Science.gov

Sample records for finite strain elasticity

  1. Finite strain crack tip fields in soft incompressible elastic solids.

    PubMed

    Krishnan, Venkat R; Hui, Chung Yuen; Long, Rong

    2008-12-16

    A finite element model (FEM) is used to study the behavior of the large deformation field near the tip of a crack in a soft incompressible plane stress fracture specimen loaded in mode I. Results are obtained for the case of a neo-Hookean solid (ideal rubber) and a hyperelastic solid with exponentially hardening behavior. In contrast to the predictions of linear elastic fracture mechanics (LEFM), the near tip stress fields are dominated by the opening stress which shows a 1/R singularity for the neo-Hookean material and a -1/(R ln R) singularity for the exponential hardening solid. We found very similar qualitative behavior in the near tip stress fields despite the very large difference in strain hardening behavior of the two material models. Our result shows that the near tip opening stress is controlled by the far field energy release rate for large applied loads. PMID:19053624

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

    NASA Technical Reports Server (NTRS)

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

    1979-01-01

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

  3. Explicit mixed strain-displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

    NASA Astrophysics Data System (ADS)

    Cervera, M.; Lafontaine, N.; Rossi, R.; Chiumenti, M.

    2016-06-01

    This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P1P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.

  4. Explicit mixed strain-displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

    NASA Astrophysics Data System (ADS)

    Cervera, M.; Lafontaine, N.; Rossi, R.; Chiumenti, M.

    2016-09-01

    This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields ( P1 P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.

  5. Homogenized mechanical properties of auxetic composite materials in finite-strain elasticity

    NASA Astrophysics Data System (ADS)

    Kochmann, Dennis M.; Venturini, Gabriela N.

    2013-08-01

    Careful microstructural design can result in materials with counterintuitive effective (macroscale) mechanical properties such as a negative Poisson’s ratio, commonly referred to as auxetic behavior. One specific approach to achieving auxetic behavior is to elastically connect structural elements with rotational degrees of freedom to result in elastic structures that unfold under uniaxial loading in specific directions, thereby giving rise to bi- or triaxial expansion, i.e. auxetic behavior (transverse expansion under uniaxial extension). This concept has been applied successfully to elastically coupled two-dimensional rigid rotational elements (such as rotating rectangles and triangles) which exhibit a negative effective in-plane Poisson’s ratio under uniaxial (ex)tension. Here, we adopt this fundamental design principle but take it to the next level by achieving auxetic behavior in finitely strained composites made of stiff inclusions in a hyperelastic matrix, and we study the resulting elastic properties under in-plane strain by numerical homogenization. Our results highlight the emergence of auxetic behavior based on geometric arrangement and properties of the base material and demonstrate a path towards simple inclusion-matrix composites with auxetic behavior.

  6. A staggered approach for the coupling of Cahn-Hilliard type diffusion and finite strain elasticity

    NASA Astrophysics Data System (ADS)

    Areias, P.; Samaniego, E.; Rabczuk, T.

    2016-02-01

    We develop an algorithm and computational implementation for simulation of problems that combine Cahn-Hilliard type diffusion with finite strain elasticity. We have in mind applications such as the electro-chemo-mechanics of lithium ion (Li-ion) batteries. We concentrate on basic computational aspects. A staggered algorithm is proposed for the coupled multi-field model. For the diffusion problem, the fourth order differential equation is replaced by a system of second order equations to deal with the issue of the regularity required for the approximation spaces. Low order finite elements are used for discretization in space of the involved fields (displacement, concentration, nonlocal concentration). Three (both 2D and 3D) extensively worked numerical examples show the capabilities of our approach for the representation of (i) phase separation, (ii) the effect of concentration in deformation and stress, (iii) the effect of strain in concentration, and (iv) lithiation. We analyze convergence with respect to spatial and time discretization and found that very good results are achievable using both a staggered scheme and approximated strain interpolation.

  7. Elastic strain reduction of finite germanium(x) silicon(1-x)/silicon structures

    NASA Astrophysics Data System (ADS)

    U'Ren, Gregory David

    The focus of this dissertation is a rigorous examination the elastic, intrinsic behavior of stress/strain for epitaxial Si1-xGe x/Si (100) structures having finite dimensions. Existing models predict that the behavior is governed primarily by geometry, which can have a profound effect should the ratio of half-width to height (l/h) be less than 50. Two main aspects of existing theories were pressed: first, the role of geometry for a fixed Si1-xGex composition and therefore strain (epsilon = 0.42%) and second, the role of misfit stress for a fixed l/b ratio of 0.5. Strict control of the fabrication process necessitated selective epitaxial growth via gas-source molecular beam epitaxy. Though experimental combinations of various thickness (50, 100, 140, and 200 nm) and variable pitch (0.09-25 mum) a wide range of l/b values was obtained (0.5-500). As the selectively grown structures are arranged into a periodic array, where the period is repeated over a large distance (mm), in addition to dynamical diffraction, Fraunhoffer diffraction was also observed. These two complementary mechanisms of diffraction were used to determine the stress distribution within these structures. Ensemble with transmission electron microscopy, a qualitative assessment of elastic strain reduction mechanisms--local curvature effects and tangential forces--was possible. The main conclusions of this dissertation are as follows: (A) An analytical reciprocal space construction was developed to facilitate the interpretation of experimental x-ray diffraction data. (B) As a corollary, arbitrary positioning and movement in reciprocal space are described, which in practice is applied to capturing scattered intensity parallel to the surface. (C) Facet growth in SiGe selective epitaxy was investigated. One key result is the persistence of a {113} facet with increasing thickness, as the {111} facet is anticipated. (D) In examining the role of geometry, elastic lattice distortions were only observed for l

  8. On constitutive relations at finite strain - Hypo-elasticity and elasto-plasticity with isotropic or kinematic hardening

    NASA Technical Reports Server (NTRS)

    Atluri, S. N.

    1984-01-01

    Nagtegaal and de Jong (1982) have studied stresses generated by simple finite shear in the case of elastic-plastic and rigid-plastic materials which exhibit anisotropic hardening. They reported that the shear stress is oscillatory in time. It was found that the occurrence of such an 'anomaly' is not restricted to anisotropic plasticity. Similar behavior in finite shear may result even in the case of hypoelasticity and classical isotropic hardening plasticity theory. The present investigation is concerned with the central problem of 'generalizing' with respect to the finite strain case, taking into account the constitutive relations of infinitesimal strain theories of classical plasticity with isotropic or kinematic hardening. The problem of hypoelasticity is also considered. It is shown that current controversies surrounding the choice of stress rate in the finite-strain generalizations of the constitutive relations and the anomalies surrounding kinematic hardening plasticity theory are easily resolvable.

  9. Beyond linear elasticity: jammed solids at finite shear strain and rate.

    PubMed

    Boschan, Julia; Vågberg, Daniel; Somfai, Ellák; Tighe, Brian P

    2016-06-28

    The shear response of soft solids can be modeled with linear elasticity, provided the forcing is slow and weak. Both of these approximations must break down when the material loses rigidity, such as in foams and emulsions at their (un)jamming point - suggesting that the window of linear elastic response near jamming is exceedingly narrow. Yet precisely when and how this breakdown occurs remains unclear. To answer these questions, we perform computer simulations of stress relaxation and shear start-up tests in athermal soft sphere packings, the canonical model for jamming. By systematically varying the strain amplitude, strain rate, distance to jamming, and system size, we identify characteristic strain and time scales that quantify how and when the window of linear elasticity closes, and relate these scales to changes in the microscopic contact network. PMID:27212139

  10. Local strain redistribution corrections for a simplified inelastic analysis procedure based on an elastic finite-element analysis

    NASA Technical Reports Server (NTRS)

    Kaufman, A.; Hwang, S. Y.

    1985-01-01

    Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction proposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite-element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure predicts stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load-cycled problems. Neuber-type corrections were derived and incorporated in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was used on a mechanically load-cycled benchmark notched-plate problem. The predicted material response agrees well with the nonlinear finite-element solutions for the problem. The simplified analysis computer program was 0.3% of the central processor unit time required for a nonlinear finite-element analysis.

  11. A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains

    NASA Astrophysics Data System (ADS)

    Wang, Z.; Rudraraju, S.; Garikipati, K.

    2016-09-01

    We present a field formulation for defects that draws from the classical representation of the cores as force dipoles. We write these dipoles as singular distributions. Exploiting the key insight that the variational setting is the only appropriate one for the theory of distributions, we arrive at universally applicable weak forms for defects in nonlinear elasticity. Remarkably, the standard, Galerkin finite element method yields numerical solutions for the elastic fields of defects that, when parameterized suitably, match very well with classical, linearized elasticity solutions. The true potential of our approach, however, lies in its easy extension to generate solutions to elastic fields of defects in the regime of nonlinear elasticity, and even more notably for Toupin's theory of gradient elasticity at finite strains (Toupin Arch. Ration. Mech. Anal., 11 (1962) 385). In computing these solutions we adopt recent numerical work on an isogeometric analytic framework that enabled the first three-dimensional solutions to general boundary value problems of Toupin's theory (Rudraraju et al. Comput. Methods Appl. Mech. Eng., 278 (2014) 705). We first present exhaustive solutions to point defects, edge and screw dislocations, and a study on the energetics of interacting dislocations. Then, to demonstrate the generality and potential of our treatment, we apply it to other complex dislocation configurations, including loops and low-angle grain boundaries.

  12. A model for a constrained, finitely deforming, elastic solid with rotation gradient dependent strain energy, and its specialization to von Kármán plates and beams

    NASA Astrophysics Data System (ADS)

    Srinivasa, A. R.; Reddy, J. N.

    2013-03-01

    The aim of this paper is to develop the governing equations for a fully constrained finitely deforming hyperelastic Cosserat continuum where the directors are constrained to rotate with the body rotation. This is the generalization of small deformation couple stress theories and would be useful for developing mathematical models for an elastic material with embedded stiff short fibers or inclusions (e.g., materials with carbon nanotubes or nematic elastomers, cellular materials with oriented hard phases, open cell foams, and other similar materials), that account for certain longer range interactions. The theory is developed as a limiting case of a regular Cosserat elastic material where the directors are allowed to rotate freely by considering the case of a high "rotational mismatch energy". The theory is developed using the formalism of Lagrangian mechanics, with the static case being based on Castigliano's first theorem. By considering the stretch U and the rotation R as additional independent variables and using the polar decomposition theorem as an additional constraint equation, we obtain the governing and as well as the boundary conditions for finite deformations. The resulting equations are further specialized for plane strain and axisymmetric finite deformations, deformations of beams and plates with small strain and moderate rotation, and for small deformation theories. We also show that the boundary conditions for this theory involve "surface tension" like terms due to the higher gradients in the strain energy function. For beams and plates, the rotational gradient dependent strain energy does not require additional variables (unlike Cosserat theories) and additional differential equations; nor do they raise the order of the differential equations, thus allowing us to include a material length scale dependent response at no extra "computational cost" even for finite deformation beam/plate theories

  13. Finite Element Analysis of 2-D Elastic Contacts Involving FGMs

    NASA Astrophysics Data System (ADS)

    Abhilash, M. N.; Murthy, H.

    2014-05-01

    The response of elastic indenters in contact with Functionally Graded Material (FGM) coated homogeneous elastic half space has been presented in the current paper. Finite element analysis has been used due to its ability to handle complex geometry, material, and boundary conditions. Indenters of different typical surface profiles have been considered and the problem has been idealized as a two-dimensional (2D) plane strain problem considering only normal loads. Initially, indenters were considered to be rigid and the results were validated with the solutions presented in the literature. The analysis has then been extended to the case of elastic indenters on FGM-coated half spaces and the results are discussed.

  14. Asymmetric quadrilateral shell elements for finite strains

    NASA Astrophysics Data System (ADS)

    Areias, P.; Dias-da-Costa, D.; Pires, E. B.; Van Goethem, N.

    2013-07-01

    Very good results in infinitesimal and finite strain analysis of shells are achieved by combining either the enhanced-metric technique or the selective-reduced integration for the in-plane shear energy and an assumed natural strain technique (ANS) in a non-symmetric Petrov-Galerkin arrangement which complies with the patch-test. A recovery of the original Wilson incompatible mode element is shown for the trial functions in the in-plane components. As a beneficial side-effect, Newton-Raphson convergence behavior for non-linear problems is improved with respect to symmetric formulations. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh accuracy is higher than with symmetric formulations. Classical test functions with assumed-metric components are required for compatibility reasons. Verification tests are performed with advantageous comparisons being observed in all of them. Applications to large displacement elasticity and finite strain plasticity are shown with both low sensitivity to mesh distortion and (relatively) high accuracy. A equilibrium-consistent (and consistently linearized) updated-Lagrangian algorithm is proposed and tested. Concerning the time-step dependency, it was found that the consistent updated-Lagrangian algorithm is nearly time-step independent and can replace the multiplicative plasticity approach if only moderate elastic strains are present, as is the case of most metals.

  15. Cyclic creep analysis from elastic finite-element solutions

    NASA Technical Reports Server (NTRS)

    Kaufman, A.; Hwang, S. Y.

    1986-01-01

    A uniaxial approach was developed for calculating cyclic creep and stress relaxation at the critical location of a structure subjected to cyclic thermomechanical loading. This approach was incorporated into a simplified analytical procedure for predicting the stress-strain history at a crack initiation site for life prediction purposes. An elastic finite-element solution for the problem was used as input for the simplified procedure. The creep analysis includes a self-adaptive time incrementing scheme. Cumulative creep is the sum of the initial creep, the recovery from the stress relaxation and the incremental creep. The simplified analysis was exercised for four cases involving a benchmark notched plate problem. Comparisons were made with elastic-plastic-creep solutions for these cases using the MARC nonlinear finite-element computer code.

  16. Finite strain discrete dislocation plasticity in a total Lagrangian setting

    NASA Astrophysics Data System (ADS)

    Irani, N.; Remmers, J. J. C.; Deshpande, V. S.

    2015-10-01

    We present two total Lagrangian formulations for finite strain discrete dislocation plasticity wherein the discrete dislocations are presumed to be adequately represented by singular linear elastic fields thereby extending the superposition method of Van der Giessen and Needleman (1995) to finite strains. The finite deformation effects accounted for are (i) finite lattice rotations and (ii) shape changes due to slip. The two formulations presented differ in the fact that in the "smeared-slip" formulation the discontinuous displacement field is smeared using finite element shape functions while in the "discrete-slip" formulation the weak form of the equilibrium statement is written to account for the slip displacement discontinuity. Both these total Lagrangian formulations use a hyper-elastic constitutive model for lattice elasticity. This overcomes the issues of using singular dislocation fields in a hypo-elastic constitutive relation as encountered in the updated Lagrangian formulation of Deshpande et al. (2003). Predictions of these formulations are presented for the relatively simple problems of tension and compression of single crystals oriented for single slip. These results show that unlike in small-strain discrete dislocation plasticity, finite strain effects result in a size dependent tension/compression asymmetry. Moreover, both formulations give nearly identical predictions and thus we expect that the "smeared-slip" formulation is likely to be preferred due to its relative computational efficiency and simplicity.

  17. Thermodynamic stability in elastic systems: Hard spheres embedded in a finite spherical elastic solid.

    PubMed

    Solano-Altamirano, J M; Goldman, Saul

    2015-12-01

    We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another. PMID:26701708

  18. Finite-element formulations for problems of large elastic-plastic deformation

    NASA Technical Reports Server (NTRS)

    Mcmeeking, R. M.; Rice, J. R.

    1975-01-01

    An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventional finite element program, for 'small strain' elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. The paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.

  19. Elastic-plastic finite-element analyses of thermally cycled single-edge wedge specimens

    NASA Technical Reports Server (NTRS)

    Kaufman, A.

    1982-01-01

    Elastic-plastic stress-strain analyses were performed for single-edge wedge alloys subjected to thermal cycling in fluidized beds. Three cases (NASA TAZ-8A alloy under one cycling condition and 316 stainless steel alloy under two cycling conditions) were analyzed by using the MARC nonlinear, finite-element computer program. Elastic solutions from MARC showed good agreement with previously reported solutions that used the NASTRAN and ISO3DQ computer programs. The NASA TAZ-8A case exhibited no plastic strains, and the elastic and elastic-plastic analyses gave identical results. Elastic-plastic analyses of the 316 stainless steel alloy showed plastic strain reversal with a shift of the mean stresses in the compressive direction. The maximum equivalent total strain ranges for these cases were 13 to 22 percent greater than that calculated from elastic analyses.

  20. Elastic-plastic finite-element analyses of thermally cycled double-edge wedge specimens

    NASA Technical Reports Server (NTRS)

    Kaufman, A.; Hunt, L. E.

    1982-01-01

    Elastic-plastic stress-strain analyses were performed for double-edge wedge specimens subjected to thermal cycling in fluidized beds at 316 and 1088 C. Four cases involving different nickel-base alloys (IN 100, Mar M-200, NASA TAZ-8A, and Rene 80) were analyzed by using the MARC nonlinear, finite element computer program. Elastic solutions from MARC showed good agreement with previously reported solutions obtained by using the NASTRAN and ISO3DQ computer programs. Equivalent total strain ranges at the critical locations calculated by elastic analyses agreed within 3 percent with those calculated from elastic-plastic analyses. The elastic analyses always resulted in compressive mean stresses at the critical locations. However, elastic-plastic analyses showed tensile mean stresses for two of the four alloys and an increase in the compressive mean stress for the highest plastic strain case.

  1. Finite element formulations for problems of large elastic-plastic deformation

    NASA Technical Reports Server (NTRS)

    Mcmeeking, R. M.; Rice, J. R.

    1974-01-01

    An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials. The formulation is given in a manner which allows any conventional finite element program, for "small strain" elasticplastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. A unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures, and a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain.

  2. Finite Element Prediction of Sheet Forming Defects Using Elastic-Plastic, Damage and Localization Models

    NASA Astrophysics Data System (ADS)

    Haddag, Badis; Abed-Meraim, Farid; Balan, Tudor

    2007-05-01

    In this work, an advanced anisotropic elastic-plasticity model is combined with a damage model and a strain localization criterion in the aim to describe accurately the mechanical behavior of sheet metals. Large strain, fully three-dimensional, implicit time integration algorithms are developed for this model and implemented in the finite element code Abaqus. The resulting code is used to predict the strain localization limits as well as the springback after forming of sheet steels. The impact of strain-path dependent hardening models on the limit strains and on the amount of springback is addressed.

  3. Finite elastic-plastic deformation of polycrystalline metals

    NASA Technical Reports Server (NTRS)

    Iwakuma, T.; Nemat-Nasser, S.

    1984-01-01

    Applying Hill's self-consistent method to finite elastic-plastic deformations, the overall moduli of polycrystalline solids are estimated. The model predicts a Bauschinger effect, hardening, and formation of vertex or corner on the yield surface for both microscopically non-hardening and hardening crystals. The changes in the instantaneous moduli with deformation are examined, and their asymptotic behavior, especially in relation to possible localization of deformations, is discussed. An interesting conclusion is that small second-order quantities, such as shape changes of grains and residual stresses (measured relative to the crystal elastic moduli), have a first-order effect on the overall response, as they lead to a loss of the overall stability by localized deformation. The predicted incipience of localization for a uniaxial deformation in two dimensions depends on the initial yield strain, but the orientation of localization is slightly less than 45 deg with respect to the tensile direction, although the numerical instability makes it very difficult to estimate this direction accurately.

  4. 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.

  5. Models for elastic shells with incompatible strains

    PubMed Central

    Lewicka, Marta; Mahadevan, L.; Pakzad, Mohammad Reza

    2014-01-01

    The three-dimensional shapes of thin lamina, such as leaves, flowers, feathers, wings, etc., are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric given on the thin sheet as a function of location in the central plane and also across its thickness. The shape is then a consequence of elastic energy minimization on the frustrated geometrical object. Here, we provide a rigorous derivation of the asymptotic theories for shapes of residually strained thin lamina with non-trivial curvatures, i.e. growing elastic shells in both the weakly and strongly curved regimes, generalizing earlier results for the growth of nominally flat plates. The different theories are distinguished by the scaling of the mid-surface curvature relative to the inverse thickness and growth strain, and also allow us to generalize the classical Föppl–von Kármán energy to theories of prestrained shallow shells. PMID:24808750

  6. Tunable thermoelectric transport in nanomeshes via elastic strain engineering

    SciTech Connect

    Piccione, Brian; Gianola, Daniel S.

    2015-03-16

    Recent experimental explorations of silicon nanomeshes have shown that the unique metastructures exhibit reduced thermal conductivity while preserving bulk electrical conductivity via feature sizes between relevant phonon and electron mean free paths, aiding in the continued promise that nanometer-scale engineering may further enhance thermoelectric behavior. Here, we introduce a strategy for tuning thermoelectric transport phenomena in semiconductor nanomeshes via heterogeneous elastic strain engineering, using silicon as a model material for demonstration of the concept. By combining analytical models for electron mobility in uniformly stressed silicon with finite element analysis of strained silicon nanomeshes in a lumped physical model, we show that the nonuniform and multiaxial strain fields defined by the nanomesh geometry give rise to spatially varying band shifts and warping, which in aggregate accelerate electron transport along directions of applied stress. This allows for global electrical conductivity and Seebeck enhancements beyond those of homogenous samples under equivalent far-field stresses, ultimately increasing thermoelectric power factor nearly 50% over unstrained samples. The proposed concept and structures—generic to a wide class of materials with large dynamic ranges of elastic strain in nanoscale volumes—may enable a new pathway for active and tunable control of transport properties relevant to waste heat scavenging and thermal management.

  7. Tunable thermoelectric transport in nanomeshes via elastic strain engineering

    NASA Astrophysics Data System (ADS)

    Piccione, Brian; Gianola, Daniel S.

    2015-03-01

    Recent experimental explorations of silicon nanomeshes have shown that the unique metastructures exhibit reduced thermal conductivity while preserving bulk electrical conductivity via feature sizes between relevant phonon and electron mean free paths, aiding in the continued promise that nanometer-scale engineering may further enhance thermoelectric behavior. Here, we introduce a strategy for tuning thermoelectric transport phenomena in semiconductor nanomeshes via heterogeneous elastic strain engineering, using silicon as a model material for demonstration of the concept. By combining analytical models for electron mobility in uniformly stressed silicon with finite element analysis of strained silicon nanomeshes in a lumped physical model, we show that the nonuniform and multiaxial strain fields defined by the nanomesh geometry give rise to spatially varying band shifts and warping, which in aggregate accelerate electron transport along directions of applied stress. This allows for global electrical conductivity and Seebeck enhancements beyond those of homogenous samples under equivalent far-field stresses, ultimately increasing thermoelectric power factor nearly 50% over unstrained samples. The proposed concept and structures—generic to a wide class of materials with large dynamic ranges of elastic strain in nanoscale volumes—may enable a new pathway for active and tunable control of transport properties relevant to waste heat scavenging and thermal management.

  8. Elastic scattering by finitely many point-like obstacles

    NASA Astrophysics Data System (ADS)

    Hu, Guanghui; Sini, Mourad

    2013-04-01

    This paper is concerned with the time-harmonic elastic scattering by a finite number N of point-like obstacles in {{R}}^n (n = 2, 3). We analyze the N-point interactions model in elasticity and derive the associated Green's tensor (integral kernel) in terms of the point positions and the scattering coefficients attached to them, following the approach in quantum mechanics for modeling N-particle interactions. In particular, explicit expressions are given for the scattered near and far fields corresponding to elastic plane waves or point-source incidences. As a result, we rigorously justify the Foldy method for modeling the multiple scattering by finitely many point-like obstacles for the Lamé model. The arguments are based on the Fourier analysis and the Weinstein-Aronszajn inversion formula of the resolvent for the finite rank perturbations of closed operators in Hilbert spaces.

  9. Finite gradient elasticity and plasticity: a constitutive mechanical framework

    NASA Astrophysics Data System (ADS)

    Bertram, Albrecht

    2015-11-01

    Following a suggestion by Forest and Sievert (Acta Mech 160:71-111, 2003), a constitutive frame for a general gradient elastoplasticity for finite deformations is established. The basic assumptions are the principle of Euclidean invariance and the isomorphy of the elastic ranges. Both the elastic and the plastic laws include the first and the second deformation gradient. The starting point is an objective expression for the stress power.

  10. Elastic-plastic finite element analysis-to-test correlation for structures subjected to dynamic loading

    SciTech Connect

    Hodge, S.C.; Minicucci, J.M.

    1997-11-01

    A test program was undertaken to demonstrate the ability of elastic-plastic finite element methods to predict dynamic inelastic response for simple structural members. Cantilever and fixed-beam specimens were tested to levels that produced plastic straining in the range of 2.0% and to 3.0% and permanent sets. Acceleration, strain, and displacement data were recorded for use in analytical correlation. Correlation analyses were performed using the ABAQUS finite element code. Results of the correlation show that current elastic-plastic analysis techniques accurately capture dynamic inelastic response (displacement, acceleration) due to rapidly applied dynamic loading. Peak elastic and inelastic surface strains are accurately predicted. To accurately capture inelastic straining near connections, a solid model, including fillet welds, is necessary. The hardening models currently available in the ABAQUS code (isotropic, kinematic) do not accurately capture inelastic strain reversals caused by specimen rebound. Analyses performed consistently underpredicted the peak strain level of the first inelastic reversal and the rebound deflection and overpredicted the permanent set of structures experiencing inelastic rebound. Based on these findings, an improved hardening model is being implemented in the ABAQUS code by the developers. The intent of this model upgrade is to improve the ability of the program to capture inelastic strain reversals and to predict permanent sets.

  11. Finite element methods for nonlinear elastostatic problems in rubber elasticity

    NASA Technical Reports Server (NTRS)

    Oden, J. T.; Becker, E. B.; Miller, T. H.; Endo, T.; Pires, E. B.

    1983-01-01

    A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.

  12. Finite element analysis of fluid-filled elastic piping systems

    NASA Technical Reports Server (NTRS)

    Everstine, G. C.; Marcus, M. S.; Quezon, A. J.

    1983-01-01

    Two finite element procedures are described for predicting the dynamic response of general 3-D fluid-filled elastic piping systems. The first approach, a low frequency procedure, models each straight pipe or elbow as a sequence of beams. The contained fluid is modeled as a separate coincident sequence axial members (rods) which are tied to the pipe in the lateral direction. The model includes the pipe hoop strain correction to the fluid sound speed and the flexibility factor correction to the elbow flexibility. The second modeling approach, an intermediate frequency procedure, follows generally the original Zienkiewicz-Newton scheme for coupled fluid-structure problems except that the velocity potential is used as the fundamental fluid unknown to symmetrize the coefficient matrices. From comparisons of the beam model predictions to both experimental data and the 3-D model, the beam model is validated for frequencies up to about two-thirds of the lowest fluid-filled labor pipe mode. Accurate elbow flexibility factors are seen to be crucial for effective beam modeling of piping systems.

  13. Influence of thermal residual stresses on the elastic phase-strain

    SciTech Connect

    Shi, N.; Bourke, M.A.M.; Goldstone, J.A.

