluctuating Brownian forces in a purely elastic solid. We show that the mechanism for such dissipation arises from the radiation of elastic waves toward the system boundaries. The frictional force associated with this mechanism is the Basset force, and it exists only when medium inertia is taken into consideration in the analysis of such a system. We consider first a one-dimensional harmonic lattice where all terms in the generalized Langevin equation--i.e., the elastic term, the memory kernel, and Brownian forces-can be found analytically from projection-operator methods. We show that the dissipation is purely from radiation of elastic waves. A similar analysis is made on a particle in a continuum, three-dimensional purely elastic solid, where the memory kernel is determined from continuum mechanics. Again, dissipation arises only from radiation of elastic shear waves toward infinite boundaries when medium inertia is taken into account. If the medium is a viscoelastic solid, Stokes-type dissipation is possible in addition to radiational dissipation so that the wave decays at the penetration depth. Inertial motion of the bead couples with the elasticity of the viscoelastic material, resulting in a possible resonant oscillation of the mean-square displacement (MSD) of the bead. On the other hand, medium inertia (the Basset force) tends to attenuate the oscillations by the dissipation mechanism described above. Thus competition between bead inertia and medium inertia determines whether or not the MSD oscillates. We find that, if the medium density is larger than 4/7 of the bead density, the Basset damping will suppress oscillations in the MSD; this criterion is sufficient but not necessary to present oscillations.

Mechanical charactization of sonar window materials

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

DeTeresa, S.J.; Groves, S.E.; Harwood, P.J.

1996-03-25

The three-dimensional mechanical behavior of thick Spectra/epoxy sonar window materials containing various special materials is summarized in this report. Three different materials, which were fabricated by two companies known as `A` and `B` were received from the Naval Warfare Center. The three materials designated `A with microspheres (A micron),` `A without microspheres (A),` and `B` were measured for all properties. The total number of tests was reduced through the assumption that the two orthogonal, in-place directions were identical. Consequently, these materials should have only six independent elastic variables. The measured constants and strengths are given.

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

DOE PAGES

Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

2015-01-01

We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

Teaching veterinary obstetrics using three-dimensional animation technology.

PubMed

Scherzer, Jakob; Buchanan, M Flint; Moore, James N; White, Susan L

2010-01-01

In this three-year study, test scores for students taught veterinary obstetrics in a classroom setting with either traditional media (photographs, text, and two-dimensional graphical presentations) were compared with those for students taught by incorporating three-dimensional (3D) media (linear animations and interactive QuickTime Virtual Reality models) into the classroom lectures. Incorporation of the 3D animations and interactive models significantly increased students' scores on essay questions designed to assess their comprehension of the subject matter. This approach to education may help to better prepare students for dealing with obstetrical cases during their final clinical year and after graduation.

The three-dimensional compressible flow in a radial inflow turbine scroll

NASA Technical Reports Server (NTRS)

Hamed, A.; Tabakoff, W.; Malak, M.

1984-01-01

This work presents the results of an analytical study and an experimental investigation of the three-dimensional flow in a turbine scroll. The finite element method is used in the iterative numerical solution of the locally linearized governing equations for the three-dimensional velocity potential field. The results of the numerical computations are compared with the experimental measurements in the scroll cross sections, which were obtained using laser Doppler velocimetry and hot wire techniques. The results of the computations show a variation in the flow conditions around the rotor periphery which was found to depend on the scroll geometry.