    1996-04-01

    The development of elastic lattice phase strains in a 15 vol. pct TiC particulate reinforced 2219-T6 Al composite was modeled as a function of tensile uniaxial loading by finite element method (FEM). In the relationship of applied stress vs. elastic lattice phase strain, the slopes vary with the applied load even before the macroscopic yielding. The slopes for the phase-strain perpendicular to loading follow nonmonotonic changes with loading, while, in the direction parallel to loading, the slopes change monotonically with the applied load. In this investigation, we have demonstrated via FEM that thermal residual stresses from thermal expansion mismatch between phases affect initiation of matrix plasticity. And the differences in the matrix plasticity initiation influence the internal stress distribution. The changes in the slope are dictated by the internal stress transfer between phases. FEM models with and without thermal history show significant differences in the response of elastic strain component, a mechanics equivalent of the lattice elastic strain. Agreement with experiment can only be obtained by including the thermal history. From a simple elasto-plastic spring model we are able to demonstrate that, with matrix plasticity propagating as predicted by FEM, the elastic strain component responds similarly to the more rigorous numerical predictions, suggesting that the morphology of elastic strain evolution is dictated by the development of matrix plasticity.

  14. Constitutive modeling and computational implementation for finite strain plasticity

    NASA Technical Reports Server (NTRS)

    Reed, K. W.; Atluri, S. N.

    1985-01-01

    This paper describes a simple alternate approach to the difficult problem of modeling material behavior. Starting from a general representation for a rate-tpe constitutive equation, it is shown by example how sets of test data may be used to derive restrictions on the scalar functions appearing in the representation. It is not possible to determine these functions from experimental data, but the aforementioned restrictions serve as a guide in their eventual definition. The implications are examined for hypo-elastic, isotropically hardening plastic, and kinematically hardening plastic materials. A simple model for the evolution of the 'back-stress,' in a kinematic-hardening plasticity theory, that is entirely analogous to a hypoelastic stress-strain relation is postulated and examined in detail in modeling finitely plastic tension-torsion test. The implementation of rate-type material models in finite element algorithms is also discussed.

  15. Automated Finite Element Analysis of Elastically-Tailored Plates

    NASA Technical Reports Server (NTRS)

    Jegley, Dawn C. (Technical Monitor); Tatting, Brian F.; Guerdal, Zafer

    2003-01-01

    A procedure for analyzing and designing elastically tailored composite laminates using the STAGS finite element solver has been presented. The methodology used to produce the elastic tailoring, namely computer-controlled steering of unidirectionally reinforced composite material tows, has been reduced to a handful of design parameters along with a selection of construction methods. The generality of the tow-steered ply definition provides the user a wide variety of options for laminate design, which can be automatically incorporated with any finite element model that is composed of STAGS shell elements. Furthermore, the variable stiffness parameterization is formulated so that manufacturability can be assessed during the design process, plus new ideas using tow steering concepts can be easily integrated within the general framework of the elastic tailoring definitions. Details for the necessary implementation of the tow-steering definitions within the STAGS hierarchy is provided, and the format of the ply definitions is discussed in detail to provide easy access to the elastic tailoring choices. Integration of the automated STAGS solver with laminate design software has been demonstrated, so that the large design space generated by the tow-steering options can be traversed effectively. Several design problems are presented which confirm the usefulness of the design tool as well as further establish the potential of tow-steered plies for laminate design.

  16. Finite-temperature elasticity of fcc Al: Atomistic simulations and ultrasonic measurements

    NASA Astrophysics Data System (ADS)

    Pham, Hieu H.; Williams, Michael E.; Mahaffey, Patrick; Radovic, Miladin; Arroyave, Raymundo; Cagin, Tahir

    2011-08-01

    Though not very often, there are some cases in the literature where discrepancies exist in the temperature dependence of elastic constants of materials. A particular example of this case is the behavior of C12 coefficient of a simple metal, aluminum. In this paper we attempt to provide insight into various contributions to temperature dependence in elastic properties by investigating the thermoelastic properties of fcc aluminum as a function of temperature through the use of two computational techniques and experiments. First, ab initio calculations based on density functional theory (DFT) are used in combination with quasiharmonic theory to calculate the elastic constants at finite temperatures through a strain-free energy approach. Molecular dynamics (MD) calculations using tight-binding potentials are then used to extract the elastic constants through a fluctuation-based formalism. Through this dynamic approach, the different contributions (Born, kinetic, and stress fluctuations) to the elastic constants are isolated and the underlying physical basis for the observed thermally induced softening is elucidated. The two approaches are then used to shed light on the relatively large discrepancies in the reported temperature dependence of the elastic constants of fcc aluminum. Finally, the polycrystalline elastic constants (and their temperature dependence) of fcc aluminum are determined using resonant ultrasound spectroscopy (RUS) and compared to previously published data as well as the atomistic calculations performed in this work.

  17. Rolling motion of an elastic cylinder induced by elastic strain gradients

    NASA Astrophysics Data System (ADS)

    Chen, Lei; Chen, Shaohua

    2014-10-01

    Recent experiment shows that an elastic strain gradient field can be utilized to transport spherical particles on a stretchable substrate by rolling, inspired by which a generalized plane-strain Johnson-Kendall-Roberts model is developed in this paper in order to verify possible rolling of an elastic cylinder adhering on an elastic substrate subject to a strain gradient. With the help of contact mechanics, closed form solutions of interface tractions, stress intensity factors, and corresponding energy release rates in the plane-strain contact model are obtained, based on which a possible rolling motion of an elastic cylinder induced by strain gradients is found and the criterion for the initiation of rolling is established. The theoretical prediction is consistent well with the existing experimental observation. The result should be helpful for understanding biological transport mechanisms through muscle contractions and the design of transport systems with strain gradient.

  18. Solution of elastic-plastic stress analysis problems by the P-version of the finite element method

    SciTech Connect

    Szabo, B.A.; Holzer, S.M.; Actis, R.L.

    1995-12-31

    The solution of small-strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus of the paper. Numerical examples, which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors, are presented.

  19. Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

    NASA Technical Reports Server (NTRS)

    Szabo, Barna A.; Actis, Ricardo L.; Holzer, Stefan M.

    1993-01-01

    The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

  20. Development of the average lattice phase-strain and global elastic macro-strain in Al/TiC composites

    SciTech Connect

    Shi, N.; Bourke, M.A.M.; Goldstone, J.A.; Allison, J.E.

    1994-02-01

    The development of elastic lattice phase strains and global elastic macro-strain in a 15 vol% TiC particle reinforced 2219-T6 Al composite was modeled by finite element method (FEM) as a function of tensile uniaxial loading. The numerical predictions are in excellent agreement with strain measurements at a spallation neutron source. Results from the measurements and modeling indicate that the lattice phase-strains go through a ``zigzag`` increase with the applied load in the direction perpendicular to the load, while the changes of slope in the parallel direction are monotonic. FEM results further showed that it is essential to consider the effect of thermal residual stresses (TRS) in understanding this anomalous behavior. It was demonstrated that, due to TRS, the site of matrix plastic flow initiation changed. On the other hand, the changes of slope of the elastic global macrostrain is solely determined by the phase-stress partition in the composite. An analytical calculation showed that both experimental and numerical slope changes during elastic global strain response under loading could be accurately reproduced by accounting for the changes of phase-stress ratio between the matrix and the matrix.

  1. Elastic finite-difference method for irregular grids

    SciTech Connect

    Oprsal, I.; Zahradnik, J.

    1999-01-01

    Finite-difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low-velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero-valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fulfills the free-surface conditions is given. Numerical validation is performed through comparison with independent methods, comparing FD with explicitly prescribed boundary conditions and finite elements. Memory and computing time needed in the studied models was only about 10 to 40% of that employing regular square grids of equal accuracy. A practical example of a synthetic seismic section, showing clear signatures of a coal seam and cavity, is presented. The method can be extended to three dimensions.

  2. Stress-dependent finite growth in soft elastic tissues.

    PubMed

    Rodriguez, E K; Hoger, A; McCulloch, A D

    1994-04-01

    Growth and remodeling in tissues may be modulated by mechanical factors such as stress. For example, in cardiac hypertrophy, alterations in wall stress arising from changes in mechanical loading lead to cardiac growth and remodeling. A general continuum formulation for finite volumetric growth in soft elastic tissues is therefore proposed. The shape change of an unloaded tissue during growth is described by a mapping analogous to the deformation gradient tensor. This mapping is decomposed into a transformation of the local zero-stress reference state and an accompanying elastic deformation that ensures the compatibility of the total growth deformation. Residual stress arises from this elastic deformation. Hence, a complete kinematic formulation for growth in general requires a knowledge of the constitutive law for stress in the tissue. Since growth may in turn be affected by stress in the tissue, a general form for the stress-dependent growth law is proposed as a relation between the symmetric growth-rate tensor and the stress tensor. With a thick-walled hollow cylinder of incompressible, isotropic hyperelastic material as an example, the mechanics of left ventricular hypertrophy are investigated. The results show that transmurally uniform pure circumferential growth, which may be similar to eccentric ventricular hypertrophy, changes the state of residual stress in the heart wall. A model of axially loaded bone is used to test a simple stress-dependent growth law in which growth rate depends on the difference between the stress due to loading and a predetermined growth equilibrium stress. PMID:8188726

  3. Finite element investigation of thermo-elastic and thermo-plastic consolidation

    SciTech Connect

    Aboustit, B.L.

    1984-01-01

    The transient response of saturated continua due to thermal as well as mechanical loads is investigated in both elastic and plastic ranges. When the two phase saturated media are subjected to thermomechanical loading, the energy equation is coupled with the mass flow and solid deformation equations resulting in the initial boundary value problem of thermal consolidation. The solid behavior may be assumed to be either elastic or elastoplastic leading to the associated theories of thermoelastic and thermoelastoplastic consolidation. The governing equations for the quasi-static infinitesimal theory of thermoelastic consolidation are developed by using the theory of mixtures. An equivalent variational principle is developed along with associated finite element formulations. Two isoparametric elements of the composite type are employed for the spatial discretization. The formulation is extended to the plastic ranges by modeling the solid phase as an elastic work hardening material with an associated flow rule. An incremental iterative scheme is developed to solve this nonlinear transient problem. Several special purpose computer codes are developed for evaluating the isothermal, thermal, elastic and elastoplastic plane strain consolidation responses. These codes have been evaluated against limiting cases available in the literature. The effects of temporal and spatial interpolation schemes are investigated for one-dimensional thermoelastic consolidation problems. An application dealing with a plane strain underground coal gasification problem is also presented.

  4. Coupling finite and boundary element methods for 2-D elasticity problems

    NASA Technical Reports Server (NTRS)

    Krishnamurthy, T.; Raju, I. S.; Sistla, R.

    1993-01-01

    A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.

  5. Three-dimensional elastic-plastic finite-element analysis of fatigue crack propagation

    NASA Technical Reports Server (NTRS)

    Goglia, G. L.; Chermahini, R. G.

    1985-01-01

    Fatigue cracks are a major problem in designing structures subjected to cyclic loading. Cracks frequently occur in structures such as aircraft and spacecraft. The inspection intervals of many aircraft structures are based on crack-propagation lives. Therefore, improved prediction of propagation lives under flight-load conditions (variable-amplitude loading) are needed to provide more realistic design criteria for these structures. The main thrust was to develop a three-dimensional, nonlinear, elastic-plastic, finite element program capable of extending a crack and changing boundary conditions for the model under consideration. The finite-element model is composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material is assumed to be elastic-perfectly plastic. The cycle stress-strain curve for the material is shown Zienkiewicz's initial-stress method, von Mises's yield criterion, and Drucker's normality condition under small-strain assumptions are used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading.

  6. Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains

    NASA Astrophysics Data System (ADS)

    Latorre, Marcos; Montáns, Francisco Javier

    2015-09-01

    In this paper a purely phenomenological formulation and finite element numerical implementation for quasi-incompressible transversely isotropic and orthotropic materials is presented. The stored energy is composed of distinct anisotropic equilibrated and non-equilibrated parts. The nonequilibrated strains are obtained from the multiplicative decomposition of the deformation gradient. The procedure can be considered as an extension of the Reese and Govindjee framework to anisotropic materials and reduces to such formulation for isotropic materials. The stress-point algorithmic implementation is based on an elastic-predictor viscous-corrector algorithm similar to that employed in plasticity. The consistent tangent moduli for the general anisotropic case are also derived. Numerical examples explain the procedure to obtain the material parameters, show the quadratic convergence of the algorithm and usefulness in multiaxial loading. One example also highlights the importance of prescribing a complete set of stress-strain curves in orthotropic materials.

  7. A solid-shell Cosserat point element ( SSCPE) for elastic thin structures at finite deformation

    NASA Astrophysics Data System (ADS)

    Jabareen, Mahmood; Mtanes, Eli

    2016-07-01

    The objective of this study is to develop a new solid-shell element using the Cosserat point theory for modeling thin elastic structures at finite deformations. The point-wise Green-Lagrange strain tensor is additively decomposed into homogeneous and inhomogeneous parts. Only the latter part of the strain tensor is modified by the assumed natural strain ANS concept to avoid both curvature-thickness locking and transverse shear locking. To the authors' knowledge, such modification has not been applied yet in the literature, and here it is referred to as the assumed natural inhomogeneous strain ANIS concept. Moreover, a new methodology for determining the constitutive coefficients of the strain energy function, which controls the inhomogeneous deformations, is proposed. The resulting coefficients ensure both accuracy, robustness, and elimination of all locking pathologies in the solid-shell Cosserat point element ( SSCPE). The performance of the developed SSCPE is verified and tested via various benchmark problems and compared to other solid, shell, and solid-shell elements. These examples demonstrate that the SSCPE is accurate, robust, stable, free of locking, and can be used for modeling thin structures at both small and finite deformations.

  8. A solid-shell Cosserat point element (SSCPE) for elastic thin structures at finite deformation

    NASA Astrophysics Data System (ADS)

    Jabareen, Mahmood; Mtanes, Eli

    2016-04-01

    The objective of this study is to develop a new solid-shell element using the Cosserat point theory for modeling thin elastic structures at finite deformations. The point-wise Green-Lagrange strain tensor is additively decomposed into homogeneous and inhomogeneous parts. Only the latter part of the strain tensor is modified by the assumed natural strain ANS concept to avoid both curvature-thickness locking and transverse shear locking. To the authors' knowledge, such modification has not been applied yet in the literature, and here it is referred to as the assumed natural inhomogeneous strain ANIS concept. Moreover, a new methodology for determining the constitutive coefficients of the strain energy function, which controls the inhomogeneous deformations, is proposed. The resulting coefficients ensure both accuracy, robustness, and elimination of all locking pathologies in the solid-shell Cosserat point element (SSCPE). The performance of the developed SSCPE is verified and tested via various benchmark problems and compared to other solid, shell, and solid-shell elements. These examples demonstrate that the SSCPE is accurate, robust, stable, free of locking, and can be used for modeling thin structures at both small and finite deformations.

  9. Atomistic modeling of diffusional phasetransformations with elastic strain

    SciTech Connect

    Mason, D R; Rudd, R E; Sutton, A P

    2003-10-31

    Phase transformations in 2xxx series aluminium alloys (Al-Cu-Mg) are investigated with an off-lattice atomistic kinetic Monte Carlo simulation incorporating the effects of strain around misfitting atoms and vacancies. Atomic interactions are modelled by Finnis-Sinclair potentials constructed for these simulations. Vacancy diffusion is modelled by comparing the energies of trial states, where the system is partially relaxed for each trial state. No special requirements are made about the description of atomic interactions, making our approach suitable for more fundamentally based models such as tight binding if sufficient computational resources are available. Only a limited precision is required for the energy of each trial state, determined by the value of kBT. Since the change in the relaxation displacement field caused by a vacancy hop decays as 1/r{sup 3} , it is sufficient to determine the next move by relaxing only those atoms in a sphere of finite radius centred on the moving vacancy. However, once the next move has been selected, the entire system is relaxed. Simulations of the early stages of phase separation in Al-Cu with elastic relaxation show an enhanced rate of clustering compared to those performed on the same system with a rigid lattice.

  10. Evidence for residual elastic strain in deformed natural quartz

    SciTech Connect

    Kunz, Martin; Chen, Kai; Tamura,Nobumichi; Wenk, Hans-Rudolf

    2009-01-30

    Residual elastic strain in naturally deformed, quartz-containing rocks can be measured quantitatively in a petrographic thin section with high spatial resolution using Laue microdiffraction with white synchrotron x-rays. The measurements with a resolution of one micrometer allow the quantitative determination of the deviatoric strain tensor as a function of position within the crystal investigated. The observed equivalent strain values of 800-1200 microstrains represent a lower bound of the actual preserved residual strain in the rock, since the stress component perpendicular to the cut sample surface plane is released. The measured equivalent strain translates into an equivalent stress in the order of {approx} 50 MPa.

  11. Visualization of elastic wavefields computed with a finite difference code

    SciTech Connect

    Larsen, S.; Harris, D.

    1994-11-15

    The authors have developed a finite difference elastic propagation model to simulate seismic wave propagation through geophysically complex regions. To facilitate debugging and to assist seismologists in interpreting the seismograms generated by the code, they have developed an X Windows interface that permits viewing of successive temporal snapshots of the (2D) wavefield as they are calculated. The authors present a brief video displaying the generation of seismic waves by an explosive source on a continent, which propagate to the edge of the continent then convert to two types of acoustic waves. This sample calculation was part of an effort to study the potential of offshore hydroacoustic systems to monitor seismic events occurring onshore.

  12. Finite gradient elasticity and plasticity: a constitutive thermodynamical framework

    NASA Astrophysics Data System (ADS)

    Bertram, Albrecht

    2016-05-01

    In Bertram (Continuum Mech Thermodyn. doi: 10.1007/s00161-014-0387-0 , 2015), a mechanical framework for finite gradient elasticity and plasticity has been given. In the present paper, this is extended to thermodynamics. The mechanical theory is only briefly repeated here. A format for a rather general constitutive theory including all thermodynamic fields is given in a Euclidian invariant setting. The plasticity theory is rate-independent and unconstrained. The Clausius-Duhem inequality is exploited to find necessary and sufficient conditions for thermodynamic consistency. The residual dissipation inequality restricts the flow and hardening rules in combination with the yield criterion.

  13. Near tip stress and strain fields for short elastic cracks

    NASA Technical Reports Server (NTRS)

    Soediono, A. H.; Kardomateas, G. A.; Carlson, R. L.

    1994-01-01

    Recent experimental fatigue crack growth studies have concluded an apparent anomalous behavior of short cracks. To investigate the reasons for this unexpected behavior, the present paper focuses on identifying the crack length circumstances under which the requirements for a single parameter (K(sub I) or delta K(sub I) if cyclic loading is considered) characterization are violated. Furthermore, an additional quantity, the T stress, as introduced by Rice, and the related biaxiality ratio, B, are calculated for several crack lengths and two configurations, the single-edge-cracked and the centrally-cracked specimen. It is postulated that a two-parameter characterization by K and T (or B) is needed for the adequate description of the stress and strain field around a short crack. To further verify the validity of this postulate, the influence of the third term of the Williams series on the stress, strain and displacement fields around the crack tip and in particular on the B parameter is also examined. It is found that the biaxiality ratio would be more negative if the third term effects are included in both geometries. The study is conducted using the finite element method with linearly elastic material and isoparametric elements and axial (mode I) loading. Moreover, it is clearly shown that it is not proper to postulate the crack size limits for 'short crack' behavior as a normalized ratio with the specimen width, a/w; it should instead be stated as an absolute, or normalized with respect to a small characteristic dimension such as the grain size. Finally, implications regarding the prediction of cyclic (fatigue) growth of short cracks are discussed.

  14. Elastic Wave Radiation from a Line Source of Finite Length

    SciTech Connect

    Aldridge, D.F.

    1998-11-04

    Straightforward algebraic expressions describing the elastic wavefield produced by a line source of finite length are derived in circular cylindrical coordinates. The surrounding elastic medium is assumed to be both homogeneous and isotropic, anc[ the source stress distribution is considered axisymmetic. The time- and space-domain formulae are accurate at all distances and directions from the source; no fa-field or long-wavelength assumptions are adopted for the derivation. The mathematics yield a unified treatment of three different types of sources: an axial torque, an axial force, and a radial pressure. The torque source radiates only azirnuthally polarized shear waves, whereas force and pressure sources generate simultaneous compressional and shear radiation polarized in planes containing the line source. The formulae reduce to more familiar expressions in the two limiting cases where the length of the line source approaches zero and infinity. Far-field approximations to the exact equations indicate that waves radiated parallel to the line source axI.s are attenuated relative to those radiated normal to the axis. The attenuation is more severe for higher I?equencies and for lower wavespeeds. Hence, shear waves are affected more than compressional waves. This fi-equency- and directiondependent attenuation is characterized by an extremely simple mathematical formula, and is readily apparent in example synthetic seismograms.

  15. Two-dimensional Finite Element Modeling for Modeling Tectonic Stress and Strain

    NASA Technical Reports Server (NTRS)

    Lyzenga, G. A.; Raefsky, A.

    1983-01-01

    Techniques of finite element analysis in two dimensional plane strain were applied to problems of geophysics and tectonics. More specifically, the flexibility of the finite element method was employed to address problems involving geological complexity and fault interactions. The modeling of effective anisotropy in material elastic properties proved useful in describing the deformation of faulted crustal blocks. The applications of this modeling work to problems of actual tectonics in southern California was explored. Preliminary models show encouraging agreement with measured tectonic strain in this region, and modeling work was done to gain an understanding of the stress state in a locked fault region with future seismic potential.

  16. Approaching the ideal elastic strain limit in silicon nanowires.

    PubMed

    Zhang, Hongti; Tersoff, Jerry; Xu, Shang; Chen, Huixin; Zhang, Qiaobao; Zhang, Kaili; Yang, Yong; Lee, Chun-Sing; Tu, King-Ning; Li, Ju; Lu, Yang

    2016-08-01

    Achieving high elasticity for silicon (Si) nanowires, one of the most important and versatile building blocks in nanoelectronics, would enable their application in flexible electronics and bio-nano interfaces. We show that vapor-liquid-solid-grown single-crystalline Si nanowires with diameters of ~100 nm can be repeatedly stretched above 10% elastic strain at room temperature, approaching the theoretical elastic limit of silicon (17 to 20%). A few samples even reached ~16% tensile strain, with estimated fracture stress up to ~20 GPa. The deformations were fully reversible and hysteresis-free under loading-unloading tests with varied strain rates, and the failures still occurred in brittle fracture, with no visible sign of plasticity. The ability to achieve this "deep ultra-strength" for Si nanowires can be attributed mainly to their pristine, defect-scarce, nanosized single-crystalline structure and atomically smooth surfaces. This result indicates that semiconductor nanowires could have ultra-large elasticity with tunable band structures for promising "elastic strain engineering" applications. PMID:27540586

  17. Approaching the ideal elastic strain limit in silicon nanowires

    PubMed Central

    Zhang, Hongti; Tersoff, Jerry; Xu, Shang; Chen, Huixin; Zhang, Qiaobao; Zhang, Kaili; Yang, Yong; Lee, Chun-Sing; Tu, King-Ning; Li, Ju; Lu, Yang

    2016-01-01

    Achieving high elasticity for silicon (Si) nanowires, one of the most important and versatile building blocks in nanoelectronics, would enable their application in flexible electronics and bio-nano interfaces. We show that vapor-liquid-solid–grown single-crystalline Si nanowires with diameters of ~100 nm can be repeatedly stretched above 10% elastic strain at room temperature, approaching the theoretical elastic limit of silicon (17 to 20%). A few samples even reached ~16% tensile strain, with estimated fracture stress up to ~20 GPa. The deformations were fully reversible and hysteresis-free under loading-unloading tests with varied strain rates, and the failures still occurred in brittle fracture, with no visible sign of plasticity. The ability to achieve this “deep ultra-strength” for Si nanowires can be attributed mainly to their pristine, defect-scarce, nanosized single-crystalline structure and atomically smooth surfaces. This result indicates that semiconductor nanowires could have ultra-large elasticity with tunable band structures for promising “elastic strain engineering” applications. PMID:27540586

  18. Finite Difference Elastic Wave Field Simulation On GPU

    NASA Astrophysics Data System (ADS)

    Hu, Y.; Zhang, W.

    2011-12-01

    Numerical modeling of seismic wave propagation is considered as a basic and important aspect in investigation of the Earth's structure, and earthquake phenomenon. Among various numerical methods, the finite-difference method is considered one of the most efficient tools for the wave field simulation. However, with the increment of computing scale, the power of computing has becoming a bottleneck. With the development of hardware, in recent years, GPU shows powerful computational ability and bright application prospects in scientific computing. Many works using GPU demonstrate that GPU is powerful . Recently, GPU has not be used widely in the simulation of wave field. In this work, we present forward finite difference simulation of acoustic and elastic seismic wave propagation in heterogeneous media on NVIDIA graphics cards with the CUDA programming language. We also implement perfectly matched layers on the graphics cards to efficiently absorb outgoing waves on the fictitious edges of the grid Simulations compared with the results on CPU platform shows reliable accuracy and remarkable efficiency. This work proves that GPU can be an effective platform for wave field simulation, and it can also be used as a practical tool for real-time strong ground motion simulation.

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

    ERIC Educational Resources Information Center

    Daskin, Alan J.

    1992-01-01

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

  20. Internal elastic strains in an IF steel following changes in strain path

    SciTech Connect

    Wilson, D.V.; Bate, P.S.

    1996-08-01

    Residual elastic strains present in an IF steel following rolling and subsequent tensile deformation have been evaluated using X-ray diffraction. It was possible to decompose diffraction profiles into two symmetrical components notionally corresponding to dislocation walls and cell interiors and so estimate the volume fractions and mean elastic strains associated with these components of the microstructure following different deformation modes. The residual long range elastic strains were very small following rolling, but they were much greater following subsequent tensile elongation to macroscopic yield. The mean strains could only account for about one-third of the strain induced anisotropy of flow stress. It is concluded that insufficient dislocations accumulate at cell walls at macroscopic yield following a path change to give homogeneous loading of the dislocation walls, and that this effect can account for the difference between the macroscopic mechanical behavior and predictions from the X-ray strain measurements.

  1. A plane stress finite element model for elastic-plastic mode I/II crack growth

    NASA Astrophysics Data System (ADS)

    James, Mark Anthony

    A finite element program has been developed to perform quasi-static, elastic-plastic crack growth simulations. The model provides a general framework for mixed-mode I/II elastic-plastic fracture analysis using small strain assumptions and plane stress, plane strain, and axisymmetric finite elements. Cracks are modeled explicitly in the mesh. As the cracks propagate, automatic remeshing algorithms delete the mesh local to the crack tip, extend the crack, and build a new mesh around the new tip. State variable mapping algorithms transfer stresses and displacements from the old mesh to the new mesh. The von Mises material model is implemented in the context of a non-linear Newton solution scheme. The fracture criterion is the critical crack tip opening displacement, and crack direction is predicted by the maximum tensile stress criterion at the crack tip. The implementation can accommodate multiple curving and interacting cracks. An additional fracture algorithm based on nodal release can be used to simulate fracture along a horizontal plane of symmetry. A core of plane strain elements can be used with the nodal release algorithm to simulate the triaxial state of stress near the crack tip. Verification and validation studies compare analysis results with experimental data and published three-dimensional analysis results. Fracture predictions using nodal release for compact tension, middle-crack tension, and multi-site damage test specimens produced accurate results for residual strength and link-up loads. Curving crack predictions using remeshing/mapping were compared with experimental data for an Arcan mixed-mode specimen. Loading angles from 0 degrees to 90 degrees were analyzed. The maximum tensile stress criterion was able to predict the crack direction and path for all loading angles in which the material failed in tension. Residual strength was also accurately predicted for these cases.

  2. 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.

  3. Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

    NASA Technical Reports Server (NTRS)

    Wu, R. W.; Witmer, E. A.

    1972-01-01

    Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

  4. On local total strain redistribution using a simplified cyclic inelastic analysis based on an elastic solution

    NASA Technical Reports Server (NTRS)

    Hwang, S. Y.; Kaufman, A.

    1985-01-01

    Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction purposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure has been found to predict stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load cycled problems. This study derived and incorporated Neuber type corrections in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was exercised on a mechanically load cycled benchmark notched plate problem. Excellent agreement was found between the predicted material response and nonlinear finite element solutions for the problem. The simplified analysis computer program used 0.3 percent of the CPU time required for a nonlinear finite element analysis.

  5. Elastic-plastic mixed-iterative finite element analysis: Implementation and performance assessment

    NASA Technical Reports Server (NTRS)

    Sutjahjo, Edhi; Chamis, Christos C.

    1993-01-01

    An elastic-plastic algorithm based on Von Mises and associative flow criteria is implemented in MHOST-a mixed iterative finite element analysis computer program developed by NASA Lewis Research Center. The performance of the resulting elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors of 4-node quadrilateral shell finite elements are tested for elastic-plastic performance. Generally, the membrane results are excellent, indicating the implementation of elastic-plastic mixed-iterative analysis is appropriate.

  6. Medical ultrasound: imaging of soft tissue strain and elasticity

    PubMed Central

    Wells, Peter N. T.; Liang, Hai-Dong

    2011-01-01

    After X-radiography, ultrasound is now the most common of all the medical imaging technologies. For millennia, manual palpation has been used to assist in diagnosis, but it is subjective and restricted to larger and more superficial structures. Following an introduction to the subject of elasticity, the elasticity of biological soft tissues is discussed and published data are presented. The basic physical principles of pulse-echo and Doppler ultrasonic techniques are explained. The history of ultrasonic imaging of soft tissue strain and elasticity is summarized, together with a brief critique of previously published reviews. The relevant techniques—low-frequency vibration, step, freehand and physiological displacement, and radiation force (displacement, impulse, shear wave and acoustic emission)—are described. Tissue-mimicking materials are indispensible for the assessment of these techniques and their characteristics are reported. Emerging clinical applications in breast disease, cardiology, dermatology, gastroenterology, gynaecology, minimally invasive surgery, musculoskeletal studies, radiotherapy, tissue engineering, urology and vascular disease are critically discussed. It is concluded that ultrasonic imaging of soft tissue strain and elasticity is now sufficiently well developed to have clinical utility. The potential for further research is examined and it is anticipated that the technology will become a powerful mainstream investigative tool. PMID:21680780

  7. Finite circular plate on elastic foundation centrally loaded by rigid spherical indenter

    NASA Technical Reports Server (NTRS)

    Wadhwa, S. K.; Yang, P. P.

    1980-01-01

    The analytical solution of a finite circular plate on an elastic foundation centrally loaded by the rigid indenter is discussed. The procedure to use NASTRAN as a subroutine to iteratively converge to this solution numerically is described.

  8. Retaining large and adjustable elastic strains of kilogram-scale Nb nanowires [Better Superconductor by Elastic Strain Engineering: Kilogram-scale Free-Standing Niobium Metal Composite with Large Retained Elastic Strains

    DOE PAGESBeta

    Hao, Shijie; Cui, Lishan; Wang, Hua; Jiang, Daqiang; Liu, Yinong; Yan, Jiaqiang; Ren, Yang; Han, Xiaodong; Brown, Dennis E.; Li, Ju

    2016-02-10

    Crystals held at ultrahigh elastic strains and stresses may exhibit exceptional physical and chemical properties. Individual metallic nanowires can sustain ultra-large elastic strains of 4-7%. However, retaining elastic strains of such magnitude in kilogram-scale nanowires is challenging. Here, we find that under active load, ~5.6% elastic strain can be achieved in Nb nanowires in a composite material. Moreover, large tensile (2.8%) and compressive (-2.4%) elastic strains can be retained in kilogram-scale Nb nanowires when the composite is unloaded to a free-standing condition. It is then demonstrated that the retained tensile elastic strains of Nb nanowires significantly increase their superconducting transitionmore » temperature and critical magnetic fields, corroborating ab initio calculations based on BCS theory. This free-standing nanocomposite design paradigm opens new avenues for retaining ultra-large elastic strains in great quantities of nanowires and elastic-strain-engineering at industrial scale.« less

  9. Elastic strain relaxation in axial Si/Ge whisker heterostructures

    SciTech Connect

    Hanke, M.; Eisenschmidt, C.; Werner, P.; Zakharov, N. D.; Syrowatka, F.; Heyroth, F.; Schaefer, P.; Konovalov, O.

    2007-04-15

    The elastic behavior of molecular beam epitaxy-grown SiGe/Si(111) nanowhiskers (NWs) has been studied by means of electron microscopy, x-ray scattering, and numerical linear elasticity theory. Highly brilliant synchrotron radiation was applied to map the diffusely scattered intensity near the asymmetric (115) reciprocal lattice point. The larger lattice parameter with respect to the Si matrix causes a lateral lattice expansion within embedded Ge layers. This enables a clear separation of scattering due to NWs and laterally confined areas aside. Finite element calculations prove a lateral lattice compression in the Si matrix close to the NW apex above buried threefold and single Ge layer stacks. This suggests an incorporation probability, which additionally depends on the radial position within heteroepitaxial NWs.

  10. Controlling surface reactions with nanopatterned surface elastic strain.

    PubMed

    Li, Zhisheng; Potapenko, Denis V; Osgood, Richard M

    2015-01-27

    The application of elastic lattice strain is a promising approach for tuning material properties, but the attainment of a systematic approach for introducing a high level of strain in materials so as to study its effects has been a major challenge. Here we create an array of intense locally varying strain fields on a TiO2 (110) surface by introducing highly pressurized argon nanoclusters at 6-20 monolayers under the surface. By combining scanning tunneling microscopy imaging and the continuum mechanics model, we show that strain causes the surface bridge-bonded oxygen vacancies (BBOv), which are typically present on this surface, to be absent from the strained area and generates defect-free regions. In addition, we find that the adsorption energy of hydrogen binding to oxygen (BBO) is significantly altered by local lattice strain. In particular, the adsorption energy of hydrogen on BBO rows is reduced by ∼ 35 meV when the local crystal lattice is compressed by ∼ 1.3%. Our results provide direct evidence of the influence of strain on atomic-scale surface chemical properties, and such effects may help guide future research in catalysis materials design. PMID:25494489

  11. Do foliation refraction patterns around buckle folds represent finite strain?

    NASA Astrophysics Data System (ADS)

    Frehner, M.; Exner, U.

    2012-04-01

    Buckle folds in the field commonly feature a characteristic syn-deformational foliation, which is sub-parallel to the fold axial plane; hence it is called axial plane foliation. As the foliation is not perfectly parallel to the axial plane, it may exhibit either a divergent or convergent fan around the fold. Convergent fans most commonly occur in the stronger rocks (the folded layer) while divergent fans rather occur in the mechanically weaker rocks (the matrix). The foliation orientation is usually thought to reflect the long axes of the finite strain ellipses, a hypothesis that we investigate in our study. To study the strain distribution around folds, we use the finite-element method to simulate two-dimensional single-layer viscous buckling. The numerical simulations allow to calculate the strain evolution during the folding process and to visualize its distribution and orientation around the fold. We use different measures of strain: (1) the finite strain (recording the strain history from the beginning of the simulation until the end), (2) the infinitesimal strain (capturing only the very last moment of the simulation), (3) the incremental strain (recording the strain history from a certain shortening value during the simulation until the end), and (4) initially layer-orthogonal passive marker lines. The shortening value, from which the incremental strain is calculated, can be anything between the beginning and the end of the simulation. The first three strain measures are tensor fields that are used to calculate and visualize the orientation of the long axis of the strain ellipses around the fold. We find that all strain measures result in a divergent fan in the mechanically weak matrix at the outer arc of the fold and that this divergent fan has almost the same geometry for all strain measures. Also, for the case of the incremental strain, the divergent fan does hardly depend on the moment from which the incremental strain is calculated. This observation

  12. Retaining Large and Adjustable Elastic Strains of Kilogram-Scale Nb Nanowires.

    PubMed

    Hao, Shijie; Cui, Lishan; Wang, Hua; Jiang, Daqiang; Liu, Yinong; Yan, Jiaqiang; Ren, Yang; Han, Xiaodong; Brown, Dennis E; Li, Ju

    2016-02-10

    Individual metallic nanowires can sustain ultralarge elastic strains of 4-7%. However, achieving and retaining elastic strains of such magnitude in kilogram-scale nanowires are challenging. Here, we find that under active load, ∼ 5.6% elastic strain can be achieved in Nb nanowires embedded in a metallic matrix deforming by detwinning. Moreover, large tensile (2.8%) and compressive (-2.4%) elastic strains can be retained in kilogram-scale Nb nanowires when the external load was fully removed, and adjustable in magnitude by processing control. It is then demonstrated that the retained tensile elastic strains of Nb nanowires can increase their superconducting transition temperature and critical magnetic field, in comparison with the unstrained original material. This study opens new avenues for retaining large and tunable elastic strains in great quantities of nanowires and elastic-strain-engineering at industrial scale. PMID:26745016

  13. Analytical solutions to general anti-plane shear problems in finite elasticity

    NASA Astrophysics Data System (ADS)

    Gao, David Yang

    2016-03-01

    This paper presents a pure complementary energy variational method for solving a general anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconvex partial differential equations for the large deformation problem are converted into an algebraic equation in dual space, which can, in principle, be solved to obtain a complete set of stress solutions. Therefore, a general analytical solution form of the deformation is obtained subjected to a compatibility condition. Applications are illustrated by examples with both convex and nonconvex stored strain energies governed by quadratic-exponential and power-law material models, respectively. Results show that the nonconvex variational problem could have multiple solutions at each material point, the complementary gap function and the triality theory can be used to identify both global and local extremal solutions, while the popular convexity conditions (including rank-one condition) provide mainly local minimal criteria and the Legendre-Hadamard condition (i.e., the so-called strong ellipticity condition) does not guarantee uniqueness of solutions. This paper demonstrates again that the pure complementary energy principle and the triality theory play important roles in finite deformation theory and nonconvex analysis.

  14. Probabilistic elastic-plastic fracture analysis of circumferentially cracked pipes with finite-length surface flaws

    SciTech Connect

    Rahman, S.

    1996-12-01

    A new probabilistic model was developed for predicting elastic-plastic fracture response of circumferentially cracked pipes with finite-length, constant-depth, internal surface flaws subject to remote bending loads. It involves engineering estimation of energy release rate, J-tearing theory for characterizing ductile fracture, and standard methods of structural reliability theory. The underlying J-estimation model is based on deformation theory of plasticity, constitutive law characterized by power law model for stress-strain curve, and an equivalence criterion incorporating reduced thickness analogy for simulating system compliance due to the presence of a crack. New equations were developed to predict J-integral and were evaluated by comparing with available finite-element results from the current literature. Both analytical and simulation methods were formulated to determine the probabilistic characteristics of J. The same methods were used later to predict the probability of crack initiation and net-section collapse as a function of the applied load. Numerical examples are provided to illustrate the proposed methodology.

  15. ISOFINEL: Isoparametric finite element code for elastic analysis of two-dimensional bodies

    NASA Technical Reports Server (NTRS)

    Marino, C.

    1975-01-01

    A formulation is presented for the development of a finite element program for the elastic analysis of two-dimensional bodies using the eight-node isoparametric quadrilateral. The program solves for both plane stress and plane strain problems. The finite element formulation based on the isoparametric displacement functions is presented. The program structure is given in the form of flow diagrams with descriptions of the numerical procedure used to obtain the element stiffness matrix, and the solution method employed to solve for nodal displacements. Three numerical examples (a plate under uniaxial tension, a plate under pure shear, and a beam under pure bending) are presented to illustrate the capability and limitations of the element implementation. The first problem is solved exactly by the element, as predicted by the form of its displacement functions. In the other two problems the accuracy of the solution is highly dependent upon the slenderness of the element, the number of elements in the map, and the numerical integration scheme used to build the element stiffness matrix.

  16. Breakdown of nonlinear elasticity in amorphous solids at finite temperatures

    NASA Astrophysics Data System (ADS)

    Procaccia, Itamar; Rainone, Corrado; Shor, Carmel A. B. Z.; Singh, Murari

    2016-06-01

    It is known [H. G. E. Hentschel et al., Phys. Rev. E 83, 061101 (2011), 10.1103/PhysRevE.83.061101] that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus, which exists, none of the higher order coefficients exist in the thermodynamic limit. Here we show that the same phenomenon persists up to temperatures comparable to that of the glass transition. The zero-temperature mechanism due to the prevalence of dangerous plastic modes of the Hessian matrix is replaced by anomalous stress fluctuations that lead to the divergence of the variances of the higher order elastic coefficients. The conclusion is that in amorphous solids elasticity can never be decoupled from plasticity: the nonlinear response is very substantially plastic.

  17. Arterial elasticity imaging: comparison of finite-element analysis models with high-resolution ultrasound speckle tracking

    PubMed Central

    2010-01-01

    Background The nonlinear mechanical properties of internal organs and tissues may be measured with unparalleled precision using ultrasound imaging with phase-sensitive speckle tracking. The many potential applications of this important noninvasive diagnostic approach include measurement of arterial stiffness, which is associated with numerous major disease processes. The accuracy of previous ultrasound measurements of arterial stiffness and vascular elasticity has been limited by the relatively low strain of nonlinear structures under normal physiologic pressure and the measurement assumption that the effect of the surrounding tissue modulus might be ignored in both physiologic and pressure equalized conditions. Methods This study performed high-resolution ultrasound imaging of the brachial artery in a healthy adult subject under normal physiologic pressure and the use of external pressure (pressure equalization) to increase strain. These ultrasound results were compared to measurements of arterial strain as determined by finite-element analysis models with and without a surrounding tissue, which was represented by homogenous material with fixed elastic modulus. Results Use of the pressure equalization technique during imaging resulted in average strain values of 26% and 18% at the top and sides, respectively, compared to 5% and 2%, at the top and sides, respectively, under physiologic pressure. In the artery model that included surrounding tissue, strain was 19% and 16% under pressure equalization versus 9% and 13% at the top and sides, respectively, under physiologic pressure. The model without surrounding tissue had slightly higher levels of strain under physiologic pressure compared to the other model, but the resulting strain values under pressure equalization were > 60% and did not correspond to experimental values. Conclusions Since pressure equalization may increase the dynamic range of strain imaging, the effect of the surrounding tissue on strain should

  18. Finite Strain Viscoplastic Modeling of Polymer Glasses

    NASA Astrophysics Data System (ADS)

    van Breemen, L. C. A.; Govaert, L. E.; Meijer, H. E. H.

    2008-07-01

    There are several techniques to probe local mechanical properties of polymer systems. Two frequently used techniques are indentation and scratching, also known as sliding friction. The first is used to determine material parameters such as Young's modulus and yield strength, the later to resolve issues concerning friction and wear properties. Both techniques are based on contact of a specimen with a well-defined indentation/scratching geometry. If we take a closer look at an indentation experiment, an indenter is pressed into the material and a force, the so called normal force, and penetration into the surface are measured. For the scratching experiment an extra sliding dimension is added and besides the normal force and penetration depth, a lateral force and sliding distance are measured. The first step of a scratching experiment is indentation; this implies that before we can start with investigation of sliding phenomena, all the phenomena governing indentation have to be captured. For polymers this technique should be used with great care, this because of the strong non-linearity and rate dependence of polymer systems. To understand both contact phenomena a combination of experiments and numerical techniques are used. To comprehend macroscopic polymer deformation a polymers' intrinsic deformation should be captured accurately. This deformation behavior is used as input for our constitutive model and subsequently the model is used for finite element calculations.

  19. Dynamically strained ferroelastics: Statistical behavior in elastic and plastic regimes

    NASA Astrophysics Data System (ADS)

    Ding, X.; Lookman, T.; Zhao, Z.; Saxena, A.; Sun, J.; Salje, E. K. H.

    2013-03-01

    The dynamic evolution in ferroelastic crystals under external shear is explored by computer simulation of a two-dimensional model. The characteristic geometrical patterns obtained during shear deformation include dynamic tweed in the elastic regime as well as interpenetrating needle domains in the plastic regime. As a result, the statistics of jerk energy differ in the elastic and plastic regimes. In the elastic regime the distributions of jerk energy are sensitive to temperature and initial configurations. However, in the plastic regime the jerk distributions are rather robust and do not depend much on the details of the configurations, although the geometrical pattern formed after yield is strongly influenced by the elastic constants of the materials and the configurations we used. Specifically, for all geometrical configurations we studied, the energy distribution of jerks shows a power-law noise pattern P(E)˜E-(γ-1)(γ-1=1.3-2) at low temperatures and a Vogel-Fulcher distribution P(E) ˜ exp-(E/E0) at high temperatures. More complex behavior occurs at the crossover between these two regimes where our simulated jerk distributions are very well described by a generalized Poisson distributions P(E)˜E-(γ-1) exp-(E/E0)n with n = 0.4-0.5 and γ-1 ≈ 0 (Kohlrausch law). The geometrical mechanisms for the evolution of the ferroelastic microstructure under strain deformation remain similar in all thermal regimes, whereas their thermodynamic behavior differs dramatically: on heating, from power-law statistics via the Kohlrausch law to a Vogel-Fulcher law. There is hence no simple way to predict the local evolution of the twin microstructure from just the observed statistical behavior of a ferroelastic crystal. It is shown that the Poisson distribution is a convenient way to describe the crossover behavior contained in all the experimental data without recourse to specific scaling functions or temperature-dependent cutoff lengths.

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

    NASA Technical Reports Server (NTRS)

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

    1987-01-01

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

  1. Dependence of the elastic strain coefficient of copper on the pre-treatment

    NASA Technical Reports Server (NTRS)

    Kuntze, Wilhelm

    1950-01-01

    The effect of various pre-treatments on the elastic strain coefficient (alpha) (defined as the reciprocal of the modulus of elasticity E) (Epsilon) and on the mechanical hysteresis of copper has been investigated. Variables comprising the pre-treatments were pre-straining by stretching in a tensile testing machine and by drawing through a die, aging at room and elevated temperatures and annealing. The variation of the elastic strain coefficient with test stress was also investigated.

  2. The Influence of Elastic Strain on Catalytic Activity in the Hydrogen Evolution Reaction.

    PubMed

    Yan, Kai; Maark, Tuhina Adit; Khorshidi, Alireza; Sethuraman, Vijay A; Peterson, Andrew A; Guduru, Pradeep R

    2016-05-17

    Understanding the role of elastic strain in modifying catalytic reaction rates is crucial for catalyst design, but experimentally, this effect is often coupled with a ligand effect. To isolate the strain effect, we have investigated the influence of externally applied elastic strain on the catalytic activity of metal films in the hydrogen evolution reaction (HER). We show that elastic strain tunes the catalytic activity in a controlled and predictable way. Both theory and experiment show strain controls reactivity in a controlled manner consistent with the qualitative predictions of the HER volcano plot and the d-band theory: Ni and Pt's activities were accelerated by compression, while Cu's activity was accelerated by tension. By isolating the elastic strain effect from the ligand effect, this study provides a greater insight into the role of elastic strain in controlling electrocatalytic activity. PMID:27079940

  3. Biaxial load effects on the crack border elastic strain energy and strain energy rate

    NASA Technical Reports Server (NTRS)

    Eftis, J.; Subramonian, N.; Liebowitz, H.

    1977-01-01

    The validity of the singular solution (first term of a series representation) is investigated for the crack tip stress and displacement field in an infinite sheet with a flat line crack with biaxial loads applied to the outer boundaries. It is shown that if one retains the second contribution to the series approximations for stress and displacement in the calculation of the local elastic strain energy density and elastic strain energy rate in the crack border region, both these quantities have significant biaxial load dependency. The value of the J-integral does not depend on the presence of the second term of the series expansion for stress and displacement. Thus J(I) is insensitive to the presence of loads applied parallel to the plane of the crack.

  4. Hysteretic nonlinear elasticity of Berea sandstone at low-vibrational strain revealed by dynamic acousto-elastic testing

    NASA Astrophysics Data System (ADS)

    Renaud, G.; RivièRe, J.; Le Bas, P.-Y.; Johnson, P. A.

    2013-02-01

    Abstract Through changes in wave speed of ultrasonic pulses traversing the sample, we measure variations in the <span class="hlt">elasticity</span> of dry Berea sandstone as a function of the applied low-frequency (LF) axial <span class="hlt">strain</span> (varied from 10-7 to 10-5). The approach, termed dynamic acousto-<span class="hlt">elasticity</span>, is the dynamic analog of static acousto-<span class="hlt">elasticity</span> where the wave speed is measured as a function of the applied static load. Dynamic acousto-<span class="hlt">elasticity</span> uses low-frequency vibrational loading of smaller <span class="hlt">strain</span> amplitude, typically below 10-4, and it includes inertial effects. At <span class="hlt">strain</span> amplitudes around 10-6, compression and tension produce a material softening of the material. In contrast, a quasi-static compression inducing a <span class="hlt">strain</span> between 10-4 and 10-3 leads to a material stiffening. At 10-5 <span class="hlt">strain</span> amplitude, elaborate hysteretic signatures of modulus <span class="hlt">strain</span> are observed. The measurements provide the first direct experimental evidence of hysteretic nonlinear (wave amplitude dependent) <span class="hlt">elasticity</span> in a sandstone at low dynamic <span class="hlt">strains</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19840024803','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19840024803"><span id="translatedtitle"><span class="hlt">Finite</span> Element Prediction of Acoustic Scattering and Radiation from Submerged <span class="hlt">Elastic</span> Structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Everstine, G. C.; Henderson, F. M.; Lipman, R. R.</p> <p>1984-01-01</p> <p>A <span class="hlt">finite</span> element formulation is derived for the scattering and radiation of acoustic waves from submerged <span class="hlt">elastic</span> structures. The formulation uses as fundamental unknowns the displacement in the structure and a velocity potential in the field. Symmetric coefficient matrices result. The outer boundary of the fluid region is terminated with an approximate local wave-absorbing boundary condition which assumes that outgoing waves are locally planar. The <span class="hlt">finite</span> element model is capable of predicting only the near-field acoustic pressures. Far-field sound pressure levels may be determined by integrating the surface pressures and velocities over the wet boundary of the structure using the Helmholtz integral. Comparison of <span class="hlt">finite</span> element results with analytic results show excellent agreement. The coupled fluid-structure problem may be solved with general purpose <span class="hlt">finite</span> element codes by using an analogy between the equations of <span class="hlt">elasticity</span> and the wave equation of linear acoustics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910006285','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910006285"><span id="translatedtitle">Estimation of the engineering <span class="hlt">elastic</span> constants of a directionally solidified superalloy for <span class="hlt">finite</span> element structural analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Abdul-Aziz, Ali; Kalluri, Sreeramesh</p> <p>1991-01-01</p> <p>The temperature-dependent engineering <span class="hlt">elastic</span> constants of a directionally solidified nickel-base superalloy were estimated from the single-crystal <span class="hlt">elastic</span> constants of nickel and MAR-MOO2 superalloy by using Wells' method. In this method, the directionally solidified (columnar-grained) nickel-base superalloy was modeled as a transversely isotropic material, and the five independent <span class="hlt">elastic</span> constants of the transversely isotropic material were determined from the three independent <span class="hlt">elastic</span> constants of a cubic single crystal. Solidification for both the single crystals and the directionally solidified superalloy was assumed to be along the (001) direction. Temperature-dependent Young's moduli in longitudinal and transverse directions, shear moduli, and Poisson's ratios were tabulated for the directionally solidified nickel-base superalloy. These engineering <span class="hlt">elastic</span> constants could be used as input for performing <span class="hlt">finite</span> element structural analysis of directionally solidified turbine engine components.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016CompM..57..277O&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016CompM..57..277O&link_type=ABSTRACT"><span id="translatedtitle">A computational framework for polyconvex large <span class="hlt">strain</span> <span class="hlt">elasticity</span> for geometrically exact beam theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ortigosa, Rogelio; Gil, Antonio J.; Bonet, Javier; Hesch, Christian</p> <p>2016-02-01</p> <p>In this paper, a new computational framework is presented for the analysis of nonlinear beam <span class="hlt">finite</span> elements subjected to large <span class="hlt">strains</span>. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) in the context of three dimensional polyconvex <span class="hlt">elasticity</span> is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55-70, 1985), the starting point of so many other <span class="hlt">finite</span> element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large <span class="hlt">strains</span>, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam <span class="hlt">strain</span> measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney-Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional <span class="hlt">elasticity</span> and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JAMTP..56..667B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JAMTP..56..667B"><span id="translatedtitle">Dynamics of the antiplane <span class="hlt">strain</span> of a nonlinear <span class="hlt">elastic</span> body</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bondar', B. D.</p> <p>2015-07-01</p> <p>The dynamic antiplane <span class="hlt">strain</span> of an incompressible cylindrical body is studied in a nonlinear formulation in actual variables. A representation of the velocity and acceleration through the displacement is obtained. The problem of the body deformation with account for geometrical and physical nonlinearities is reduced to an initial boundary-value problem for the displacement. The displacement found is used to determine the pressure and stresses. For a body with a quadratic <span class="hlt">elastic</span> potential, plane waves and self-similar motion are studied. The linear potential is used to investigate the deformation of a hollow elliptical cylinder for which analytical expressions for displacement and stresses are found and the external load is determined. It is shown that, due to the degeneration of the inner cavity of the body to a plane section, the load on the section remains limited.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CMT....27..739W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CMT....27..739W"><span id="translatedtitle">Harmonic three-phase circular inclusions in <span class="hlt">finite</span> <span class="hlt">elasticity</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wang, Xu; Schiavone, Peter</p> <p>2015-09-01</p> <p>We study the exterior stress field in a three-phase circular inclusion which is bonded to the surrounding matrix through an intermediate interphase layer. All three phases belong to a particular class of compressible hyperelastic materials of harmonic type. We focus on the design of a harmonic <span class="hlt">elastic</span> inclusion which by definition, does not disturb the sum of the normal stresses in the surrounding matrix. We show that in order to make the coated inclusion harmonic, certain inequalities concerning the material and geometric parameters of the three-phase composite must first be satisfied. The corresponding remote loading parameters can then be uniquely determined while keeping the associated phase angles arbitrary. Our results allow for both uniform and non-uniform remote loading. We show that the stress field inside the inclusion is uniform when the remote loading is uniform.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2015CompM..56...87H&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2015CompM..56...87H&link_type=ABSTRACT"><span id="translatedtitle">Tangential differential calculus and the <span class="hlt">finite</span> element modeling of a large deformation <span class="hlt">elastic</span> membrane problem</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hansbo, Peter; Larson, Mats G.; Larsson, Fredrik</p> <p>2015-07-01</p> <p>We develop a <span class="hlt">finite</span> element method for a large deformation membrane <span class="hlt">elasticity</span> problem on meshed curved surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also applied to form finding problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/440691','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/440691"><span id="translatedtitle">A mixed <span class="hlt">finite</span> element domain decomposition method for nearly <span class="hlt">elastic</span> wave equations in the frequency domain</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Feng, Xiaobing</p> <p>1996-12-31</p> <p>A non-overlapping domain decomposition iterative method is proposed and analyzed for mixed <span class="hlt">finite</span> element methods for a sequence of noncoercive elliptic systems with radiation boundary conditions. These differential systems describe the motion of a nearly <span class="hlt">elastic</span> solid in the frequency domain. The convergence of the iterative procedure is demonstrated and the rate of convergence is derived for the case when the domain is decomposed into subdomains in which each subdomain consists of an individual element associated with the mixed <span class="hlt">finite</span> elements. The hybridization of mixed <span class="hlt">finite</span> element methods plays a important role in the construction of the discrete procedure.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/biblio/665159','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/biblio/665159"><span id="translatedtitle">On the measurement of <span class="hlt">strain</span> in coatings formed on a wrinkled <span class="hlt">elastic</span> substrate</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Gong, X.Y.; Clarke, D.R.</p> <p>1998-12-01</p> <p>Highly stressed coatings, such as those formed by oxidation can, on occasion, wrinkle. Such wrinkling has been suggested as a mode of deformation by which the overall <span class="hlt">strain</span> energy in a compressively stressed coating can be reduced. One of the consequences of wrinkling is that the <span class="hlt">strain</span> in the coating does not remain independent of position, but rather varies over the wavelength of the wrinkling. The <span class="hlt">strain</span> variation caused by sinusoidal wrinkling is calculated using <span class="hlt">finite</span>-element methods and the effects on both photostimulated Cr{sup 3+} luminescence piezospectroscopy measurements and X-ray measurements calculated. Wrinkling is shown to decease the <span class="hlt">elastic-strain</span>-energy density in the coating. A direct measure of the decrease in the shift in the R2 Cr{sup 3+} luminescence line and the X-ray diffraction peaks. Wrinkling of a compressive coating also causes stresses to be created perpendicular to the coating-substrate interface, tensile at the crests in the wrinkles, and compressive stress at the troughs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900019298','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900019298"><span id="translatedtitle">A hybrid-stress <span class="hlt">finite</span> element for linear anisotropic <span class="hlt">elasticity</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Fly, Gerald W.; Oden, J. Tinsley; Pearson, Mark L.</p> <p>1988-01-01</p> <p>Standard assumed displacement <span class="hlt">finite</span> elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012MSMSE..20c5016I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012MSMSE..20c5016I"><span id="translatedtitle">Crystal plasticity based <span class="hlt">finite</span> element modelling of large <span class="hlt">strain</span> deformation in AM30 magnesium alloy</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Izadbakhsh, Adel; Inal, Kaan; Mishra, Raja K.</p> <p>2012-04-01</p> <p>In this paper, the <span class="hlt">finite</span> <span class="hlt">strain</span> plastic deformation of AM30 magnesium alloy has been simulated using the crystal plasticity <span class="hlt">finite</span> element method. The simulations have been carried out using a rate-dependent <span class="hlt">elastic</span>-viscoplastic crystal plasticity constitutive model implemented in a user defined material subroutine (UMAT) in the commercial software LS-DYNA. The plastic deformation mechanisms accounted for in the model are the slip systems in the matrix (parent grain), extension twinning systems and the slip systems inside the extension twinned regions. The parameters of the constitutive model have been calibrated using the experimental data. The calibrated model has then been used to predict the deformation of AM30 magnesium alloy in bending and simple shear. For the bending <span class="hlt">strain</span> path, the effects of texture on the <span class="hlt">strain</span> accommodated by the deformation mechanisms and bending moment have been investigated. For simple shear, the effects of texture on the relative activity of deformation mechanisms, shear stress and texture evolution have been investigated. Also, the effect of twinning on shear stress and texture evolution has been studied. The numerical analyses predicted a more uniform <span class="hlt">strain</span> distribution during bending and simple shear for rolled texture compared with extruded texture.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/biblio/20034181','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/biblio/20034181"><span id="translatedtitle">Experimental investigation of stress and <span class="hlt">strain</span> fields in a ductile matrix surrounding an <span class="hlt">elastic</span> inclusion</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Nugent, E.E.; Calhoun, R.B.; Mortensen, A.</p> <p>2000-04-19</p> <p>A method for measuring stress and <span class="hlt">strain</span> distributions within a ductile material deforming by dislocational slip is developed. The method exploits the transparency and room-temperature ductility of silver chloride, and combines the techniques of photoelasticity and marker tracking. This method is used to investigate the deformation of an elasto-plastic ductile matrix surrounding an isolated stiff fiber, the grain size of the material being slightly smaller than the fiber length. The data are compared to predictions of <span class="hlt">finite</span> element calculations which take the matrix to be an isotropic elasto-plastic von Mises continuum. It is found that this model does not fully capture all of the features of the experimental data. Data suggest that the cause for observed discrepancies is the strong influence exerted by grain boundaries and grain orientation on the distribution of stress and <span class="hlt">strain</span> within the matrix. A comparison is also made between the data and predictions of the Eshelby equivalent inclusion calculation, to show that a far higher level of discrepancy results than with the <span class="hlt">finite</span> element calculations; this is caused by the fact that the Eshelby equivalent inclusion calculation is essentially <span class="hlt">elastic</span> and thus allows significant stress concentrations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4058877','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4058877"><span id="translatedtitle">Bulk metallic glass composite with good tensile ductility, high strength and large <span class="hlt">elastic</span> <span class="hlt">strain</span> limit</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Wu, Fu-Fa; Chan, K. C.; Jiang, Song-Shan; Chen, Shun-Hua; Wang, Gang</p> <p>2014-01-01</p> <p>Bulk metallic glasses exhibit high strength and large <span class="hlt">elastic</span> <span class="hlt">strain</span> limit but have no tensile ductility. However, bulk metallic glass composites reinforced by in-situ dendrites possess significantly improved toughness but at the expense of high strength and large <span class="hlt">elastic</span> <span class="hlt">strain</span> limit. Here, we report a bulk metallic glass composite with strong <span class="hlt">strain</span>-hardening capability and large <span class="hlt">elastic</span> <span class="hlt">strain</span> limit. It was found that, by plastic predeformation, the bulk metallic glass composite can exhibit both a large <span class="hlt">elastic</span> <span class="hlt">strain</span> limit and high strength under tension. These unique <span class="hlt">elastic</span> mechanical properties are attributed to the reversible B2↔B19′ phase transformation and the plastic-predeformation-induced complicated stress state in the metallic glass matrix and the second phase. These findings are significant for the design and application of bulk metallic glass composites with excellent mechanical properties. PMID:24931632</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3171755','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3171755"><span id="translatedtitle">A Micromechanics <span class="hlt">Finite-Strain</span> Constitutive Model of Fibrous Tissue</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Chen, Huan; Liu, Yi; Zhao, Xuefeng; Lanir, Yoram; Kassab, Ghassan S.</p> <p>2011-01-01</p> <p>Biological tissues have unique mechanical properties due to the wavy fibrous collagen and elastin microstructure. In inflation, a vessel easily distends under low pressure but becomes stiffer when the fibers are straightened to take up the load. The current microstructural models of blood vessels assume affine deformation; i.e., the deformation of each fiber is assumed to be identical to the macroscopic deformation of the tissue. This uniform-field (UF) assumption leads to the macroscopic (or effective) <span class="hlt">strain</span> energy of the tissue that is the volumetric sum of the contributions of the tissue components. Here, a micromechanics-based constitutive model of fibrous tissue is developed to remove the affine assumption and to take into consideration the heterogeneous interactions between the fibers and the ground substance. The development is based on the framework of a recently developed second-order homogenization theory, and takes into account the waviness, orientations, and spatial distribution of the fibers, as well as the material nonlinearity at <span class="hlt">finite-strain</span> deformation. In an illustrative simulation, the predictions of the macroscopic stress-<span class="hlt">strain</span> relation, and the statistical deformation of the fibers are compared to the UF model, as well as <span class="hlt">finite</span>-element (FE) simulation. Our predictions agree well with the FE results, while the UF predictions significantly overestimate. The effects of fiber distribution and waviness on the macroscopic stress-<span class="hlt">strain</span> relation are also investigated. The present mathematical model may serves as a foundation for native as well as for engineered tissues and biomaterials. PMID:21927506</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011JMPSo..59.1823C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011JMPSo..59.1823C"><span id="translatedtitle">A micromechanics <span class="hlt">finite-strain</span> constitutive model of fibrous tissue</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chen, Huan; Liu, Yi; Zhao, Xuefeng; Lanir, Yoram; Kassab, Ghassan S.</p> <p>2011-09-01</p> <p>Biological tissues have unique mechanical properties due to the wavy fibrous collagen and elastin microstructure. In inflation, a vessel easily distends under low pressure but becomes stiffer when the fibers are straightened to take up the load. The current microstructural models of blood vessels assume affine deformation, i.e., the deformation of each fiber is assumed to be identical to the macroscopic deformation of the tissue. This uniform-field (UF) assumption leads to the macroscopic (or effective) <span class="hlt">strain</span> energy of the tissue that is the volumetric sum of the contributions of the tissue components. Here, a micromechanics-based constitutive model of fibrous tissue is developed to remove the affine assumption and to take into consideration the heterogeneous interactions between the fibers and the ground substance. The development is based on the framework of a recently developed second-order homogenization theory, and takes into account the waviness, orientations and spatial distribution of the fibers, as well as the material nonlinearity at <span class="hlt">finite-strain</span> deformation. In an illustrative simulation, the predictions of the macroscopic stress-<span class="hlt">strain</span> relation and the statistical deformation of the fibers are compared to the UF model, as well as <span class="hlt">finite</span>-element (FE) simulation. Our predictions agree well with the FE results, while the UF predictions significantly overestimate. The effects of fiber distribution and waviness on the macroscopic stress-<span class="hlt">strain</span> relation are also investigated. The present mathematical model may serves as a foundation for native as well as for engineered tissues and biomaterials.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995ApOpt..34.4993P&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995ApOpt..34.4993P&link_type=ABSTRACT"><span id="translatedtitle"><span class="hlt">Elastic</span> transducers incorporating <span class="hlt">finite</span>-length optical paths</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Peters, Kara J.; Washabaugh, Peter D.</p> <p>1995-08-01</p> <p>Frequently, when designing a structure to incorporate integrated sensors, one sacrifices the stiffness of the system to improve sensitivity. However, the use of interferometric displacement sensors that tessellate throughout the volume of a structure has the potential to allow the precision and range of the component measurement to scale with the geometry of the device rather than the maximum <span class="hlt">strain</span> in the structure. The design of stiff structures that measure all six resultant-load components is described. In addition, an advanced torsion sensor and a linear acceleration transducer are also discussed. Finally, invariant paths are presented that allow the in situ integrity of a structural volume to be monitored with a single pair of displacement sensors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006IJCEM...7..331Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006IJCEM...7..331Z"><span id="translatedtitle">On a New Concept and Foundations of an Arbitrary Reference Configuration (ARC) Theory and Formulation for Computational <span class="hlt">Finite</span> Deformation Applications—Part I: <span class="hlt">Elasticity</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhou, X.; Sha, D.; Tamma, K. K.</p> <p>2006-10-01</p> <p>Of interest here are the class of static/dynamic <span class="hlt">finite</span> deformation problems that arise in computational mechanics, and the question of the suitability in employing the total <span class="hlt">strain</span> measure for this class of problems is raised. An attempt to resolve the problem by proposing a new arbitrary reference configuration (ARC) framework is described in this exposition. The ARC framework consists of the ARC <span class="hlt">elasticity</span>, which bridges the Truesdell stress rate hypo-<span class="hlt">elasticity</span> and the St. Venant-Kirchhoff hyperelasticity, and the ARC Lagrangian formulation, which bridges the updated Lagrangian formulation and the total Lagrangian formulation. The ARC framework serves as a generalized computational framework to handle both the computational infinitesimal and the <span class="hlt">finite</span> deformation/<span class="hlt">strain</span> deformation applications in a consistent and unified manner. In part II of the paper [1], we further extend the ARC framework to elasto-plasticity.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li class="active"><span>5</span></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_5 --> <div id="page_6" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li class="active"><span>6</span></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="101"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015AGUFMMR21A2608Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015AGUFMMR21A2608Y"><span id="translatedtitle">Three-dimensional analysis of pore effect on composite <span class="hlt">elasticity</span> by means of <span class="hlt">finite</span> element method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yoneda, A.</p> <p>2015-12-01</p> <p>A three-dimensional buffer-layer <span class="hlt">finite</span> element method (FEM) model was developed to investigate the porosity effect on macroscopic <span class="hlt">elasticity</span>. Using the three-dimensional model, the effect of pores on bulk effective <span class="hlt">elastic</span> properties were systematically analyzed by changing the degree of porosity, the aspect ratio of the ellipsoidal pore, and the <span class="hlt">elasticity</span> of the material. The present results in 3D space was compared with the previous ones in 2D space. Derivatives of normalized <span class="hlt">elastic</span> stiffness constants with respect to needle-type porosity are integers, if the Poisson ratio of a matrix material is zero; those derivatives of normalized stiffness <span class="hlt">elastic</span> constants for C33, C44, C11, and C66 converge to -1, -2, -3, and -4, respectively, at the corresponding condition. We proposed a criterion of R <~1/3, where the mutual interaction between pores becomes negligible for macroscopic composite <span class="hlt">elasticity</span>. These derivatives are nearly constant below 5% porosity in the case of spherical pore, suggesting that the interaction between neighboring pores is insignificant if the representative size of the pore is less than one-third of the mean distance between neighboring pores. The relations we obtained in this work were successfully applied to invert bulk modulus and rigidity of Cmcm-CaIrO3 as a case study; the performance of the inverting scheme was confirmed through this assessment. Thus the present scheme is applicable to predict macroscopic <span class="hlt">elasticity</span> of porous object as well.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JMPSo..84..293N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JMPSo..84..293N"><span id="translatedtitle">A theory of <span class="hlt">finite</span> <span class="hlt">strain</span> magneto-poromechanics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nedjar, B.</p> <p>2015-11-01</p> <p>The main purpose of this paper is the multi-physics modeling of magnetically sensitive porous materials. We develop for this a magneto-poromechanics formulation suitable for the description of such a coupling. More specifically, we show how the current state of the art in the mathematical modeling of magneto-mechanics can easily be integrated within the unified framework of continuum thermodynamics of open media, which is crucial in setting the convenient forms of the state laws to fully characterize the behavior of porous materials. Moreover, due to the soft nature of these materials in general, the formulation is directly developed within the <span class="hlt">finite</span> <span class="hlt">strain</span> range. In a next step, a modeling example is proposed and detailed for the particular case of magneto-active foams with reversible deformations. In particular, due to their potentially high change in porosity, a nonlinear porosity law recently proposed is used to correctly describe the fluid flow through the interconnected pores when the solid skeleton is <span class="hlt">finitely</span> <span class="hlt">strained</span> causing fluid release or reabsorption. From the numerical point of view, the variational formulation together with an algorithmic design is described for an easy implementation within the context of the <span class="hlt">finite</span> element method. Finally, a set of numerical simulations is presented to illustrate the effectiveness of the proposed framework.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/319661','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/319661"><span id="translatedtitle">Simple structures test for <span class="hlt">elastic</span>-plastic <span class="hlt">strain</span> acceptance criterion validation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Trimble, T.F.; Krech, G.R.</p> <p>1997-11-01</p> <p>A Simple Structures Test Program was performed where several cantilevered beam and fixed-end beam test specimens (fabricated from HY-80 steel) were subjected to a series of analytically predetermined rapidly applied transient dynamic input loads. The primary objective of the test program was to obtain dynamic nonlinear response for simple structures subjected to these load inputs. Data derived from these tests was subsequently used to correlate to analysis predictions to assess the capability to analytically predict <span class="hlt">elastic</span>-plastic nonlinear material behavior in structures using typical time-dependent (transient) design methods and the ABAQUS <span class="hlt">finite</span> element analysis code. The installation of a significant amount of instrumentation on these specimens and post-test measurements enabled the monitoring and recording of <span class="hlt">strain</span> levels, displacements, accelerations, and permanent set. An assessment of modeling parameters such as the element type and mesh refinement was made using these test results. In addition, currently available material models and the incremental time step procedure used in the transient analyses were evaluated. Comparison of test data to analysis results shows that displacements, accelerations, and peak <span class="hlt">strain</span> can be predicted with a reasonable level of accuracy using detailed solid models of the tested specimens. Permanent set is overpredicted by a factor of approximately two. However, the accuracy of the prediction of permanent set is being enhanced by updating material modeling in the ABAQUS code to account for effects of <span class="hlt">strain</span> reversal in oscillatory behavior of dynamically loaded specimens.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFD.R8005T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFD.R8005T"><span id="translatedtitle">Mechanisms of <span class="hlt">elastic</span> enhancement and hindrance for <span class="hlt">finite</span> length undulatory swimmers in viscoelastic fluids</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Thomases, Becca; Guy, Robert</p> <p>2014-11-01</p> <p>A computational model of <span class="hlt">finite</span>-length undulatory swimmers is used to examine the physical origin of the effect of <span class="hlt">elasticity</span> on swimming speed. We explore two distinct target swimming strokes, one derived from the motion of C. elegans, with large head undulations, and a contrasting stroke with large tail undulations. We show that both favorable stroke asymmetry and swimmer <span class="hlt">elasticity</span> contribute to a speed-up, but a substantial boost results only when these two effects work together. We reproduce conflicting results from the literature simply by changing relevant physical parameters.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhRvL.113i8102T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhRvL.113i8102T"><span id="translatedtitle">Mechanisms of <span class="hlt">Elastic</span> Enhancement and Hindrance for <span class="hlt">Finite</span>-Length Undulatory Swimmers in Viscoelastic Fluids</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Thomases, Becca; Guy, Robert D.</p> <p>2014-08-01</p> <p>A computational model of <span class="hlt">finite</span>-length undulatory swimmers is used to examine the physical origin of the effect of <span class="hlt">elasticity</span> on swimming speed. We explore two distinct target swimming strokes: one derived from the motion of Caenorhabditis elegans, with large head undulations, and a contrasting stroke with large tail undulations. We show that both favorable stroke asymmetry and swimmer <span class="hlt">elasticity</span> contribute to a speed-up, but a substantial boost results only when these two effects work together. We reproduce conflicting results from the literature simply by changing relevant physical parameters.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CMT....28..477N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CMT....28..477N"><span id="translatedtitle">The exponentiated Hencky-logarithmic <span class="hlt">strain</span> energy: part III—coupling with idealized multiplicative isotropic <span class="hlt">finite</span> <span class="hlt">strain</span> plasticity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Neff, Patrizio; Ghiba, Ionel-Dumitrel</p> <p>2016-03-01</p> <p>We investigate an immediate application in <span class="hlt">finite</span> <span class="hlt">strain</span> multiplicative plasticity of the family of isotropic volumetric-isochoric decoupled <span class="hlt">strain</span> energies F mapsto W_eH(F):= widehat{W}_eH(U) := μ/k e^{k | dev_n log {U}|^2}+κ/2 {widehat{k}} e^{widehat{k} [ tr(log U)]^2}&quad if& det F > 0, + ∞ & quad if & det F ≤ 0, based on the Hencky-logarithmic (true, natural) <span class="hlt">strain</span> tensor {log U} . Here, {μ > 0} is the infinitesimal shear modulus, {κ=2 μ+3λ/3 > 0} is the infinitesimal bulk modulus with λ the first Lamé constant, {k,widehat{k}} are additional dimensionless material parameters, {F=nabla \\varphi} is the gradient of deformation, {U=√{F^T F}} is the right stretch tensor, and dev n {log {U} =log {U}-1/n tr(log {U})\\cdot{1}} is the deviatoric part of the <span class="hlt">strain</span> tensor {log U} . Based on the multiplicative decomposition {F=F_e F_p} , we couple these energies with some isotropic elasto-plastic flow rules {F_p {dt}/[F_p^{-1}]in-partial χ(dev_3 Σe)} defined in the plastic distortion F p , where {partial χ} is the subdifferential of the indicator function {χ} of the convex <span class="hlt">elastic</span> domain {E_e({Σe},1/3{σ}_{y}^2)} in the mixed-variant {Σe} -stress space, {Σe=F_e^T D_{F_e}W_iso(F_e)} , and {W_iso(F_e)} represents the isochoric part of the energy. While {W_eH} may loose ellipticity, we show that loss of ellipticity is effectively prevented by the coupling with plasticity, since the ellipticity domain of {W_eH} on the one hand and the <span class="hlt">elastic</span> domain in {Σe} -stress space on the other hand are closely related. Thus, the new formulation remains elliptic in <span class="hlt">elastic</span> unloading at any given plastic predeformation. In addition, in this domain, the true stress-true <span class="hlt">strain</span> relation remains monotone, as observed in experiments.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/837670','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/837670"><span id="translatedtitle">Probing the <span class="hlt">Elastic</span>-Plastic, Time-Dependant Response of Test Fasteners using <span class="hlt">Finite</span> Element Analysis (FEA)</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>ML Renauld; H Lien</p> <p>2004-12-13</p> <p>The evolution of global and local stress/<span class="hlt">strain</span> conditions in test fasteners under test conditions is investigated using <span class="hlt">elastic</span>-plastic, time-dependent <span class="hlt">finite</span> element analyses (FEA). For <span class="hlt">elastic</span>-plastic response, tensile data from multiple specimens, material heats and test temperatures are integrated into a single, normalized flow curve from which temperature dependency is extracted. A primary creep model is calibrated with specimen- and fastener-based thermal relaxation data generated under a range of times, temperatures, stress levels and environments. These material inputs are used in analytical simulations of experimental test conditions for several types of fasteners. These fastener models are constructed with automated routines and contact conditions prescribed at all potentially mating surfaces. Thermal or mechanical room temperature pre-loading, as appropriate for a given fastener, is followed by a temperature ramp and a dwell time at constant temperature. While the amount of thermal stress relaxation is limited for the conditions modeled, local stress states are highly dependent upon geometry (thread root radius, for example), pre-loading history and thermal expansion differences between the test fastener and test fixture. Benefits of this FE approach over an <span class="hlt">elastic</span> methodology for stress calculation will be illustrated with correlations of Stress Corrosion Cracking (SCC) initiation time and crack orientations in stress concentrations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014AGUFM.V23D4825A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014AGUFM.V23D4825A"><span id="translatedtitle">Numerical solution of an <span class="hlt">elastic</span> and viscoelastic gravitational models by the <span class="hlt">finite</span> element method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Arjona Almodóvar, A.; Chacón Rebollo, T.; Gómez Marmol, M.</p> <p>2014-12-01</p> <p>Volcanic areas present a lower effective viscosity than usually in the Earth's crust. Both the <span class="hlt">elastic</span>-gravitational and the viscoelastic-gravitational models allow the computation of gravity, deformation, and gravitational potential changes in order to investigate crustal deformations of Earth (see for instance Battaglia & Segall, 2004; Fernández et al. 1999, 2001; Rundle 1980 and 1983). These models can be represented by a coupled system of linear parabolic (for the <span class="hlt">elastic</span> deformations), hyperbolic (for the viscoelastic deformations) and elliptic partial differential equations (for gravitational potential changes) (see for instance Arjona et al. 2008 and 2010). The existence and uniqueness of weak solutions for both the <span class="hlt">elastic</span>-gravitational and viscoelastic-gravitational problem was demonstrated in Arjona et al. (2008 and 2014). The stabilization to solutions of the associated stationary system was proved in Arjona and Díaz (2007). Here we consider the internal source as response to the effect of a pressurized magma reservoir into a multilayered, <span class="hlt">elastic</span>-gravitational and viscoelastic-gravitational earth model. We introduce the numerical analysis of a simplified steady <span class="hlt">elastic</span>-gravitational model, solved by means of the <span class="hlt">finite</span> element method. We also present some numerical tests in realistic situations that confirm the predictions of theoretical order of convergence. Finally, we describe the methodology for both the <span class="hlt">elastic</span>-gravitational and the viscoelastic-gravitational models using 2D and 3D test examples performed with FreeFEM++.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/biblio/22257086','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/biblio/22257086"><span id="translatedtitle">On the origin of <span class="hlt">elastic</span> <span class="hlt">strain</span> limit of bulk metallic glasses</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ding, J. Ma, E.; Cheng, Y. Q.</p> <p>2014-01-06</p> <p>All bulk metallic glasses exhibit a large and almost universal <span class="hlt">elastic</span> <span class="hlt">strain</span> limit. Here, we show that the magnitude of the yield <span class="hlt">strain</span> of the glass state can be quantitatively derived from a characteristic property of the flow state typical in running shear bands (the root cause of yielding). The <span class="hlt">strain</span> in the shear flow is mostly plastic, but associated with it there is an effective <span class="hlt">elastic</span> atomic <span class="hlt">strain</span>. The latter is almost identical for very different model systems in our molecular dynamics simulations, such that the corresponding yield <span class="hlt">strain</span> is universal at any given homologous temperature.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19770021577','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19770021577"><span id="translatedtitle">Three-dimensional <span class="hlt">elastic</span> stress and displacement analysis of <span class="hlt">finite</span> geometry solids containing cracks</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kring, J.; Gyekenyesi, J.; Mendelson, A.</p> <p>1977-01-01</p> <p>The line method of analysis is applied to the Navier-Cauchy equations of <span class="hlt">elastic</span> equilibrium to calculate the displacement fields in <span class="hlt">finite</span> geometry bars containing central, surface, and double-edge cracks under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Normal stresses and the stress intensity factor variation along the crack periphery are calculated using the obtained displacement field. The reported results demonstrate the usefulness of this method in calculating stress intensity factors for commonly encountered crack geometries in <span class="hlt">finite</span> solids.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19730016164','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19730016164"><span id="translatedtitle">Three-dimensional <span class="hlt">elastic</span> stress and displacement analysis of <span class="hlt">finite</span> circular geometry solids containing cracks</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Gyekenyesi, J. P.; Mendelson, A.; Kring, J.</p> <p>1973-01-01</p> <p>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 <span class="hlt">elasticity</span>. Stress and displacement distributions are calculated in an axisymmetric, circular bar of <span class="hlt">finite</span> dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/27480733','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/27480733"><span id="translatedtitle">A multiscale modelling of bone ultrastructure <span class="hlt">elastic</span> proprieties using <span class="hlt">finite</span> elements simulation and neural network method.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Barkaoui, Abdelwahed; Tlili, Brahim; Vercher-Martínez, Ana; Hambli, Ridha</p> <p>2016-10-01</p> <p>Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the <span class="hlt">elastic</span> properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the <span class="hlt">elastic</span> properties of the bone tissue in a multiscale approach including a sensitivity analysis of the <span class="hlt">elastic</span> behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and <span class="hlt">finite</span> elements method (FEM) analysis. The <span class="hlt">elastic</span> properties are estimated using a neural network simulation that previously has been trained with the database results of the <span class="hlt">finite</span> element models. In the results of this work, parametric analysis and averaged <span class="hlt">elastic</span> constants for each length scale are provided. Likewise, the influence of the <span class="hlt">elastic</span> constants of the tissue constituents is also depicted. Results highlight</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GeoJI.204..780J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GeoJI.204..780J"><span id="translatedtitle">Dramatic effect of <span class="hlt">elasticity</span> on thermal softening and <span class="hlt">strain</span> localization during lithospheric shortening</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jaquet, Yoann; Duretz, Thibault; Schmalholz, Stefan M.</p> <p>2016-02-01</p> <p>We present two-dimensional numerical simulations for shortening a viscoelastoplastic lithosphere to quantify the impact of <span class="hlt">elasticity</span> on <span class="hlt">strain</span> localization due to thermal softening. The model conserves energy and mechanical work is converted into heat or stored as <span class="hlt">elastic</span> <span class="hlt">strain</span> energy. For a shear modulus G = 1010 Pa, a prominent lithospheric shear zone forms and <span class="hlt">elastic</span> energy release increases the localization intensity (<span class="hlt">strain</span> rate amplification). For G = 5 × 1010 Pa shear zones still form but deformation is less localized. For G = 1012 Pa, the lithosphere behaves effectively viscoplastic and no shear zones form during homogeneous thickening. Maximal shearing-related increase of surface heat flux is 15-25 mW m-2 and of temperature at lower crustal depth is ˜150 °C, whereby these peak values are transient (0.1-1 My). <span class="hlt">Elasticity</span> and related energy release can significantly contribute to <span class="hlt">strain</span> localization and plate-like behaviour of the lithosphere required for plate tectonics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006PhDT........42N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006PhDT........42N"><span id="translatedtitle">Inverse <span class="hlt">finite</span> element methods for extracting <span class="hlt">elastic</span>-poroviscoelastic properties of cartilage and other soft tissues from indentation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Namani, Ravi</p> <p></p> <p>Mechanical properties are essential for understanding diseases that afflict various soft tissues, such as osteoarthritic cartilage and hypertension which alters cardiovascular arteries. Although the linear <span class="hlt">elastic</span> modulus is routinely measured for hard materials, standard methods are not available for extracting the nonlinear <span class="hlt">elastic</span>, linear <span class="hlt">elastic</span> and time-dependent properties of soft tissues. Consequently, the focus of this work is to develop indentation methods for soft biological tissues; since analytical solutions are not available for the general context, <span class="hlt">finite</span> element simulations are used. First, parametric studies of <span class="hlt">finite</span> indentation of hyperelastic layers are performed to examine if indentation has the potential to identify nonlinear <span class="hlt">elastic</span> behavior. To answer this, spherical, flat-ended conical and cylindrical tips are examined and the influence of thickness is exploited. Also the influence of the specimen/substrate boundary condition (slip or non-slip) is clarified. Second, a new inverse method---the hyperelastic extraction algorithm (HPE)---was developed to extract two nonlinear <span class="hlt">elastic</span> parameters from the indentation force-depth data, which is the basic measurement in an indentation test. The accuracy of the extracted parameters and the influence of noise in measurements on this accuracy were obtained. This showed that the standard Berkovitch tip could only extract one parameter with sufficient accuracy, since the indentation force-depth curve has limited sensitivity to both nonlinear <span class="hlt">elastic</span> parameters. Third, indentation methods for testing tissues from small animals were explored. New methods for flat-ended conical tips are derived. These account for practical test issues like the difficulty in locating the surface or soft specimens. Also, <span class="hlt">finite</span> element simulations are explored to elucidate the influence of specimen curvature on the indentation force-depth curve. Fourth, the influence of inhomogeneity and material anisotropy on the extracted</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/biblio/22230856','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/biblio/22230856"><span id="translatedtitle">Variational integrators for the dynamics of thermo-<span class="hlt">elastic</span> solids with <span class="hlt">finite</span> speed thermal waves</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Mata, Pablo</p> <p>2014-01-15</p> <p>This paper formulates variational integrators for <span class="hlt">finite</span> element discretizations of deformable bodies with heat conduction in the form of <span class="hlt">finite</span> speed thermal waves. The cornerstone of the construction consists in taking advantage of the fact that the Green–Naghdi theory of type II for thermo-<span class="hlt">elastic</span> solids has a Hamiltonian structure. Thus, standard techniques to construct variational integrators can be applied to <span class="hlt">finite</span> element discretizations of the problem. The resulting discrete-in-time trajectories are then consistent with the laws of thermodynamics for these systems: for an isolated system, they exactly conserve the total entropy, and nearly exactly conserve the total energy over exponentially long periods of time. Moreover, linear and angular momenta are also exactly conserved whenever the exact system does. For definiteness, we construct an explicit second-order accurate algorithm for affine tetrahedral elements in two and three dimensions, and demonstrate its performance with numerical examples.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013PMB....58.8457B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PMB....58.8457B"><span id="translatedtitle">A direct vulnerable atherosclerotic plaque <span class="hlt">elasticity</span> reconstruction method based on an original material-<span class="hlt">finite</span> element formulation: theoretical framework</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bouvier, Adeline; Deleaval, Flavien; Doyley, Marvin M.; Yazdani, Saami K.; Finet, Gérard; Le Floc'h, Simon; Cloutier, Guy; Pettigrew, Roderic I.; Ohayon, Jacques</p> <p>2013-12-01</p> <p>The peak cap stress (PCS) amplitude is recognized as a biomechanical predictor of vulnerable plaque (VP) rupture. However, quantifying PCS in vivo remains a challenge since the stress depends on the plaque mechanical properties. In response, an iterative material <span class="hlt">finite</span> element (FE) <span class="hlt">elasticity</span> reconstruction method using <span class="hlt">strain</span> measurements has been implemented for the solution of these inverse problems. Although this approach could resolve the mechanical characterization of VPs, it suffers from major limitations since (i) it is not adapted to characterize VPs exhibiting high material discontinuities between inclusions, and (ii) does not permit real time <span class="hlt">elasticity</span> reconstruction for clinical use. The present theoretical study was therefore designed to develop a direct material-FE algorithm for <span class="hlt">elasticity</span> reconstruction problems which accounts for material heterogeneities. We originally modified and adapted the extended FE method (Xfem), used mainly in crack analysis, to model material heterogeneities. This new algorithm was successfully applied to six coronary lesions of patients imaged in vivo with intravascular ultrasound. The results demonstrated that the mean relative absolute errors of the reconstructed Young's moduli obtained for the arterial wall, fibrosis, necrotic core, and calcified regions of the VPs decreased from 95.3±15.56%, 98.85±72.42%, 103.29±111.86% and 95.3±10.49%, respectively, to values smaller than 2.6 × 10-8±5.7 × 10-8% (i.e. close to the exact solutions) when including modified-Xfem method into our direct <span class="hlt">elasticity</span> reconstruction method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016CompM..57..193K&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016CompM..57..193K&link_type=ABSTRACT"><span id="translatedtitle">Mixed boundary conditions for FFT-based homogenization at <span class="hlt">finite</span> <span class="hlt">strains</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kabel, Matthias; Fliegener, Sascha; Schneider, Matti</p> <p>2016-02-01</p> <p>In this article we introduce a Lippmann-Schwinger formulation for the unit cell problem of periodic homogenization of <span class="hlt">elasticity</span> at <span class="hlt">finite</span> <span class="hlt">strains</span> incorporating arbitrary mixed boundary conditions. Such problems occur frequently, for instance when validating computational results with tensile tests, where the deformation gradient in loading direction is fixed, as is the stress in the corresponding orthogonal plane. Previous Lippmann-Schwinger formulations involving mixed boundary can only describe tensile tests where the vector of applied force is proportional to a coordinate direction. Utilizing suitable orthogonal projectors we develop a Lippmann-Schwinger framework for arbitrary mixed boundary conditions. The resulting fixed point and Newton-Krylov algorithms preserve the positive characteristics of existing FFT-algorithms. We demonstrate the power of the proposed methods with a series of numerical examples, including continuous fiber reinforced laminates and a complex nonwoven structure of a long fiber reinforced thermoplastic, resulting in a speed-up of some computations by a factor of 1000.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/18996702','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/18996702"><span id="translatedtitle"><span class="hlt">Finite</span>-element study of <span class="hlt">strain</span> field in <span class="hlt">strained</span>-Si MOSFET.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Liu, H H; Duan, X F; Xu, Q X</p> <p>2009-02-01</p> <p>The <span class="hlt">strain</span> field in the channel of a p-type metal-oxide-semiconductor field effect transistor fabricated by integrating Ge pre-amorphization implantation for source/drain regions is evaluated using a <span class="hlt">finite</span>-element method combining with large angle convergent-beam electron diffraction (LACBED). The <span class="hlt">finite</span>-element calculation shows that there is a very large compressive <span class="hlt">strain</span> in the top layer of the channel region caused by a low dose of Ge ion implantation in the source and drain extension regions. Moreover, a transition region is formed in the bottom of the channel region and the top of the Si substrate. These calculation results are in good agreement with the LACBED experiments. PMID:18996702</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JMPSo..68..161P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JMPSo..68..161P"><span id="translatedtitle">Singularity-free dislocation dynamics with <span class="hlt">strain</span> gradient <span class="hlt">elasticity</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Po, Giacomo; Lazar, Markus; Seif, Dariush; Ghoniem, Nasr</p> <p>2014-08-01</p> <p>The singular nature of the <span class="hlt">elastic</span> 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 <span class="hlt">elasticity</span>, attempts to regularize the <span class="hlt">elastic</span> fields of discrete dislocations encounter intrinsic difficulties. On the other hand, in gradient <span class="hlt">elasticity</span>, the issue of singularity can be removed at the outset and smooth <span class="hlt">elastic</span> 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 <span class="hlt">elasticity</span> 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 <span class="hlt">elasticity</span> 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 <span class="hlt">elasticity</span> 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</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1177388','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1177388"><span id="translatedtitle">An <span class="hlt">Elastic</span> Plastic Contact Model with <span class="hlt">Strain</span> Hardening for the LAMMPS Granular Package</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Kuhr, Bryan; Brake, Matthew Robert; Lechman, Jeremy B.</p> <p>2015-03-01</p> <p>The following details the implementation of an analytical <span class="hlt">elastic</span> plastic contact model with <span class="hlt">strain</span> hardening for normal im pacts into the LAMMPS granular package. The model assumes that, upon impact, the co llision has a period of <span class="hlt">elastic</span> loading followed by a period of mixed <span class="hlt">elastic</span> plas tic loading, with contributions to each mechanism estimated by a hyperbolic seca nt weight function. This function is implemented in the LAMMPS source code as the pair style gran/ep/history. Preliminary tests, simulating the pouring of pure nickel spheres, showed the <span class="hlt">elastic</span>/plastic model took 1.66x as long as similar runs using gran/hertz/history.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li class="active"><span>6</span></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_6 --> <div id="page_7" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li class="active"><span>7</span></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="121"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013AGUFMMR13A2246R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AGUFMMR13A2246R"><span id="translatedtitle">On the influence of <span class="hlt">strain</span> rate in acousto-<span class="hlt">elasticity</span> : experimental results for Berea sandstone</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Riviere, J. V.; Candela, T.; Scuderi, M.; Marone, C.; Guyer, R. A.; Johnson, P. A.</p> <p>2013-12-01</p> <p><span class="hlt">Elastic</span> nonlinear effects are pervasive in the Earth, including during strong ground motion, tidal forcing and earthquake slip processes. We study <span class="hlt">elastic</span> nonlinear effects in the laboratory with the goal of developing new methods to probe <span class="hlt">elastic</span> changes in the Earth, and to characterize and understand their origins. Here we report on nonlinear, frequency dispersion effects by applying a method termed dynamic acousto-<span class="hlt">elasticity</span> (DAE), analogous to quasi-static acousto-<span class="hlt">elasticity</span>. DAE allows one to obtain the <span class="hlt">elastic</span> behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. We perform DAE on samples of Berea sandstone subject to 0.5 MPa uniaxial and biaxial loading conditions with oscillating loads at frequencies from 0.001 to 10 Hz and amplitudes of a few 100 kPa. We compare results to DAE measurements made in the kHz range. We observe that the average decrease in modulus due to nonlinear material softening increases with frequency, suggesting a frequency and/or a <span class="hlt">strain</span> rate dependence. Previous quasi-static measurements (Claytor et al., GRL 2009) show that stress-<span class="hlt">strain</span> nonlinear hysteretic behavior disappears when the experiment is performed at a very low <span class="hlt">strain</span>-rate, implying that a rate dependent nonlinear <span class="hlt">elastic</span> model would be useful (Gusev et al., PRB 2004). Our results also suggest that when <span class="hlt">elastic</span> nonlinear Earth processes are studied, stress forcing frequency is an important consideration, and may lead to unexpected behaviors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/750170','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/750170"><span id="translatedtitle">Spatial parallelism of a 3D <span class="hlt">finite</span> difference, velocity-stress <span class="hlt">elastic</span> wave propagation code</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Minkoff, S.E.</p> <p>1999-12-01</p> <p><span class="hlt">Finite</span> difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately, <span class="hlt">finite</span> difference simulations for 3D <span class="hlt">elastic</span> wave propagation are expensive. The authors model waves in a 3D isotropic <span class="hlt">elastic</span> earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered <span class="hlt">finite</span> difference operators. Staggered schemes allow one to obtain additional accuracy (via centered <span class="hlt">finite</span> differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MPI library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing <span class="hlt">finite</span> difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speedup. Because I/O is handled largely outside of the time-step loop (the most expensive part of the simulation) the authors have opted for straight-forward broadcast and reduce operations to handle I/O. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ghost cells. When this communication is balanced against computation by allocating subdomains of reasonable size, they observe excellent scaled speedup. Allocating subdomains of size 25 x 25 x 25 on each node, they achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/15182','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/15182"><span id="translatedtitle">Spatial Parallelism of a 3D <span class="hlt">Finite</span> Difference, Velocity-Stress <span class="hlt">Elastic</span> Wave Propagation Code</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>MINKOFF,SUSAN E.</p> <p>1999-12-09</p> <p><span class="hlt">Finite</span> difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. <span class="hlt">finite</span> difference simulations for 3D <span class="hlt">elastic</span> wave propagation are expensive. We model waves in a 3D isotropic <span class="hlt">elastic</span> earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered <span class="hlt">finite</span> difference operators. Staggered schemes allow one to obtain additional accuracy (via centered <span class="hlt">finite</span> differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing <span class="hlt">finite</span> difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GeoJI.tmp..108Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GeoJI.tmp..108Z"><span id="translatedtitle">A new spectral <span class="hlt">finite</span> volume method for <span class="hlt">elastic</span> wave modelling on unstructured meshes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhang, Wensheng; Zhuang, Yuan; Chung, Eric T.</p> <p>2016-04-01</p> <p>In this paper, we consider a new spectral <span class="hlt">finite</span> volume method for the <span class="hlt">elastic</span> wave equations. Our new <span class="hlt">finite</span> volume method is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order <span class="hlt">finite</span> volume method and the spectral <span class="hlt">finite</span> volume method. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles, and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an over-determined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard <span class="hlt">finite</span> volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2D problems, but the same methodology can be applied to 3D.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20160006415','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20160006415"><span id="translatedtitle"><span class="hlt">Elastic</span> and Piezoelectric Properties of Boron Nitride Nanotube Composites. Part II; <span class="hlt">Finite</span> Element Model</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kim, H. Alicia; Hardie, Robert; Yamakov, Vesselin; Park, Cheol</p> <p>2015-01-01</p> <p>This paper is the second part of a two-part series where the first part presents a molecular dynamics model of a single Boron Nitride Nanotube (BNNT) and this paper scales up to multiple BNNTs in a polymer matrix. This paper presents <span class="hlt">finite</span> element (FE) models to investigate the effective <span class="hlt">elastic</span> and piezoelectric properties of (BNNT) nanocomposites. The nanocomposites studied in this paper are thin films of polymer matrix with aligned co-planar BNNTs. The FE modelling approach provides a computationally efficient way to gain an understanding of the material properties. We examine several FE models to identify the most suitable models and investigate the effective properties with respect to the BNNT volume fraction and the number of nanotube walls. The FE models are constructed to represent aligned and randomly distributed BNNTs in a matrix of resin using 2D and 3D hollow and 3D filled cylinders. The homogenisation approach is employed to determine the overall <span class="hlt">elastic</span> and piezoelectric constants for a range of volume fractions. These models are compared with an analytical model based on Mori-Tanaka formulation suitable for <span class="hlt">finite</span> length cylindrical inclusions. The model applies to primarily single-wall BNNTs but is also extended to multi-wall BNNTs, for which preliminary results will be presented. Results from the Part 1 of this series can help to establish a constitutive relationship for input into the <span class="hlt">finite</span> element model to enable the modeling of multiple BNNTs in a polymer matrix.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19860016596','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19860016596"><span id="translatedtitle">A fourth order accurate <span class="hlt">finite</span> difference scheme for the computation of <span class="hlt">elastic</span> waves</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.</p> <p>1986-01-01</p> <p>A <span class="hlt">finite</span> difference for <span class="hlt">elastic</span> waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-<span class="hlt">elastic</span> interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19770003340','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19770003340"><span id="translatedtitle">Some convergence properties of <span class="hlt">finite</span> element approximations of problems in nonlinear <span class="hlt">elasticity</span> with multi-valued solutions</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Oden, J. T.</p> <p>1976-01-01</p> <p>Some results of studies of convergence and accuracy of <span class="hlt">finite</span> element approximations of certain nonlinear problems encountered in <span class="hlt">finite</span> <span class="hlt">elasticity</span> are presented. A general technique for obtaining error bounds is also described together with an existence theorem. Numerical results obtained by solving a representative problem are also included.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013RMRE...46..315P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013RMRE...46..315P"><span id="translatedtitle">Is there Link between the Type of the Volumetric <span class="hlt">Strain</span> Curve and <span class="hlt">Elastic</span> Constants, Porosity, Stress and <span class="hlt">Strain</span> Characteristics ?</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Palchik, V.</p> <p>2013-03-01</p> <p>The stress [crack damage stress ( σ cd) and uniaxial compressive strength ( σ c)] and <span class="hlt">strain</span> characteristics [maximum total volumetric <span class="hlt">strain</span> ( ɛ cd), axial failure <span class="hlt">strain</span> ( ɛ af)], porosity ( n) and <span class="hlt">elastic</span> constants [<span class="hlt">elastic</span> modulus ( E) and Poisson's ratio ( ν)] and their ratios were coordinated with the existence of two different types (type 1 and type 2) of volumetric <span class="hlt">strain</span> curve. Type 1 volumetric <span class="hlt">strain</span> curve has a reversal point and, therefore, σ cd is less than the uniaxial compressive strength ( σ c). Type 2 has no reversal point, and the bulk volume of rock decreases until its failure occurs (i.e., σ cd = σ c). It is confirmed that the ratio between the <span class="hlt">elastic</span> modulus ( E) and the parameter λ = n/ ɛ cd strongly affects the crack damage stress ( σ cd) for both type 1 and type 2 volumetric <span class="hlt">strain</span> curves. It is revealed that heterogeneous carbonate rock samples exhibit different types of the volumetric <span class="hlt">strain</span> curve even within the same rock formation, and the range of σ cd/ σ c = 0.54-1 for carbonate rocks is wider than the range (0.71 < σ cd/ σ c < 0.84) obtained by other researchers for granites, sandstones and quartzite. It is established that there is no connection between the type of the volumetric <span class="hlt">strain</span> curve and values of n, E, σ cd, ν, E/(1 - 2 ν), M R = E/ σ c and E/ λ. On the other hand, the type of volumetric <span class="hlt">strain</span> curve is connected with the values of λ and the ratio between the axial failure <span class="hlt">strain</span> ( ɛ af) and the maximum total volumetric <span class="hlt">strain</span> ( ɛ cd). It is argued that in case of small ɛ af/ ɛ cd-small λ, volumetric <span class="hlt">strain</span> curve follows the type 2.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CompM..56.1039W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CompM..56.1039W"><span id="translatedtitle">A <span class="hlt">strain</span>-morphed nonlocal meshfree method for the regularized particle simulation of <span class="hlt">elastic</span>-damage induced <span class="hlt">strain</span> localization problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wu, C. T.; Wu, Youcai; Koishi, M.</p> <p>2015-12-01</p> <p>In this work, a <span class="hlt">strain</span>-morphed nonlocal meshfree method is developed to overcome the computational challenges for the simulation of <span class="hlt">elastic</span>-damage induced <span class="hlt">strain</span> localization problem when the spatial domain integration is performed based on the background cells and Gaussian quadrature rule. The new method is established by introducing the decomposed <span class="hlt">strain</span> fields from a meshfree <span class="hlt">strain</span> smoothing to the penalized variational formulation. While the stabilization <span class="hlt">strain</span> field circumvents the onerous zero-energy modes inherent in the direct nodal integration scheme, the regularization <span class="hlt">strain</span> field aims to avoid the pathological localization of deformation in Galerkin meshfree solution using the weak-discontinuity approach. A <span class="hlt">strain</span> morphing algorithm is introduced to couple the locality and non-locality of the decomposed <span class="hlt">strain</span> approximations such that the continuity condition in the coupled <span class="hlt">strain</span> field is met under the Galerkin meshfree framework using the direct nodal integration scheme. Three numerical benchmarks are examined to demonstrate the effectiveness and accuracy of the proposed method for the regularization of <span class="hlt">elastic</span>-damage induced <span class="hlt">strain</span> localization problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960025213','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960025213"><span id="translatedtitle">Non-Reflecting Regions for <span class="hlt">Finite</span> Difference Methods in Modeling of <span class="hlt">Elastic</span> Wave Propagation in Plates</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kishoni, Doron; Taasan, Shlomo</p> <p>1994-01-01</p> <p>Solution of the wave equation using techniques such as <span class="hlt">finite</span> difference or <span class="hlt">finite</span> element methods can model <span class="hlt">elastic</span> wave propagation in solids. This requires mapping the physical geometry into a computational domain whose size is governed by the size of the physical domain of interest and by the required resolution. This computational domain, in turn, dictates the computer memory requirements as well as the calculation time. Quite often, the physical region of interest is only a part of the whole physical body, and does not necessarily include all the physical boundaries. Reduction of the calculation domain requires positioning an artificial boundary or region where a physical boundary does not exist. It is important however that such a boundary, or region, will not affect the internal domain, i.e., it should not cause reflections that propagate back into the material. This paper concentrates on the issue of constructing such a boundary region.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010MsT..........8P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010MsT..........8P"><span id="translatedtitle"><span class="hlt">Finite</span> Element Modeling of the Behavior of Armor Materials Under High <span class="hlt">Strain</span> Rates and Large <span class="hlt">Strains</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Polyzois, Ioannis</p> <p></p> <p>For years high strength steels and alloys have been widely used by the military for making armor plates. Advances in technology have led to the development of materials with improved resistance to penetration and deformation. Until recently, the behavior of these materials under high <span class="hlt">strain</span> rates and large <span class="hlt">strains</span> has been primarily based on laboratory testing using the Split Hopkinson Pressure Bar apparatus. With the advent of sophisticated computer programs, computer modeling and <span class="hlt">finite</span> element simulations are being developed to predict the deformation behavior of these metals for a variety of conditions similar to those experienced during combat. In the present investigation, a modified direct impact Split Hopkinson Pressure Bar apparatus was modeled using the <span class="hlt">finite</span> element software ABAQUS 6.8 for the purpose of simulating high <span class="hlt">strain</span> rate compression of specimens of three armor materials: maraging steel 300, high hardness armor (HHA), and aluminum alloy 5083. These armor materials, provided by the Canadian Department of National Defence, were tested at the University of Manitoba by others. In this study, the empirical Johnson-Cook visco-plastic and damage models were used to simulate the deformation behavior obtained experimentally. A series of stress-time plots at various projectile impact momenta were produced and verified by comparison with experimental data. The impact momentum parameter was chosen rather than projectile velocity to normalize the initial conditions for each simulation. Phenomena such as the formation of adiabatic shear bands caused by deformation at high <span class="hlt">strains</span> and <span class="hlt">strain</span> rates were investigated through simulations. It was found that the Johnson-Cook model can accurately simulate the behavior of body-centered cubic (BCC) metals such as steels. The maximum shear stress was calculated for each simulation at various impact momenta. The <span class="hlt">finite</span> element model showed that shear failure first occurred in the center of the cylindrical specimen and</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/24113298','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/24113298"><span id="translatedtitle">Cement lines and interlamellar areas in compact bone as <span class="hlt">strain</span> amplifiers - contributors to <span class="hlt">elasticity</span>, fracture toughness and mechanotransduction.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Nobakhti, Sabah; Limbert, Georges; Thurner, Philipp J</p> <p>2014-01-01</p> <p>Bone is multi-scale hierarchical composite material making the prediction of fragility, as well as pinning it to a certain cause, complicated. For proper mechanical simulation and reflection of bone properties in models, microscopic structural features of bone tissue need to be included. This study sets out to gain a mechanistic insight into the role of various microstructural features of bone tissue in particular cement lines and interlamellar areas. Further the hypothesis that compliant interlamellar areas and cement lines within osteonal bone act as <span class="hlt">strain</span> amplifiers was explored. To this end, a series of experimentally-based micromechanical <span class="hlt">finite</span> element models of bovine osteonal bone were developed. Different levels of detail for the bone microstructure were considered and combined with the results of physical three-point bending tests and an analytical composite model of a single osteon. The objective was to examine local and global effects of interface structures. The geometrical and microstructural characteristics of the bone samples were derived from microscopy imaging. Parametric <span class="hlt">finite</span> element studies were conducted to determine optimal values of the <span class="hlt">elastic</span> modulus of interstitial bone and interlamellar areas. The average isotropic <span class="hlt">elastic</span> modulus of interfaces suggested in this study is 88.5MPa. Based on the modelling results, it is shown that interfaces are areas of accumulated <span class="hlt">strain</span> in bone and are likely to act as potential paths for crack propagation. The <span class="hlt">strain</span> amplification capability of interface structures in the order of 10 predicted by the models suggests a new explanation for the levels of <span class="hlt">strain</span> required in bone homoeostasis for maintenance and adaptation. PMID:24113298</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/663574','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/663574"><span id="translatedtitle"><span class="hlt">Elastic</span>-plastic <span class="hlt">strain</span> acceptance criterion for structures subject to rapidly applied transient dynamic loading</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Solonick, W.</p> <p>1996-11-01</p> <p>Rapidly applied transient dynamic loads produce stresses and deflections in structures that typically exceed those from static loading conditions. Previous acceptance criteria for structures designed for rapidly applied transient dynamic loading limited stresses to those determined from <span class="hlt">elastic</span> analysis. Different stress limits were established for different grades of structure depending upon the amount of permanent set considered acceptable. Structure allowed to sustain very limited permanent set is designed to stress limits not significantly greater than yield stress. Greater permanent set in structure under rapidly applied transient dynamic loading conditions is permitted by establishing stress limits that are significantly greater than yield stress but still provide adequate safety margin (with respect to failure). This paper presents a <span class="hlt">strain</span>-based <span class="hlt">elastic</span>-plastic (i.e., inelastic) analysis criterion developed as an alternative to the more conservative stress-based <span class="hlt">elastic</span> analysis stress criterion for structures subjected to rapidly applied transient dynamic loading. The <span class="hlt">strain</span> limits established are based on a fraction of the <span class="hlt">strain</span> at ultimate stress obtained from an engineering stress/<span class="hlt">strain</span> curve of the material. <span class="hlt">Strains</span> limits are categorized by type as membrane or surface and by region as general, local, or concentrated. The application of the <span class="hlt">elastic</span>-plastic criterion provides a more accurate, less conservative design/analysis basis for structures than that used in <span class="hlt">elastic</span> stress-based analysis criteria, while still providing adequate safety margins.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/815192','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/815192"><span id="translatedtitle"><span class="hlt">Elastic</span>-Plastic <span class="hlt">Strain</span> Acceptance Criteria for Structures Subject to Rapidly Applied Transient Dynamic Loading</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>W.R. Solonick</p> <p>2003-04-01</p> <p>Rapidly applied transient dynamic loads produce stresses and deflections in structures that typically exceed those from static loading conditions. Previous acceptance criteria for structures designed for rapidly applied transient dynamic loading limited stresses to those determined from <span class="hlt">elastic</span> analysis. Different stress limits were established for different grades of structure depending upon the amount of permanent set considered acceptable. Structure allowed to sustain very limited permanent set is designed to stress limits not significantly greater than yield stress. Greater permanent set in structure under rapidly applied transient dynamic loading conditions is permitted by establishing stress limits that are significantly greater than yield stress but still provide adequate safety margin (with respect to failure). This paper presents a <span class="hlt">strain</span>-based <span class="hlt">elastic</span>-plastic (i.e., inelastic) analysis criterion developed as an alternative to the more conservative stress-based <span class="hlt">elastic</span> analysis stress criterion for structures subjected to rapidly applied transient dynamic loading. The <span class="hlt">strain</span> limits established are based on material ductility considerations only and are set as a fraction of the <span class="hlt">strain</span> at ultimate stress obtained from an engineering stress/<span class="hlt">strain</span> curve of the material. <span class="hlt">Strains</span> limits are categorized by type as membrane or surface and by region as general, local , or concentrated. The application of the <span class="hlt">elastic</span>-plastic criterion provides a more accurate, less conservative design/analysis basis for structures than that used in <span class="hlt">elastic</span> stress-based analysis criteria, while still providing adequate safety margins.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940010246','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940010246"><span id="translatedtitle"><span class="hlt">Elastic</span>-plastic <span class="hlt">finite</span> element analyses of an unidirectional, 9 vol percent tungsten fiber reinforced copper matrix composite</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Sanfeliz, Jose G.</p> <p>1993-01-01</p> <p>Micromechanical modeling via <span class="hlt">elastic</span>-plastic <span class="hlt">finite</span> element analyses were performed to investigate the effects that the residual stresses and the degree of matrix work hardening (i.e., cold-worked, annealed) have upon the behavior of a 9 vol percent, unidirectional W/Cu composite, undergoing tensile loading. The inclusion of the residual stress-containing state as well as the simulated matrix material conditions proved to be significant since the Cu matrix material exhibited plastic deformation, which affected the subsequent tensile response of the composite system. The stresses generated during cooldown to room temperature from the manufacturing temperature were more of a factor on the annealed-matrix composite, since they induced the softened matrix to plastically flow. This event limited the total load-carrying capacity of this matrix-dominated, ductile-ductile type material system. Plastic deformation of the hardened-matrix composite during the thermal cooldown stage was not considerable, therefore, the composite was able to sustain a higher stress before showing any appreciable matrix plasticity. The predicted room temperature, stress-<span class="hlt">strain</span> response, and deformation stages under both material conditions represented upper and lower bounds characteristic of the composite's tensile behavior. The initial deformation stage for the hardened material condition showed negligible matrix plastic deformation while for the annealed state, its initial deformation stage showed extensive matrix plasticity. Both material conditions exhibited a final deformation stage where the fiber and matrix were <span class="hlt">straining</span> plastically. The predicted stress-<span class="hlt">strain</span> results were compared to the experimental, room temperature, tensile stress-<span class="hlt">strain</span> curve generated from this particular composite system. The analyses indicated that the actual thermal-mechanical state of the composite's Cu matrix, represented by the experimental data, followed the annealed material condition.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016JPCM...28C5302T&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016JPCM...28C5302T&link_type=ABSTRACT"><span id="translatedtitle">Directional anisotropy, <span class="hlt">finite</span> size effect and <span class="hlt">elastic</span> properties of hexagonal boron nitride</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Thomas, Siby; Ajith, K. M.; Valsakumar, M. C.</p> <p>2016-07-01</p> <p>Classical molecular dynamics simulations have been performed to analyze the <span class="hlt">elastic</span> and mechanical properties of two-dimensional (2D) hexagonal boron nitride (h-BN) using a Tersoff-type interatomic empirical potential. We present a systematic study of h-BN for various system sizes. Young’s modulus and Poisson’s ratio are found to be anisotropic for <span class="hlt">finite</span> sheets whereas they are isotropic for the infinite sheet. Both of them increase with system size in accordance with a power law. It is concluded from the computed values of <span class="hlt">elastic</span> constants that h-BN sheets, <span class="hlt">finite</span> or infinite, satisfy Born’s criterion for mechanical stability. Due to the the strong in-plane sp2 bonds and the small mass of boron and nitrogen atoms, h-BN possesses high longitudinal and shear velocities. The variation of bending rigidity with system size is calculated using the Foppl–von Karman approach by coupling the in-plane bending and out-of-plane stretching modes of the 2D h-BN.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JMPSo..74..175H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JMPSo..74..175H"><span id="translatedtitle">A micromechanical damage and fracture model for polymers based on fractional <span class="hlt">strain</span>-gradient <span class="hlt">elasticity</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Heyden, S.; Li, B.; Weinberg, K.; Conti, S.; Ortiz, M.</p> <p>2015-01-01</p> <p>We formulate a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. We show that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain <span class="hlt">elasticity</span> and failure regularized by means of fractional <span class="hlt">strain</span>-gradient <span class="hlt">elasticity</span>. In particular, we derive optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely, the critical energy-release rate of the material, and micromechanical parameters pertaining to the <span class="hlt">elasticity</span> and strength of the polymer chains and to the <span class="hlt">strain</span>-gradient <span class="hlt">elasticity</span> regularization. We show how the critical energy-release rate of specific materials can be determined from test data. Finally, we demonstrate the scope and fidelity of the model by means of an example of application, namely, Taylor-impact experiments of polyurea 1000 rods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JGE....12..435A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JGE....12..435A"><span id="translatedtitle"><span class="hlt">Finite</span> difference <span class="hlt">elastic</span> wave modeling with an irregular free surface using ADER scheme</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Almuhaidib, Abdulaziz M.; Nafi Toksöz, M.</p> <p>2015-06-01</p> <p>In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D <span class="hlt">finite</span> difference solver for the <span class="hlt">elastic</span> wave equation that combines a 4th- order ADER scheme (Arbitrary high-order accuracy using DERivatives), which is widely used in aeroacoustics, with the characteristic variable method at the free surface boundary. The idea is to treat the free surface boundary explicitly by using ghost values of the solution for points beyond the free surface to impose the physical boundary condition. The method is based on the velocity-stress formulation. The ultimate goal is to develop a numerical solver for the <span class="hlt">elastic</span> wave equation that is stable, accurate and computationally efficient. The solver treats smooth arbitrary-shaped boundaries as simple plane boundaries. The computational cost added by treating the topography is negligible compared to flat free surface because only a small number of grid points near the boundary need to be computed. In the presence of topography, using 10 grid points per shortest shear-wavelength, the solver yields accurate results. Benchmark numerical tests using several complex models that are solved by our method and other independent accurate methods show an excellent agreement, confirming the validity of the method for modeling <span class="hlt">elastic</span> waves with an irregular free surface.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/24084656','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/24084656"><span id="translatedtitle"><span class="hlt">Elastic</span> bending modulus of single-layer molybdenum disulfide (MoS2): <span class="hlt">finite</span> thickness effect.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Jiang, Jin-Wu; Qi, Zenan; Park, Harold S; Rabczuk, Timon</p> <p>2013-11-01</p> <p>We derive, from an empirical interaction potential, an analytic formula for the <span class="hlt">elastic</span> bending modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained <span class="hlt">elastic</span> bending modulus of 9.61 eV in SLMoS2 is significantly higher than the bending modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory with experimentally obtained values for the <span class="hlt">elastic</span> constants of SLMoS2. This increase in bending modulus as compared to monolayer graphene is attributed, through our analytic expression, to the <span class="hlt">finite</span> thickness of SLMoS2. Specifically, while each monolayer of S atoms contributes 1.75 eV to the bending modulus, which is similar to the 1.4 eV bending modulus of monolayer graphene, the additional pairwise and angular interactions between out of plane Mo and S atoms contribute 5.84 eV to the bending modulus of SLMoS2. PMID:24084656</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4667184','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4667184"><span id="translatedtitle">Revealing ultralarge and localized <span class="hlt">elastic</span> lattice <span class="hlt">strains</span> in Nb nanowires embedded in NiTi matrix</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Zang, Ketao; Mao, Shengcheng; Cai, Jixiang; Liu, Yinong; Li, Haixin; Hao, Shijie; Jiang, Daqiang; Cui, Lishan</p> <p>2015-01-01</p> <p>Freestanding nanowires have been found to exhibit ultra-large <span class="hlt">elastic</span> <span class="hlt">strains</span> (4 to 7%) and ultra-high strengths, but exploiting their intrinsic superior mechanical properties in bulk forms has proven to be difficult. A recent study has demonstrated that ultra-large <span class="hlt">elastic</span> <span class="hlt">strains</span> of ~6% can be achieved in Nb nanowires embedded in a NiTi matrix, on the principle of lattice <span class="hlt">strain</span> matching. To verify this hypothesis, this study investigated the <span class="hlt">elastic</span> deformation behavior of a Nb nanowire embedded in NiTi matrix by means of in situ transmission electron microscopic measurement during tensile deformation. The experimental work revealed that ultra-large local <span class="hlt">elastic</span> lattice <span class="hlt">strains</span> of up to 8% are induced in the Nb nanowire in regions adjacent to stress-induced martensite domains in the NiTi matrix, whilst other parts of the nanowires exhibit much reduced lattice <span class="hlt">strains</span> when adjacent to the untransformed austenite in the NiTi matrix. These observations provide a direct evidence of the proposed mechanism of lattice <span class="hlt">strain</span> matching, thus a novel approach to designing nanocomposites of superior mechanical properties. PMID:26625854</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li class="active"><span>7</span></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_7 --> <div id="page_8" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li class="active"><span>8</span></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="141"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JMPSo..78..298L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JMPSo..78..298L"><span id="translatedtitle">A higher-order nonlocal <span class="hlt">elasticity</span> and <span class="hlt">strain</span> gradient theory and its applications in wave propagation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lim, C. W.; Zhang, G.; Reddy, J. N.</p> <p>2015-05-01</p> <p>In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the <span class="hlt">strain</span> gradient theories. The modified couple stress theory, which also accounts for a material length scale, is a form of a <span class="hlt">strain</span> gradient theory. The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain. The present paper has the objective of establishing the fact that the length scales present in nonlocal <span class="hlt">elasticity</span> and <span class="hlt">strain</span> gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale. By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal <span class="hlt">elasticity</span> and <span class="hlt">strain</span> gradient theory and it results in a higher-order nonlocal <span class="hlt">strain</span> gradient theory. In this theory, a higher-order nonlocal <span class="hlt">strain</span> gradient <span class="hlt">elasticity</span> system which considers higher-order stress gradients and <span class="hlt">strain</span> gradient nonlocality is proposed. It is based on the nonlocal effects of the <span class="hlt">strain</span> field and first gradient <span class="hlt">strain</span> field. This theory intends to generalize the classical nonlocal <span class="hlt">elasticity</span> theory by introducing a higher-order <span class="hlt">strain</span> tensor with nonlocality into the stored energy function. The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common <span class="hlt">strain</span> gradient theory only considers local higher-order <span class="hlt">strain</span> gradients without nonlocal effects in a global sense. By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016TePhL..42..121G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016TePhL..42..121G"><span id="translatedtitle">Determination of third-order <span class="hlt">elastic</span> moduli via parameters of bulk <span class="hlt">strain</span> solitons</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Garbuzov, F. E.; Samsonov, A. M.; Semenov, A. A.; Shvartz, A. G.</p> <p>2016-02-01</p> <p>A method is proposed aimed for determination of the third-order <span class="hlt">elastic</span> moduli (Murnaghan moduli) based on the estimation of measured parameters of bulk <span class="hlt">strain</span> solitons in the three main waveguide configurations, a rod, a plate, and a shell. Formulas connecting the third-order moduli of the waveguide material and the parameters of a solitary <span class="hlt">strain</span> wave (amplitude, velocity, full width at half-maximum) are derived. If the soliton parameters measured in three waveguide types manufactured from the same material are available, determination of the third-order <span class="hlt">elastic</span> moduli is reduced to the solution of a system of three algebraic equations with a nondegenerate matrix.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/biblio/1051435','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/biblio/1051435"><span id="translatedtitle">Application Of <span class="hlt">Elastic</span> Perfectly Plastic Cyclic Analysis To Assessment Of Creep <span class="hlt">Strain</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Carter, Peter; Jetter, Robert I; Sham, Sam</p> <p>2012-01-01</p> <p>A cyclic <span class="hlt">elastic</span>-perfectly plastic analysis method is proposed which provides a conservative estimate to cyclic creep <span class="hlt">strain</span> accumulation within the ratchet boundary. The method is to check for ratcheting based on an <span class="hlt">elastic</span>-perfectly material with a temperature-dependent pseudo yield stress defined by temperature, time and stress to give 1% creep <span class="hlt">strain</span>. It does not require stress classification and is also applicable to a full range of temperature above and below the creep regime. This simplified method could be used as a rapid screening calculation, with full time-dependent creep analysis used if necessary.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/25585402','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/25585402"><span id="translatedtitle">Analytical phase-tracking-based <span class="hlt">strain</span> estimation for ultrasound <span class="hlt">elasticity</span>.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Yuan, Lili; Pedersen, Peder C</p> <p>2015-01-01</p> <p>A new <span class="hlt">strain</span> estimator for quasi-static elastography is presented, based on tracking of the analytical signal phase as a function of the external force. Two implementations are introduced: zero-phase search with moving window (SMW) and zero-phase band tracking using connected component labeling (CCL). Low analytical signal amplitude caused by local destructive interference is associated with large error in the phase trajectories, and amplitude thresholding can thus be used to terminate the phase tracking along a particular path. Interpolation is then applied to estimate displacement in the eliminated path. The paper describes first a mathematical analysis based on 1-D multi-scatter modeling, followed by a statistical study of the displacement and <span class="hlt">strain</span> error. Simulation and experiment with an inhomogeneous phantom indicate that SMW and CCL are capable of reliably estimating tissue displacement and <span class="hlt">strain</span> over a larger range of deformation than standard timedomain cross-correlation (SCC). Results also show that SMW is roughly 40 times faster than SCC with comparable or even better accuracy. CCL is slower than SMW, but more noise robust. Simulation assessment at compression level 3% and 6% with SNR 20 dB demonstrates average <span class="hlt">strain</span> error for SMW and CCL of 10%, whereas SCC achieves 18%. PMID:25585402</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997PhDT.......174H&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997PhDT.......174H&link_type=ABSTRACT"><span id="translatedtitle">Statistical model for the prediction of <span class="hlt">elastic</span> wave scattering from <span class="hlt">finite</span> complicated shells</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>He, Hua</p> <p></p> <p>This thesis develops a simple statistical model to estimate bistatic <span class="hlt">elastic</span> scattering from <span class="hlt">finite</span> complicated shells in the mid-frequency range, 3 < ka/ < 10. The model has three parts: (1) sound power injection into the shell; (2) coupling among the <span class="hlt">elastic</span> waves in the shell and wave power equipartition (3) sound radiation from the shell. Within 30o of beam aspect, sound power injection into the shell is mainly caused by acoustic trace matching, and is estimated by using an infinitely long shell model. Once trace matched, the compressional and shear waves can couple to each other and to the subsonic flexural waves at shell discontinuities such as bulkheads and endcaps. Under extensive wave conversion, wave power, defined as energy density multiplied by axial group speed, is hypothesized to be equipartitioned among the <span class="hlt">elastic</span> wave types. Numerical calculations are conducted and the results show that the wave power equipartition hypothesis is plausible for a <span class="hlt">finite</span> endcapped shell with four heavy deep rings. Using the wave power equipartition hypothesis, the shell motion is then converted to sound pressure in the surrounding fluid using Green's theorem. The sound radiation is further extended to the time domain, using random phase realizations and a decay rate model, which considers various dissipation mechanisms in the shells. The predicted target strength is compared with measured data for the ringed shell and the internalled shell, with the internal structures resiliently mounted to the rings. In terms of the mean target strength over the frequency region 3 < ka/ < 10 and the observation region within 30o of beam aspect, the prediction differs from the measured data by less than 2.5 dB for the second and third roundtrip of the trace matched wave in the shells, as well as for a time integrated case. The ring influence on <span class="hlt">elastic</span> wave speeds is also studied. Inclusion of the influence in the model does not generally yield a better agreement with the</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940025112','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940025112"><span id="translatedtitle">Computation of vibration mode <span class="hlt">elastic</span>-rigid and effective weight coefficients from <span class="hlt">finite</span>-element computer program output</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Levy, R.</p> <p>1991-01-01</p> <p>Post-processing algorithms are given to compute the vibratory <span class="hlt">elastic</span>-rigid coupling matrices and the modal contributions to the rigid-body mass matrices and to the effective modal inertias and masses. Recomputation of the <span class="hlt">elastic</span>-rigid coupling matrices for a change in origin is also described. A computational example is included. The algorithms can all be executed by using standard <span class="hlt">finite</span>-element program eigenvalue analysis output with no changes to existing code or source programs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005JSG....27.2135V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005JSG....27.2135V"><span id="translatedtitle">Influence of object concentration on <span class="hlt">finite</span> <span class="hlt">strain</span> and effective viscosity contrast: insights from naturally deformed packstones</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Vitale, Stefano; Mazzoli, Stefano</p> <p></p> <p>Deformed conglomerates and ooidal/oncoidal packstones are commonly used to evaluate <span class="hlt">finite</span> <span class="hlt">strain</span> in deformed sedimentary successions. In order to obtain a correct estimate of <span class="hlt">finite</span> <span class="hlt">strain</span>, it is necessary to consider not only the different behaviour of matrix and objects, but also object concentration. The analysis of two-component rocks characterised by high values of packing commonly results in a substantial underestimate of bulk <span class="hlt">strain</span> and of viscosity contrast between objects and matrix. In this study, the effects of the volumetric fraction of competent inclusions on both object and bulk measured <span class="hlt">finite</span> <span class="hlt">strain</span>, as well as on apparent viscosity contrast, have been investigated in naturally deformed packstones characterised by variable object concentration on the scale of the hand specimen (and hence for homogenous viscosity contrast). Object <span class="hlt">finite</span> <span class="hlt">strain</span> has been obtained by Rf/ ϕ analysis, whereas the Fry method provides a measure of whole-rock <span class="hlt">strain</span> that is also a function of inclusion concentration. Therefore, the <span class="hlt">finite</span> <span class="hlt">strain</span> measured by the Fry method is better termed effective bulk <span class="hlt">strain</span>. In order to investigate the role of object concentration, this parameter has been plotted against object and effective bulk <span class="hlt">strain</span>, and also against viscosity contrast. These diagrams show that: (i) for high values of packing, measured object and effective bulk <span class="hlt">strain</span> show values that are significantly lower with respect to the calculated maximum value (that would result in the ideal case of no particle interaction and represents therefore the real bulk <span class="hlt">strain</span> of the samples); (ii) the viscosity contrast shows lower values with respect to the calculated maximum one (that is equal for the three principal sections of the <span class="hlt">finite</span> <span class="hlt">strain</span> ellipsoid), and as packing reaches the maximum value, the viscosity contrast approaches a unit value. Empirical equations have also been found that link object concentration with both object and effective bulk <span class="hlt">finite</span> <span class="hlt">strain</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://ntrs.nasa.gov/search.jsp?R=19900037329&hterms=assumed+strain&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dassumed%2Bstrain','NASA-TRS'); return false;" href="http://ntrs.nasa.gov/search.jsp?R=19900037329&hterms=assumed+strain&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dassumed%2Bstrain"><span id="translatedtitle">A variational justification of the assumed natural <span class="hlt">strain</span> formulation of <span class="hlt">finite</span> elements. I - Variational principles. II - The C(0) four-node plate element</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Militello, Carmelo; Felippa, Carlos A.</p> <p>1990-01-01</p> <p>The assumed natural <span class="hlt">strain</span> formulation of <span class="hlt">finite</span> elements is interpreted from a variational standpoint. The approach is based on hybrid extensions of the Reissner-type functional which uses the <span class="hlt">strains</span> and displacements as independent fields. Consideration is restricted to linear <span class="hlt">elasticity</span>. The four-node C(0) plate-bending quadrilateral is used as a specific example to illustrate the application of the present interpretation. A key finding is that any change in the <span class="hlt">strain</span>-displacement interpolation from the variationally consistent interpolation must be associated in some way to the addition of incompatible displacement modes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012JaJAP..51g6702J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012JaJAP..51g6702J"><span id="translatedtitle">Determination of Constant <span class="hlt">Strain</span> Gradients of <span class="hlt">Elastically</span> Bent Crystal Using X-ray Mirage Fringes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jongsukswat, Sukswat; Fukamachi, Tomoe; Hirano, Kenji; Ju, Dongying; Negishi, Riichirou; Shimojo, Masayuki; Hirano, Keiichi; Kawamura, Takaaki</p> <p>2012-07-01</p> <p>Two experimental approaches are studied to determine a parameter of the <span class="hlt">strain</span> gradient in an <span class="hlt">elastically</span> bent crystal. In one approach, the parameter is determined by measuring the third peak of the X-ray mirage interference fringes and in the other, by measuring the region where no mirage diffraction beam reaches on the lateral surface of the crystal. Using the X-rays from synchrotron radiation, the mirage fringes have been observed in the 220 reflection of the Si crystal whose <span class="hlt">strain</span> is controlled in cantilever bending. These two approaches both give accurate values of the parameter of the <span class="hlt">strain</span> gradient, showing good agreement with the values calculated using <span class="hlt">elastic</span> theory. In addition, the residual <span class="hlt">strain</span> due to gravity is observed by measuring mirage fringes when the bending force becomes zero.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19740006471','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19740006471"><span id="translatedtitle">Three-dimensional <span class="hlt">elastic</span> stress and displacement analysis of <span class="hlt">finite</span> geometry solids containing cracks</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Gyekenyesi, J. P.; Mendelson, A.</p> <p>1974-01-01</p> <p>The line method of analysis is applied to the Navier-Cauchy equations of <span class="hlt">elastic</span> equilibrium to calculate the displacement distributions in various bodies containing cracks. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The results obtained show a considerable potential for using this method in the three-dimensional analysis of <span class="hlt">finite</span> geometry solids and suggest a possible extension of this technique to nonlinear material behavior.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://ntrs.nasa.gov/search.jsp?R=19850038605&hterms=crack+growth+analysis&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dcrack%2Bgrowth%2Banalysis','NASA-TRS'); return false;" href="http://ntrs.nasa.gov/search.jsp?R=19850038605&hterms=crack+growth+analysis&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dcrack%2Bgrowth%2Banalysis"><span id="translatedtitle">An <span class="hlt">elastic</span>-plastic <span class="hlt">finite</span> element analysis of crack initiation, stable crack growth, and instability</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Newman, J. C., Jr.</p> <p>1984-01-01</p> <p>Studies have been conducted to develop efficient techniques to simulate crack extension and to examine various local and global fracture criteria. Of the considered criteria, the crack-tip-opening angle (CTOA) or displacement (CTOD) at a specified distance from the crack tip was shown to be most suited for modeling stable crack growth and instability during the fracture process. The results obtained in a number of studies show the necessity for studying different crack configurations when assessing the validity of any fracture criteria. One of the objectives of the present investigation is related to a critical evaluation of the CTOD growth criterion using an <span class="hlt">elastic</span>-plastic <span class="hlt">finite</span> element analysis under monotonic loading to failure. The analysis was found to predict three stages of crack growth behavior under monotonic loading to failure. Calculated CTOD values agreed well with experimental values for crack growth initiation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19730012184','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19730012184"><span id="translatedtitle"><span class="hlt">Elastic</span> plate spallation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Oline, L.; Medaglia, J.</p> <p>1972-01-01</p> <p>The dynamic <span class="hlt">finite</span> element method was used to investigate <span class="hlt">elastic</span> stress waves in a plate. <span class="hlt">Strain</span> displacement and stress <span class="hlt">strain</span> relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of <span class="hlt">finite</span> element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/10955613','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/10955613"><span id="translatedtitle">Sound propagation over layered poro-<span class="hlt">elastic</span> ground using a <span class="hlt">finite</span>-difference model</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Dong; Kaynia; Madshus; Hovem</p> <p>2000-08-01</p> <p>This article presents an axisymmetric pressure-velocity <span class="hlt">finite</span>-difference formulation (PV-FD) based on Biot's poro-<span class="hlt">elastic</span> theory for modeling sound propagation in a homogeneous atmosphere over layered poro-<span class="hlt">elastic</span> ground. The formulation is coded in a computer program and a simulation of actual measurements from airblast tests is carried out. The article presents typical results of simulation comprising synthetic time histories of overpressure in the atmosphere and ground vibration as well as snapshots of the response of the atmosphere-ground system at selected times. Comparisons with the measurements during airblast tests performed in Haslemoen, Norway, as well as the simulations by a frequency-wave number FFP formulation are presented to confirm the soundness of the proposed model. In particular, the generation of Mach surfaces in the ground motion, which is the result of the sound speed being greater than the Rayleigh wave velocity in the ground, is demonstrated with the help of snapshot plots. PMID:10955613</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016SPIE.9804E..26T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016SPIE.9804E..26T"><span id="translatedtitle"><span class="hlt">Finite</span> element simulation for damage detection of surface rust in steel rebars using <span class="hlt">elastic</span> waves</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tang, Qixiang; Yu, Tzuyang</p> <p>2016-04-01</p> <p>Steel rebar corrosion reduces the integrity and service life of reinforced concrete (RC) structures and causes their gradual and sudden failures. Early stage detection of steel rebar corrosion can improve the efficiency of routine maintenance and prevent sudden failures from happening. In this paper, detecting the presence of surface rust in steel rebars is investigated by the <span class="hlt">finite</span> element method (FEM) using surface-generated <span class="hlt">elastic</span> waves. Simulated wave propagation mimics the sensing scheme of a fiber optic acoustic generator mounted on the surface of steel rebars. Formation of surface rust in steel rebars is modeled by changing material's property at local elements. In this paper, various locations of a fiber optic acoustic transducer and a receiver were considered. Megahertz <span class="hlt">elastic</span> waves were used and different sizes of surface rust were applied. Transient responses of surface displacement and pressure were studied. It is found that surface rust is most detectable when the rust location is between the transducer and the receiver. Displacement response of intact steel rebar is needed in order to obtain background-subtracted response with a better signal-to-noise ratio. When the size of surface rust increases, reduced amplitude in displacement was obtained by the receiver.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/645602','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/645602"><span id="translatedtitle">Application of equivalent <span class="hlt">elastic</span> methods in three-dimensional <span class="hlt">finite</span> element structural analysis</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Jones, D.P.; Gordon, J.L.; Hutula, D.N.; Holliday, J.E.; Jandrasits, W.G.</p> <p>1998-02-01</p> <p>This paper describes use of equivalent solid (EQS) modeling to obtain efficient solutions to perforated material problems using three-dimensional <span class="hlt">finite</span> element analysis (3D-FEA) programs. It is shown that the accuracy of EQS methods in 3D-FEA depends on providing sufficient equivalent <span class="hlt">elastic</span> properties to allow the EQS material to respond according to the <span class="hlt">elastic</span> symmetry of the pattern. Peak stresses and ligament stresses are calculated from the EQS stresses by an appropriate 3D-FEA submodel approach. The method is demonstrated on the problem of a transversely pressurized simply supported plate with a central divider lane separating two perforated regions with circular penetrations arranged in a square pattern. A 3D-FEA solution for a model that incorporates each penetration explicitly is used for comparison with results from an EQS solution for the plate. Results for deflection and stresses from the EQS solution are within 3% of results from the explicit 3D-FE model. A solution to the sample problem is also provided using the procedures in the ASME B and PV Code. The ASME B and PV Code formulas for plate deflection were shown to overestimate the stiffening effects of the divider lane and the outer stiffening ring.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AcAau.119....1A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AcAau.119....1A"><span id="translatedtitle">Bending analysis of embedded carbon nanotubes resting on an <span class="hlt">elastic</span> foundation using <span class="hlt">strain</span> gradient theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Akgöz, Bekir; Civalek, Ömer</p> <p>2016-02-01</p> <p>In this study, static bending response of single-walled carbon nanotubes (SWCNTs) embedded in an <span class="hlt">elastic</span> medium is investigated on the basis of higher-order shear deformation microbeam models in conjunction with modified <span class="hlt">strain</span> gradient theory. The governing differential equations and related boundary conditions are obtained by implementing a variational principle. The interactions between SWCNTs and surrounding <span class="hlt">elastic</span> medium are simulated by Winkler <span class="hlt">elastic</span> foundation model. The Navier-type solution is utilized to obtain an analytical solution for the bending problem of the simply supported embedded SWCNTs under uniform and sinusoidal loads. The influences of material length scale parameter-to-diameter ratio, slenderness ratio, loading type, shear correction factor and Winkler modulus on deflections of the embedded SWCNTs are discussed in detail. The present results illustrate that the bending behavior of SWCNTs is dependent on the small-size, stiffness of the <span class="hlt">elastic</span> foundation and also effects of shear deformation, especially for smaller slenderness ratios.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GeoRL..43.3226R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GeoRL..43.3226R"><span id="translatedtitle">Frequency, pressure, and <span class="hlt">strain</span> dependence of nonlinear <span class="hlt">elasticity</span> in Berea Sandstone</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rivière, Jacques; Pimienta, Lucas; Scuderi, Marco; Candela, Thibault; Shokouhi, Parisa; Fortin, Jérôme; Schubnel, Alexandre; Marone, Chris; Johnson, Paul A.</p> <p>2016-04-01</p> <p>Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static (f→0) and dynamic (few kilohertz) nonlinear <span class="hlt">elastic</span> response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on <span class="hlt">strain</span> amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2-3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear <span class="hlt">elasticity</span> of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear <span class="hlt">elasticity</span>. These findings can be used to improve theories relating the macroscopic <span class="hlt">elastic</span> response to microstructural features.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014IJCEM..15..422P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014IJCEM..15..422P"><span id="translatedtitle">Sensitivity Analysis of Linear <span class="hlt">Elastic</span> Cracked Structures Using Generalized <span class="hlt">Finite</span> Element Method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pal, Mahendra Kumar; Rajagopal, Amirtham</p> <p>2014-09-01</p> <p>In this work, a sensitivity analysis of linear <span class="hlt">elastic</span> cracked structures using two-scale Generalized <span class="hlt">Finite</span> Element Method (GFEM) is presented. The method is based on computation of material derivatives, mutual potential energies, and direct differentiation. In a computational setting, the discrete form of the mutual potential energy release rate is simple and easy to calculate, as it only requires the multiplication of the displacement vectors and stiffness sensitivity matrices. By judiciously choosing the velocity field, the method only requires displacement response in a sub-domain close to the crack tip, thus making the method computationally efficient. The method thus requires an exact computation of displacement response in a sub-domain close to the crack tip. To this end, in this study we have used a two-scale GFEM for sensitivity analysis. GFEM is based on the enrichment of the classical <span class="hlt">finite</span> element approximation. These enrichment functions incorporate the discontinuity response in the domain. Three numerical examples which comprise mode-I and mixed mode deformations are presented to evaluate the accuracy of the fracture parameters calculated by the proposed method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016GeoJI.206..292Z&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016GeoJI.206..292Z&link_type=ABSTRACT"><span id="translatedtitle">A new spectral <span class="hlt">finite</span> volume method for <span class="hlt">elastic</span> wave modelling on unstructured meshes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhang, Wensheng; Zhuang, Yuan; Chung, Eric T.</p> <p>2016-07-01</p> <p>In this paper, we consider a new spectral <span class="hlt">finite</span> volume method (FVM) for the <span class="hlt">elastic</span> wave equations. Our new FVM is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order FVM and the spectral FVM. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an overdetermined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard <span class="hlt">finite</span> volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2-D problems, but the same methodology can be applied to 3-D.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/27140623','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/27140623"><span id="translatedtitle"><span class="hlt">Strain</span>-enhanced stress relaxation impacts nonlinear <span class="hlt">elasticity</span> in collagen gels.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Nam, Sungmin; Hu, Kenneth H; Butte, Manish J; Chaudhuri, Ovijit</p> <p>2016-05-17</p> <p>The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear <span class="hlt">elasticity</span>, undergoing <span class="hlt">strain</span> stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear <span class="hlt">elasticity</span> and viscoelasticity of ECM, yet little is known about the connection between nonlinear <span class="hlt">elasticity</span> and viscoelasticity. Here, we report that, as <span class="hlt">strain</span> is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which <span class="hlt">elastic</span> energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that <span class="hlt">strain</span>-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of <span class="hlt">strain</span>-enhanced stress relaxation is to rapidly diminish <span class="hlt">strain</span> stiffening over time. These results reveal the interplay between nonlinear <span class="hlt">elasticity</span> and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction. PMID:27140623</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li class="active"><span>8</span></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_8 --> <div id="page_9" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li class="active"><span>9</span></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="161"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/16686414','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/16686414"><span id="translatedtitle">Biotelemetric passive sensor injected within tendon for <span class="hlt">strain</span> and <span class="hlt">elasticity</span> measurement.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Pichorim, Sérgio Francisco; Abatti, Paulo José</p> <p>2006-05-01</p> <p>A passive and injectable (using hypodermic needle) biotelemetric sensor for measurements of tendon length changes has been developed. From these measurements tendon <span class="hlt">strain</span> and Young's modulus of <span class="hlt">elasticity</span> can be derived. The sensor (about 2.1 x 29 mm) is a LC circuit fixed in tendon by metallic anchors (barbs), where the value of the resonance frequency is modulated by displacement of a mobile ferrite core. The sensor was injected into digital extensor tendon of pig, allowing the determination of its stress-<span class="hlt">strain</span> curve and, consequently, of Young's modulus of <span class="hlt">elasticity</span> of the tendon. Practical results, such as sensitivity of 18.199 kHz/mm (correlation coefficient of 0.9891) for <span class="hlt">strains</span> up to 5.17%, mechanical hysteresis of 6.5%, and Young's modulus of 0.9146 GPa for a pig tendon (post mortem), are presented and discussed. PMID:16686414</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..SHK.D4005C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..SHK.D4005C"><span id="translatedtitle"><span class="hlt">Elastic</span> precursor shock waves in tantalum at very high <span class="hlt">strain</span> rates</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Crowhurst, Jonathan; Armstrong, Michael; Gates, Sean; Radousky, Harry; Zaug, Joseph</p> <p>2015-06-01</p> <p>We have obtained data from micron-thick tantalum films using our ultrafast laser shock platform. By measuring free surface velocity time histories at breakout, and shock wave arrival times at different film thicknesses, we have been able to estimate the dependence of particle and shock velocities on propagation distances and <span class="hlt">strain</span> rates. We will show how <span class="hlt">elastic</span> precursor shock waves depend on <span class="hlt">strain</span> rate in the regime up to and above 109 s-1. We find that while <span class="hlt">elastic</span> amplitudes are very large at very early times decay occurs rapidly as propagation distance increases. Finally we will consider the prospects for using these data to obtain the dynamic strength of tantalum at these very high <span class="hlt">strain</span> rates. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 with Laboratory directed Research and Development funding (12ERD042).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..MARA34002C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..MARA34002C"><span id="translatedtitle"><span class="hlt">Elastic</span> precursor shock waves in tantalum at very high <span class="hlt">strain</span> rates</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Crowhurst, Jonathan; Armstrong, Michael; Radousky, Harry; Zaug, Joseph; Gates, Sean</p> <p>2015-03-01</p> <p>We have obtained data from micron-thick tantalum films using our ultrafast laser shock platform. By measuring free surface velocity time histories at breakout, and shock wave arrival times at different film thicknesses, we have been able to estimate the dependence of particle and shock velocities on propagation distances and <span class="hlt">strain</span> rates. We will show how <span class="hlt">elastic</span> precursor shock waves depend on <span class="hlt">strain</span> rate in the regime up to and above 109 s-1. We find that while <span class="hlt">elastic</span> amplitudes are very large at very early times decay occurs rapidly as propagation distance increases. Finally we will consider the prospects for using these data to obtain the dynamic strength of tantalum at these very high <span class="hlt">strain</span> rates. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 with Laboratory directed Research and Development funding (12ERD042).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008JCoAM.221..234B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008JCoAM.221..234B"><span id="translatedtitle">Dual mixed <span class="hlt">finite</span> element methods for the <span class="hlt">elasticity</span> problem with Lagrange multipliers</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Boulaajine, L.; Nicaise, S.; Paquet, L.; Rafilipojaona</p> <p>2008-11-01</p> <p>We study a dual mixed formulation of the <span class="hlt">elasticity</span> system in a polygonal domain of the plane with mixed boundary conditions and its numerical approximation. The (essential) Neumann boundary conditions (or traction boundary condition) are imposed using a discontinuous Lagrange multiplier corresponding to the trace of the displacement field. Moreover, a <span class="hlt">strain</span> tensor is introduced as a new unknown and its symmetry is relaxed, also by the use of a Lagrange multiplier (the rotation). The singular behaviour of the solution requires us to use refined meshes to restore optimal rates of convergence. Uniform error estimates in the Lamé coefficient [lambda] are obtained for large [lambda]. The hybridization of the problem is performed and numerical tests are presented confirming our theoretical results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CompM.tmp...26G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CompM.tmp...26G"><span id="translatedtitle">On the modelling of complex kinematic hardening and nonquadratic anisotropic yield criteria at <span class="hlt">finite</span> <span class="hlt">strains</span>: application to sheet metal forming</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Grilo, Tiago J.; Vladimirov, Ivaylo N.; Valente, Robertt A. F.; Reese, Stefanie</p> <p>2016-02-01</p> <p>In the present paper, a <span class="hlt">finite</span> <span class="hlt">strain</span> model for complex combined isotropic-kinematic hardening is presented. It accounts for <span class="hlt">finite</span> <span class="hlt">elastic</span> and <span class="hlt">finite</span> plastic <span class="hlt">strains</span> and is suitable for any anisotropic yield criterion. In order to model complex cyclic hardening phenomena, the kinematic hardening is described by several back stress components. To that end, a new procedure is proposed in which several multiplicative decompositions of the plastic part of the deformation gradient are considered. The formulation incorporates a completely general format of the yield function, which means that any yield function can by employed by following a procedure that ensures the principle of material frame indifference. The constitutive equations are derived in a thermodynamically consistent way and numerically integrated by means of a backward-Euler algorithm based on the exponential map. The performance of the constitutive model is assessed via numerical simulations of industry-relevant sheet metal forming processes (U-channel forming and draw/re-draw of a panel benchmarks), the results of which are compared to experimental data. The comparison between numerical and experimental results shows that the use of multiple back stress components is very advantageous in the description of springback. This holds in particular if one carries out a comparison with the results of using only one component. Moreover, the numerically obtained results are in excellent agreement with the experimental data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016CompM..57..931G&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016CompM..57..931G&link_type=ABSTRACT"><span id="translatedtitle">On the modelling of complex kinematic hardening and nonquadratic anisotropic yield criteria at <span class="hlt">finite</span> <span class="hlt">strains</span>: application to sheet metal forming</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Grilo, Tiago J.; Vladimirov, Ivaylo N.; Valente, Robertt A. F.; Reese, Stefanie</p> <p>2016-06-01</p> <p>In the present paper, a <span class="hlt">finite</span> <span class="hlt">strain</span> model for complex combined isotropic-kinematic hardening is presented. It accounts for <span class="hlt">finite</span> <span class="hlt">elastic</span> and <span class="hlt">finite</span> plastic <span class="hlt">strains</span> and is suitable for any anisotropic yield criterion. In order to model complex cyclic hardening phenomena, the kinematic hardening is described by several back stress components. To that end, a new procedure is proposed in which several multiplicative decompositions of the plastic part of the deformation gradient are considered. The formulation incorporates a completely general format of the yield function, which means that any yield function can by employed by following a procedure that ensures the principle of material frame indifference. The constitutive equations are derived in a thermodynamically consistent way and numerically integrated by means of a backward-Euler algorithm based on the exponential map. The performance of the constitutive model is assessed via numerical simulations of industry-relevant sheet metal forming processes (U-channel forming and draw/re-draw of a panel benchmarks), the results of which are compared to experimental data. The comparison between numerical and experimental results shows that the use of multiple back stress components is very advantageous in the description of springback. This holds in particular if one carries out a comparison with the results of using only one component. Moreover, the numerically obtained results are in excellent agreement with the experimental data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/27402932','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/27402932"><span id="translatedtitle">Large <span class="hlt">elastic</span> <span class="hlt">strain</span> and elastocaloric effect caused by lattice softening in an iron-palladium alloy.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kakeshita, Tomoyuki; Xiao, Fei; Fukuda, Takashi</p> <p>2016-08-13</p> <p>A Fe-31.2Pd (at.%) alloy exhibits a weak first-order martensitic transformation from a cubic structure to a tetragonal structure near 230 K. This transformation is associated with significant softening of <span class="hlt">elastic</span> constant C'. Because of the softening, the alloy shows a large <span class="hlt">elastic</span> <span class="hlt">strain</span> of more than 6% in the [001] direction. In addition, the alloy has a critical point and shows a high elastocaloric effect in a wide temperature range for both the parent and the martensite phases.This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'. PMID:27402932</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/biblio/22280602','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/biblio/22280602"><span id="translatedtitle"><span class="hlt">Elastic</span> <span class="hlt">strains</span> at interfaces in InAs/AlSb multilayer structures for quantum cascade lasers</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Nicolai, J.; Gatel, Ch.; Warot-Fonrose, B.; Ponchet, A.; Teissier, R.; Baranov, A. N.; Magen, C.</p> <p>2014-01-20</p> <p>InAs/AlSb multilayers similar to those used in quantum cascade lasers have been grown by molecular beam epitaxy on (001) InAs substrates. <span class="hlt">Elastic</span> <span class="hlt">strain</span> is investigated by high resolution transmission electron microscopy. Thin interfacial regions with lattice distortions significantly different from the <span class="hlt">strain</span> of the AlSb layers themselves are revealed from the geometrical phase analysis. <span class="hlt">Strain</span> profiles are qualitatively compared to the chemical contrast of high angle annular dark field images obtained by scanning transmission electron microscopy. The <span class="hlt">strain</span> and chemical profiles are correlated with the growth sequences used to form the interfaces. Tensile <span class="hlt">strained</span> AlAs-like interfaces tend to form predominantly due to the high thermal stability of AlAs. Strongly asymmetric interfaces, AlAs-rich and (Al, In)Sb, respectively, can also be achieved by using appropriate growth sequences.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/26211247','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/26211247"><span id="translatedtitle">[Three-dimensional <span class="hlt">Finite</span> Element Analysis of Biomechanical Effect of Rigid Fixation and <span class="hlt">Elastic</span> Fixation on Lumbar Interbody Fusion].</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Wei, Jiangbo; Song, Yueming; Liu, Limin; Zhou, Chunguan; Yang, Xi</p> <p>2015-04-01</p> <p>This study was aimed to compare the mechanical characteristics under different physiological load conditions with three-dimensional <span class="hlt">finite</span> element model of rigid fixation and <span class="hlt">elastic</span> fixation in the lumbar. We observed the stress distribution characteristics of a sample of healthy male volunteer modeling under vertical, flexion and extension torque situation. The outcomes showed that there existed 4-6 times pressure on the connecting rod of rigid fixation compared with the <span class="hlt">elastic</span> fixations under different loads, and the stress peak and area of force on <span class="hlt">elastic</span> fixation were much higher than that of the rigid fixations. The <span class="hlt">elastic</span> fixation has more biomechanical advantages than rigid fixation in promoting interbody lumbar fusion after surgery. PMID:26211247</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/11737110','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/11737110"><span id="translatedtitle">Anisotropic <span class="hlt">elasticity</span> of cortical and cancellous bone in the posterior mandible increases peri-implant stress and <span class="hlt">strain</span> under oblique loading.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>O'Mahony, A M; Williams, J L; Spencer, P</p> <p>2001-12-01</p> <p>The aim of this study was to compare implant-bone interface stresses and peri-implant principal <span class="hlt">strains</span> in anisotropic versus isotropic three-dimensional <span class="hlt">finite</span> element models of an osseointegrated implant in the posterior mandible. We obtained anisotropic (transversely isotropic) <span class="hlt">elastic</span> constants for mandibular bone and derived equivalent isotropic constants by averaging over all possible spatial orientations. A <span class="hlt">finite</span> element model was constructed using ten-node tetrahedral p-elements, providing curved edges where necessary and increasing the accuracy of the results in regions of high stress gradients. Perfect bonding was assumed at the implant-bone interface. An oblique load was applied at the coronal aspect of the crown with 100 N vertical and 20 N bucco-to-lingual components. Implant-bone interface stresses exceeded reported bond strengths and principal <span class="hlt">strains</span> reached yield <span class="hlt">strain</span> levels in the cortical crest. Anisotropy increased what were already high levels of stress and <span class="hlt">strain</span> in the isotropic case by 20 to 30% in the cortical crest. In cancellous bone, anisotropy increased what were relatively low levels of interface stress in the isotropic case by three- to four-fold to exceed bond strength levels. Anisotropy has subtle, yet significant effects on interface stresses and peri-implant <span class="hlt">strains</span> and careful consideration should be given to its use in <span class="hlt">finite</span> element studies of dental implants. PMID:11737110</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/26240030','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/26240030"><span id="translatedtitle">Stress and <span class="hlt">strain</span> distribution in demineralized enamel: A micro-CT based <span class="hlt">finite</span> element study.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Neves, Aline Almeida; Coutinho, Eduardo; Alves, Haimon Diniz Lopes; de Assis, Joaquim Teixeira</p> <p>2015-10-01</p> <p>Physiological oral mechanical forces may play a role on the progression of enamel carious lesions to cavitation. Thus, the aim of this study was to describe, by 3D <span class="hlt">finite</span> element analysis, stress, and <span class="hlt">strain</span> patterns in sound and carious enamel after a simulated occlusal load. Micro-CT based models were created and meshed with tetrahedral elements (based on an extracted third molar), namely: a sound (ST) and a carious tooth (CT). For the CT, enamel material properties were assigned according to the micro-CT gray values. Below the threshold corresponding to the enamel lesion (2.5 g/cm(3) ) lower and isotropic <span class="hlt">elastic</span> modulus was assigned (E = 18 GPa against E1  = 80 GPa, E2  = E3  = 20 GPa for sound enamel). Both models were imported into a FE solver where boundary conditions were assigned and a pressure load (500 MPa) was applied at the occlusal surface. A linear static analysis was performed, considering anisotropy in sound enamel. ST showed a more efficient transfer of maximum principal stress from enamel to the dentin layer, while for the CT, enamel layer was subjected to higher and concentrated loads. Maximum principal <span class="hlt">strain</span> distributions were seen at the carious enamel surface, especially at the central fossa, correlating to the enamel cavity seen at the original micro-CT model. It is possible to conclude that demineralized enamel compromises appropriate stress transfer from enamel to dentin, contributing to the odds of fracture and cavitation. Enamel fracture over a dentin lesion may happen as one of the normal pathways to caries progression and may act as a confounding factor during clinical diagnostic decisions. PMID:26240030</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006MMTA...37.3629P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006MMTA...37.3629P"><span id="translatedtitle">Synchrotron X-ray measurement and <span class="hlt">finite</span> element analysis of residual <span class="hlt">strain</span> in tungsten inert gas welded aluminum alloy 2024</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Preston, R. V.; Shercliff, H. R.; Withers, P. J.; Hughes, D. J.; Smith, S. D.; Webster, P. J.</p> <p>2006-12-01</p> <p>Residual <span class="hlt">strains</span> have been measured in a tungsten inert gas (TIG) butt-welded 2024 aluminum alloy plate using synchrotron X-ray diffraction. Novel two-dimensional <span class="hlt">strain</span> maps spanning the entire plate reveal steep gradients in residual stress and provide detailed validation data for <span class="hlt">finite</span> element (FE) analysis. Two variants of a FE model have been used to predict the residual <span class="hlt">strain</span> distributions, incorporating different levels of plate constraint. The model uses decoupled thermal and <span class="hlt">elastic</span>-plastic mechanical analyses and successfully predicts the longitudinal and transverse residual <span class="hlt">strain</span> field over the entire weld. For butt weld geometries, the degree of transverse constraint is shown to be a significant boundary condition, compared to simpler bead-on-plate analyses. The importance of transverse residual <span class="hlt">strains</span> for detailed model validation is highlighted, together with the need for care in selecting the location for line scans. The residual stress is largest in the heat-affected zone (HAZ), being equal to the local postweld yield stress, though the strength increases subsequently by natural aging. In addition, a halving of the diffraction line width has been observed local to the weld, and this correlates with the microstructural changes in the region.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013FrME....8..181M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013FrME....8..181M"><span id="translatedtitle">A model for creep life prediction of thin tube using <span class="hlt">strain</span> energy density as a function of stress triaxiality under quasistatic loading employing <span class="hlt">elastic</span>-creep & <span class="hlt">elastic</span>-plastic-creep deformation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mahmood, Tahir; Kanapathipillai, Sangarapillai; Chowdhury, Mahiuddin</p> <p>2013-06-01</p> <p>This paper demonstrates the application of a new multiaxial creep damage model developed by authors using stress traixiality to predict the failure time of a component made of 0.5%Cr-0.5%Mo-0.25%V low alloy steel. The model employs <span class="hlt">strain</span> energy density and assumes that the uniaxial <span class="hlt">strain</span> energy density of a component can be easily calculated and can be converted to multi-axial <span class="hlt">strain</span> energy density by multiplying it to a function of stress trixiality which is a ratio of mean stress to equivalent stress. For comparison, an <span class="hlt">elastic</span>-creep and <span class="hlt">elastic</span>-plastic-creep <span class="hlt">finite</span> element analysis (FEA) is performed to get multi-axial <span class="hlt">strain</span> energy density of the component which is compared with the calculated <span class="hlt">strain</span> energy density for both cases. The verification and application of the model are demonstrated by applying it to thin tube for which the experimental data are available. The predicted failure times by the model are compared with the experimental results. The results show that the proposed model is capable of predicting failure times of the component made of the above-mentioned material with an accuracy of 4.0%.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CompM..55..673A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CompM..55..673A"><span id="translatedtitle">A semi-implicit <span class="hlt">finite</span> <span class="hlt">strain</span> shell algorithm using in-plane <span class="hlt">strains</span> based on least-squares</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Areias, P.; Rabczuk, T.; de Sá, J. César; Natal Jorge, R.</p> <p>2015-04-01</p> <p>The use of a semi-implicit algorithm at the constitutive level allows a robust and concise implementation of low-order effective shell elements. We perform a semi-implicit integration in the stress update algorithm for <span class="hlt">finite</span> <span class="hlt">strain</span> plasticity: rotation terms (highly nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the (in this case evolving) reference configuration and relative Green-Lagrange <span class="hlt">strains</span> (quadratic) are used to account for change in the equilibrium configuration implicitly. We parametrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use a common configuration. A <span class="hlt">finite</span> <span class="hlt">strain</span> quadrilateral element with least-squares assumed in-plane shear <span class="hlt">strains</span> (in curvilinear coordinates) and classical transverse shear assumed <span class="hlt">strains</span> is introduced. It is an alternative to enhanced-assumed-<span class="hlt">strain</span> (EAS) formulations and, contrary to this, produces an element satisfying ab-initio the Patch test. No additional degrees-of-freedom are present, contrasting with EAS. Least-squares fit allows the derivation of invariant <span class="hlt">finite</span> <span class="hlt">strain</span> elements which are both in-plane and out-of-plane shear-locking free and amenable to standardization in commercial codes. Two thickness parameters per node are adopted to reproduce the Poisson effect in bending. Metric components are fully deduced and exact linearization of the shell element is performed. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/957782','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/957782"><span id="translatedtitle">Defect-induced incompatability of <span class="hlt">elastic</span> <span class="hlt">strains</span>: dislocations within the Landau theory of martensitic phase transformations</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Groger, Roman1; Lockman, Turab; Saxena, Avadh</p> <p>2008-01-01</p> <p>In dislocation-free martensites the components of the <span class="hlt">elastic</span> <span class="hlt">strain</span> tensor are constrained by the Saint-Venant compatibility condition which guarantees continuity of the body during external loading. However, in dislocated materials the plastic part of the distortion tensor introduces a displacement mismatch that is removed by <span class="hlt">elastic</span> relaxation. The <span class="hlt">elastic</span> <span class="hlt">strains</span> are then no longer compatible in the sense of the Saint-Venant law and the ensuing incompatibility tensor is shown to be proportional to the gradients of the Nye dislocation density tensor. We demonstrate that the presence of this incompatibility gives rise to an additional long-range contribution in the inhomogeneous part of the Landau energy functional and to the corresponding stress fields. Competition among the local and long-range interactions results in frustration in the evolving order parameter (<span class="hlt">elastic</span>) texture. We show how the Peach-Koehler forces and stress fields for any distribution of dislocations in arbitrarily anisotropic media can be calculated and employed in a Fokker-Planck dynamics for the dislocation density. This approach represents a self-consistent scheme that yields the evolutions of both the order parameter field and the continuous dislocation density. We illustrate our method by studying the effects of dislocations on microstructure, particularly twinned domain walls, in an Fe-Pd alloy undergoing a martensitic transformation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/biblio/687523','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/biblio/687523"><span id="translatedtitle">Application of equivalent <span class="hlt">elastic</span> methods in three-dimensional <span class="hlt">finite</span> element structural analysis</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Jones, D.P.; Gordon, J.L.; Hutula, D.N.; Holliday, J.E.; Jandrasits, W.G.</p> <p>1999-08-01</p> <p>This paper describes use of equivalent solid (EQS) modeling to obtain efficient solutions to perforated material problems using three-dimensional <span class="hlt">finite</span> element analysis (3-D-FEA) programs. It is shown that EQS modeling in 3-D-FEA requires an EQS constitutive relationship with a sufficient number of independent constants to allow the EQS material to respond according to the <span class="hlt">elastic</span> symmetry of the penetration pattern. It is also shown that a 3-D-FEA submodel approach to calculate peak stresses and ligament stresses from EQS results is very accurate and preferred over more traditional stress multiplier approaches. The method is demonstrated on the problem of a transversely pressurized simply supported plate with a central divider lane separating two perforated regions with circular penetrations arranged in a square pattern. A 3-D-FEA solution for a model that incorporates each penetration explicitly is used for comparison with results from an EQS solution for the plate. Results for deflection and stresses from the EQS solution are within 3% of results from the explicit 3-D-FE model. A solution to the sample problem is also provided using the procedures in the ASME B and PV Code. The ASME B and PV Code formulas for plate deflection were shown to overestimate the stiffening effects of the divider lane and the outer stiffening ring.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1156935','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1156935"><span id="translatedtitle">A 3D Orthotropic <span class="hlt">Strain</span>-Rate Dependent <span class="hlt">Elastic</span> Damage Material Model.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>English, Shawn Allen</p> <p>2014-09-01</p> <p>A three dimensional orthotropic <span class="hlt">elastic</span> constitutive model with continuum damage and cohesive based fracture is implemented for a general polymer matrix composite lamina. The formulation assumes the possibility of distributed (continuum) damage followed b y localized damage. The current damage activation functions are simply partially interactive quadratic <span class="hlt">strain</span> criteria . However, the code structure allows for changes in the functions without extraordinary effort. The material model formulation, implementation, characterization and use cases are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009SPIE.7292E..0SM','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009SPIE.7292E..0SM"><span id="translatedtitle">High-fidelity conical piezoelectric transducers and <span class="hlt">finite</span> element models utilized to quantify <span class="hlt">elastic</span> waves generated from ball collisions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>McLaskey, Gregory C.; Glaser, Steven D.</p> <p>2009-03-01</p> <p>Experimental studies were performed using high-fidelity broadband Glaser-NIST conical transducers to quantify stress waves produced by the <span class="hlt">elastic</span> collision of a tiny ball and a massive plate. These sensors are sensitive to surface-normal displacements down to picometers in amplitude, in a frequency range of 20 kHz to over 1 MHz. Both the collision and the resulting transient <span class="hlt">elastic</span> waves are modeled with the <span class="hlt">finite</span> element program ABAQUS and described theoretically through a marriage of the Hertz theory of contact and a full elastodynamic Green's function found using generalized ray theory. The calculated displacements were compared to those measured through the Glaser-NIST sensors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/27093600','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/27093600"><span id="translatedtitle">Local, atomic-level <span class="hlt">elastic</span> <span class="hlt">strain</span> measurements of metallic glass thin films by electron diffraction.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ebner, C; Sarkar, R; Rajagopalan, J; Rentenberger, C</p> <p>2016-06-01</p> <p>A novel technique is used to measure the atomic-level <span class="hlt">elastic</span> <span class="hlt">strain</span> tensor of amorphous materials by tracking geometric changes of the first diffuse ring of selected area electron diffraction patterns (SAD). An automatic procedure, which includes locating the centre and fitting an ellipse to the diffuse ring with sub-pixel precision is developed for extracting the 2-dimensional <span class="hlt">strain</span> tensor from the SAD patterns. Using this technique, atomic-level principal <span class="hlt">strains</span> from micrometre-sized regions of freestanding amorphous Ti0.45Al0.55 thin films were measured during in-situ TEM tensile deformation. The thin films were deformed using MEMS based testing stages that allow simultaneous measurement of the macroscopic stress and <span class="hlt">strain</span>. The calculated atomic-level principal <span class="hlt">strains</span> show a linear dependence on the applied stress, and good correspondence with the measured macroscopic <span class="hlt">strains</span>. The calculated Poisson's ratio of 0.23 is reasonable for brittle metallic glasses. The technique yields a <span class="hlt">strain</span> accuracy of about 1×10(-4) and shows the potential to obtain localized <span class="hlt">strain</span> profiles/maps of amorphous thin film samples. PMID:27093600</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvB..93x5107S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvB..93x5107S"><span id="translatedtitle">Unified ab initio formulation of flexoelectricity and <span class="hlt">strain</span>-gradient <span class="hlt">elasticity</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Stengel, Massimiliano</p> <p>2016-06-01</p> <p>The theory of flexoelectricity and that of nonlocal <span class="hlt">elasticity</span> are closely related, and are often considered together when modeling <span class="hlt">strain</span>-gradient effects in solids. Here I show, based on a first-principles lattice-dynamical analysis, that their relationship is much more intimate than previously thought, and their consistent simultaneous treatment is crucial for obtaining correct physical answers. In particular, I identify a gauge invariance in the theory, whereby the energies associated to <span class="hlt">strain</span>-gradient <span class="hlt">elasticity</span> and flexoelectrically induced electric fields are individually reference dependent, and only when summed up they yield a well-defined result. To illustrate this, I construct a minimal thermodynamic functional incorporating <span class="hlt">strain</span>-gradient effects, and establish a formal link between the continuum description and ab initio phonon dispersion curves to calculate the relevant tensor quantities. As a practical demonstration, I apply such a formalism to bulk SrTiO3, where I find an unusually strong contribution of nonlocal <span class="hlt">elasticity</span>, mediated by the interaction between the ferroelectric soft mode and the transverse acoustic branches. These results have important implications towards the construction of well-defined thermodynamic theories where flexoelectricity and ferroelectricity coexist. More generally, they open exciting new avenues for the implementation of hierarchical multiscale concepts in the first-principles simulation of crystalline insulators.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li class="active"><span>9</span></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_9 --> <div id="page_10" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li class="active"><span>10</span></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="181"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/944324','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/944324"><span id="translatedtitle">A stable <span class="hlt">finite</span> difference method for the <span class="hlt">elastic</span> wave equation on complex geometries with free surfaces</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Appelo, D; Petersson, N A</p> <p>2007-12-17</p> <p>The isotropic <span class="hlt">elastic</span> wave equation governs the propagation of seismic waves caused by earthquakes and other seismic events. It also governs the propagation of waves in solid material structures and devices, such as gas pipes, wave guides, railroad rails and disc brakes. In the vast majority of wave propagation problems arising in seismology and solid mechanics there are free surfaces. These free surfaces have, in general, complicated shapes and are rarely flat. Another feature, characterizing problems arising in these areas, is the strong heterogeneity of the media, in which the problems are posed. For example, on the characteristic length scales of seismological problems, the geological structures of the earth can be considered piecewise constant, leading to models where the values of the <span class="hlt">elastic</span> properties are also piecewise constant. Large spatial contrasts are also found in solid mechanics devices composed of different materials welded together. The presence of curved free surfaces, together with the typical strong material heterogeneity, makes the design of stable, efficient and accurate numerical methods for the <span class="hlt">elastic</span> wave equation challenging. Today, many different classes of numerical methods are used for the simulation of <span class="hlt">elastic</span> waves. Early on, most of the methods were based on <span class="hlt">finite</span> difference approximations of space and time derivatives of the equations in second order differential form (displacement formulation), see for example [1, 2]. The main problem with these early discretizations were their inability to approximate free surface boundary conditions in a stable and fully explicit manner, see e.g. [10, 11, 18, 20]. The instabilities of these early methods were especially bad for problems with materials with high ratios between the P-wave (C{sub p}) and S-wave (C{sub s}) velocities. For rectangular domains, a stable and explicit discretization of the free surface boundary conditions is presented in the paper [17] by Nilsson et al. In summary</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19740006477','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19740006477"><span id="translatedtitle"><span class="hlt">Finite</span> element stress analysis of polymers at high <span class="hlt">strains</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Durand, M.; Jankovich, E.</p> <p>1973-01-01</p> <p>A numerical analysis is presented for the problem of a flat rectangular rubber membrane with a circular rigid inclusion undergoing high <span class="hlt">strains</span> due to the action of an axial load. The neo-hookean constitutive equations are introduced into the general purpose TITUS program by means of equivalent hookean constants and initial <span class="hlt">strains</span>. The convergence is achieved after a few iterations. The method is not limited to any specific program. The results are in good agreement with those of a company sponsored photoelastic stress analysis. The theoretical and experimental deformed shapes also agree very closely with one another. For high <span class="hlt">strains</span> it is demonstrated that using the conventional HOOKE law the stress concentration factor obtained is unreliable in the case of rubberlike material.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3972043','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3972043"><span id="translatedtitle">In vivo bone <span class="hlt">strain</span> and <span class="hlt">finite</span> element modeling of the mandible of Alligator mississippiensis</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Porro, Laura B; Metzger, Keith A; Iriarte-Diaz, Jose; Ross, Callum F</p> <p>2013-01-01</p> <p>Forces experienced during feeding are thought to strongly influence the morphology of the vertebrate mandible; in vivo <span class="hlt">strain</span> data are the most direct evidence for deformation of the mandible induced by these loading regimes. Although many studies have documented bone <span class="hlt">strains</span> in the mammalian mandible, no information is available on <span class="hlt">strain</span> magnitudes, orientations or patterns in the sauropsid lower jaw during feeding. Furthermore, <span class="hlt">strain</span> gage experiments record the mechanical response of bone at a few locations, not across the entire mandible. In this paper, we present bone <span class="hlt">strain</span> data recorded at various sites on the lower jaw of Alligator mississippiensis during in vivo feeding experiments. These data are used to understand how changes in loading regime associated with changes in bite location are related to changes in <span class="hlt">strain</span> regime on the working and balancing sides of the mandible. Our results suggest that the working side mandible is bent dorsoventrally and twisted about its long-axis during biting, and the balancing side experiences primarily dorsoventral bending. <span class="hlt">Strain</span> orientations are more variable on the working side than on the balancing side with changes in bite point and between experiments; the balancing side exhibits higher <span class="hlt">strain</span> magnitudes. In the second part of this paper, we use principal <span class="hlt">strain</span> orientations and magnitudes recorded in vivo to evaluate a <span class="hlt">finite</span> element model of the alligator mandible. Our comparison demonstrates that <span class="hlt">strain</span> orientations and mandibular deformation predicted by the model closely match in vivo results; however, absolute <span class="hlt">strain</span> magnitudes are lower in the <span class="hlt">finite</span> element model. PMID:23855772</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/21920526','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/21920526"><span id="translatedtitle">Stress distributions and material properties determined in articular cartilage from MRI-based <span class="hlt">finite</span> <span class="hlt">strains</span>.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Butz, Kent D; Chan, Deva D; Nauman, Eric A; Neu, Corey P</p> <p>2011-10-13</p> <p>The noninvasive measurement of <span class="hlt">finite</span> <span class="hlt">strains</span> in biomaterials and tissues by magnetic resonance imaging (MRI) enables mathematical estimates of stress distributions and material properties. Such methods allow for non-contact and patient-specific modeling in a manner not possible with traditional mechanical testing or <span class="hlt">finite</span> element techniques. Here, we employed three constitutive (i.e. linear Hookean, and nonlinear Neo-Hookean and Mooney-Rivlin) relations with known loading conditions and MRI-based <span class="hlt">finite</span> <span class="hlt">strains</span> to estimate stress patterns and material properties in the articular cartilage of tibiofemoral joints. Displacement-encoded MRI was used to determine two-dimensional <span class="hlt">finite</span> <span class="hlt">strains</span> in juvenile porcine joints, and an iterative technique estimated stress distributions and material properties with defined constitutive relations. Stress distributions were consistent across all relations, although the stress magnitudes varied. Material properties for femoral and tibial cartilage were found to be consistent with those reported in literature. Further, the stress estimates from Hookean and Neo-Hookean, but not Mooney-Rivlin, relations agreed with <span class="hlt">finite</span> element-based simulations. A nonlinear Neo-Hookean relation provided the most appropriate model for the characterization of complex and spatially dependent stresses using two-dimensional MRI-based <span class="hlt">finite</span> <span class="hlt">strain</span>. These results demonstrate the feasibility of a new and computationally efficient technique incorporating MRI-based deformation with mathematical modeling to non-invasively evaluate the mechanical behavior of biological tissues and materials. PMID:21920526</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JMPSo..65...93M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JMPSo..65...93M"><span id="translatedtitle">Phase field modeling of fracture in rubbery polymers. Part I: <span class="hlt">Finite</span> <span class="hlt">elasticity</span> coupled with brittle failure</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Miehe, Christian; Schänzel, Lisa-Marie</p> <p>2014-04-01</p> <p>This work presents a new phase field model for rate-independent crack propagation in rubbery polymers at large <span class="hlt">strains</span> and considers details of its numerical implementation. The approach accounts for micro-mechanically based features of both the <span class="hlt">elastic</span> bulk response as well as the crack toughness of idealized polymer networks. The proposed diffusive crack modeling based on the introduction of a crack phase field overcomes difficulties associated with the computational realization of sharp crack discontinuities, in particular when it comes to complex crack topologies. The crack phase field governs a crack density function, which describes the macroscopic crack surface in the polymer per unit of the reference volume. It provides the basis for the constitutive modeling of a degrading free energy storage and a crack threshold function with a Griffith-type critical energy release rate, that governs the crack propagation in the polymer. Both the energy storage as well as the critical energy release due to fracture can be related to classical statistical network theories of polymers. The proposed framework of diffusive fracture in polymers is formulated in terms of a rate-type variational principle that determines the evolution of the coupled primary variable fields, i.e. the deformation field and the crack phase field. On the computational side, we outline a staggered solution procedure based on a one-pass operator split of the coupled equations, that successively updates in a typical time step the crack phase field and the displacement field. Such a solution algorithm is extremely robust, easy to implement and ideally suited for engineering problems. We finally demonstrate the performance of the phase field formulation of fracture at large <span class="hlt">strains</span> by means of representative numerical examples.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/27079489','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/27079489"><span id="translatedtitle">Experimental study and <span class="hlt">finite</span> element analysis based on equivalent load method for laser ultrasonic measurement of <span class="hlt">elastic</span> constants.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo</p> <p>2016-07-01</p> <p>The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an <span class="hlt">elastic</span> plate is studied by experiment and <span class="hlt">finite</span> element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The <span class="hlt">finite</span> element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the <span class="hlt">elastic</span> constants are demonstrated. PMID:27079489</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/25818950','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/25818950"><span id="translatedtitle">Development of Ti-Nb-Zr alloys with high <span class="hlt">elastic</span> admissible <span class="hlt">strain</span> for temporary orthopedic devices.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ozan, Sertan; Lin, Jixing; Li, Yuncang; Ipek, Rasim; Wen, Cuie</p> <p>2015-07-01</p> <p>A new series of beta Ti-Nb-Zr (TNZ) alloys with considerable plastic deformation ability during compression test, high <span class="hlt">elastic</span> admissible <span class="hlt">strain</span>, and excellent cytocompatibility have been developed for removable bone tissue implant applications. TNZ alloys with nominal compositions of Ti-34Nb-25Zr, Ti-30Nb-32Zr, Ti-28Nb-35.4Zr and Ti-24.8Nb-40.7Zr (wt.% hereafter) were fabricated using the cold-crucible levitation technique, and the effects of alloying element content on their microstructures, mechanical properties (tensile strength, yield strength, compressive yield strength, Young's modulus, <span class="hlt">elastic</span> energy, toughness, and micro-hardness), and cytocompatibilities were investigated and compared. Microstructural examinations revealed that the TNZ alloys consisted of β phase. The alloy samples displayed excellent ductility with no cracking, or fracturing during compression tests. Their tensile strength, Young's modulus, elongation at rupture, and <span class="hlt">elastic</span> admissible <span class="hlt">strain</span> were measured in the ranges of 704-839 MPa, 62-65 GPa, 9.9-14.8% and 1.08-1.31%, respectively. The tensile strength, Young's modulus and elongation at rupture of the Ti-34Nb-25Zr alloy were measured as 839 ± 31.8 MPa, 62 ± 3.6 GPa, and 14.8 ± 1.6%, respectively; this alloy exhibited the <span class="hlt">elastic</span> admissible <span class="hlt">strain</span> of approximately 1.31%. Cytocompatibility tests indicated that the cell viability ratios (CVR) of the alloys are greater than those of the control group; thus the TNZ alloys possess excellent cytocompatibility. PMID:25818950</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://ntrs.nasa.gov/search.jsp?R=19850029452&hterms=Factor+AF2&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DFactor%2BAF2','NASA-TRS'); return false;" href="http://ntrs.nasa.gov/search.jsp?R=19850029452&hterms=Factor+AF2&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DFactor%2BAF2"><span id="translatedtitle">Strainrange partitioning - A total <span class="hlt">strain</span> range version. [for creep fatigue life prediction by summing inelastic and <span class="hlt">elastic</span> <span class="hlt">strain</span>-range-life relations for two Ni base superalloys</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Halford, G. R.; Saltsman, J. F.</p> <p>1983-01-01</p> <p>Procedures are presented for expressing the Strainrange Partitioning (SRP) method for creep fatigue life prediction in terms of total <span class="hlt">strain</span> range. Inelastic and <span class="hlt">elastic</span> <span class="hlt">strain</span>-range - life relations are summed to give total <span class="hlt">strain</span>-range - life relations. The life components due to inelastic <span class="hlt">strains</span> are dealt with using conventional SRP procedures while the life components due to <span class="hlt">elastic</span> <span class="hlt">strains</span> are expressed as families of time-dependent terms for each type of SRP cycle. Cyclic constitutive material behavior plays an important role in establishing the <span class="hlt">elastic</span> <span class="hlt">strain</span>-range life relations as well as the partitioning of the inelastic <span class="hlt">strains</span>. To apply the approach, however, it is not necessary to have to determine the magnitude of the inelastic <span class="hlt">strain</span> range. The total <span class="hlt">strain</span> SRP approach is evaluated and verified using two nickel base superalloys, AF2-1DA and Rene 95. Excellent agreement is demonstrated between observed and predicted cyclic lifetimes with 70 to 80 percent of the predicted lives falling within factors of two of the observed lives. The total <span class="hlt">strain</span>-range SRP approach should be of considerable practical value to designers who are faced with creep-fatigue problems for which the inelastic <span class="hlt">strains</span> cannot be calculated with sufficient accuracy to make reliable life predictions by the conventional inelastic <span class="hlt">strain</span> range SRP approach.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.305...44R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.305...44R"><span id="translatedtitle">Non-conforming curved <span class="hlt">finite</span> element schemes for time-dependent <span class="hlt">elastic</span>-acoustic coupled problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rodríguez-Rozas, Ángel; Diaz, Julien</p> <p>2016-01-01</p> <p>High-order numerical methods for solving time-dependent acoustic-<span class="hlt">elastic</span> coupled problems are introduced. These methods, based on <span class="hlt">Finite</span> Element techniques, allow for a flexible coupling between the fluid and the solid domain by using non-conforming meshes and curved elements. Since characteristic waves travel at different speeds through different media, specific levels of granularity for the mesh discretization are required on each domain, making impractical a possible conforming coupling in between. Advantageously, physical domains may be independently discretized in our framework due to the non-conforming feature. Consequently, an important increase in computational efficiency may be achieved compared to other implementations based on conforming techniques, namely by reducing the total number of degrees of freedom. Differently from other non-conforming approaches proposed so far, our technique is relatively simpler and requires only a geometrical adjustment at the coupling interface at a preprocessing stage, so that no extra computations are necessary during the time evolution of the simulation. On the other hand, as an advantage of using curvilinear elements, the geometry of the coupling interface between the two media of interest is faithfully represented up to the order of the scheme used. In other words, higher order schemes are in consonance with higher order approximations of the geometry. Concerning the time discretization, we analyze both explicit and implicit schemes. These schemes are energy conserving and, for the explicit case, the stability is guaranteed by a CFL condition. In order to illustrate the accuracy and convergence of these methods, a set of representative numerical tests are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4673877','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4673877"><span id="translatedtitle">Giant <span class="hlt">elastic</span> tunability in <span class="hlt">strained</span> BiFeO3 near an electrically induced phase transition</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Li, Q; Cao, Y.; Yu, P.; Vasudevan, R. K.; Laanait, N.; Tselev, A.; Xue, F.; Chen, L. Q.; Maksymovych, P.; Kalinin, S. V.; Balke, N.</p> <p>2015-01-01</p> <p><span class="hlt">Elastic</span> anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation <span class="hlt">elastic</span>/piezoresponse spectroscopy, we probed sub-MHz <span class="hlt">elastic</span> dynamics of a tip bias-induced rhombohedral−tetragonal phase transition of <span class="hlt">strained</span> (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ∼103 nm3 sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with two- to three-fold enhancement of local piezoresponse. Coupled with phase-field modelling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (for example, domain walls) on the kinetics of this phase transition, thereby providing fresh insights into the morphotropic phase boundary in ferroelectrics. Furthermore, the giant electrically tunable <span class="hlt">elastic</span> stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on the utilization of the soft modes underlying successive ferroelectric phase transitions. PMID:26597483</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/pages/biblio/1244194-giant-elastic-tunability-strained-bifeo3-near-electrically-induced-phase-transition','SCIGOV-DOEP'); return false;" href="http://www.osti.gov/pages/biblio/1244194-giant-elastic-tunability-strained-bifeo3-near-electrically-induced-phase-transition"><span id="translatedtitle">Giant <span class="hlt">elastic</span> tunability in <span class="hlt">strained</span> BiFeO3 near an electrically induced phase transition</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGESBeta</a></p> <p>Yu, Pu; Vasudevan, Rama K.; Tselev, Alexander; Xue, Fei; Chen, Long -Qing; Maksymovych, Petro; Kalinin, Sergei V.; Balke, Nina; Li, Q.; Cao, Y.; et al</p> <p>2015-01-01</p> <p><span class="hlt">Elastic</span> anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation <span class="hlt">elastic</span>/piezoresponse spectroscopy, we probed sub-MHz <span class="hlt">elastic</span> dynamics of a tip bias-induced rhombohedral–tetragonal phase transition of <span class="hlt">strained</span> (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ~103 nm3 sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with 2-3 folds enhancement of local piezoresponse. Coupled with phase-field modeling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (e.g., domain walls) on the kinetics ofmore » this phase transition, thereby providing fresh insights into the morphotropic phase boundary (MPB) in ferroelectrics. Moreover, the giant electrically tunable <span class="hlt">elastic</span> stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on utilization of the soft modes underlying successive ferroelectric phase transitions.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015NatCo...6E8985L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015NatCo...6E8985L"><span id="translatedtitle">Giant <span class="hlt">elastic</span> tunability in <span class="hlt">strained</span> BiFeO3 near an electrically induced phase transition</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Li, Q.; Cao, Y.; Yu, P.; Vasudevan, R. K.; Laanait, N.; Tselev, A.; Xue, F.; Chen, L. Q.; Maksymovych, P.; Kalinin, S. V.; Balke, N.</p> <p>2015-11-01</p> <p><span class="hlt">Elastic</span> anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation <span class="hlt">elastic</span>/piezoresponse spectroscopy, we probed sub-MHz <span class="hlt">elastic</span> dynamics of a tip bias-induced rhombohedral-tetragonal phase transition of <span class="hlt">strained</span> (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ~103 nm3 sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with two- to three-fold enhancement of local piezoresponse. Coupled with phase-field modelling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (for example, domain walls) on the kinetics of this phase transition, thereby providing fresh insights into the morphotropic phase boundary in ferroelectrics. Furthermore, the giant electrically tunable <span class="hlt">elastic</span> stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on the utilization of the soft modes underlying successive ferroelectric phase transitions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/pages/biblio/1296688-frequency-pressure-strain-dependence-nonlinear-elasticity-berea-sandstone','SCIGOV-DOEP'); return false;" href="http://www.osti.gov/pages/biblio/1296688-frequency-pressure-strain-dependence-nonlinear-elasticity-berea-sandstone"><span id="translatedtitle">Frequency, pressure and <span class="hlt">strain</span> dependence of nonlinear <span class="hlt">elasticity</span> in Berea Sandstone</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGESBeta</a></p> <p>Riviere, Jacques; Johnson, Paul Allan; Marone, Chris; Pimienta, Lucas; Scuderi, Marco; Candela, Thibault; Shokouhi, Parisa; Schubnel, Alexandre; Fortin, Jerome</p> <p>2016-04-14</p> <p>Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static ( f → 0) and dynamic (few kilohertz) nonlinear <span class="hlt">elastic</span> response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on <span class="hlt">strain</span> amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1fmore » appears frequency independent. This result corroborates previous studies showing that the nonlinear <span class="hlt">elasticity</span> of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear <span class="hlt">elasticity</span>. Furthermore, these findings can be used to improve theories relating the macroscopic <span class="hlt">elastic</span> response to microstructural features.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/26597483','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/26597483"><span id="translatedtitle">Giant <span class="hlt">elastic</span> tunability in <span class="hlt">strained</span> BiFeO3 near an electrically induced phase transition.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Li, Q; Cao, Y; Yu, P; Vasudevan, R K; Laanait, N; Tselev, A; Xue, F; Chen, L Q; Maksymovych, P; Kalinin, S V; Balke, N</p> <p>2015-01-01</p> <p><span class="hlt">Elastic</span> anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation <span class="hlt">elastic</span>/piezoresponse spectroscopy, we probed sub-MHz <span class="hlt">elastic</span> dynamics of a tip bias-induced rhombohedral-tetragonal phase transition of <span class="hlt">strained</span> (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ∼10(3) nm(3) sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with two- to three-fold enhancement of local piezoresponse. Coupled with phase-field modelling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (for example, domain walls) on the kinetics of this phase transition, thereby providing fresh insights into the morphotropic phase boundary in ferroelectrics. Furthermore, the giant electrically tunable <span class="hlt">elastic</span> stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on the utilization of the soft modes underlying successive ferroelectric phase transitions. PMID:26597483</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20020027541','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20020027541"><span id="translatedtitle"><span class="hlt">Finite-Strain</span> Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)</p> <p>2002-01-01</p> <p>Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal <span class="hlt">straining</span>. It was not until 1997 that Drozdov introduced the first <span class="hlt">finite-strain</span> FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for <span class="hlt">finite-strain</span> analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study <span class="hlt">finite-strain</span> FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a <span class="hlt">finite</span> element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a <span class="hlt">finite</span> model, which can number into the millions in today's analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCoPh.295..161G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCoPh.295..161G"><span id="translatedtitle">Generalized Multiscale <span class="hlt">Finite</span>-Element Method (GMsFEM) for <span class="hlt">elastic</span> wave propagation in heterogeneous, anisotropic media</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin</p> <p>2015-08-01</p> <p>It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as <span class="hlt">finite</span>-difference method and <span class="hlt">finite</span>-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale <span class="hlt">Finite</span>-Element Method (GMsFEM) for <span class="hlt">elastic</span> wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional <span class="hlt">finite</span>-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the <span class="hlt">elastic</span> wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1221548','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1221548"><span id="translatedtitle">Generalized multiscale <span class="hlt">finite</span>-element method (GMsFEM) for <span class="hlt">elastic</span> wave propagation in heterogeneous, anisotropic media</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin</p> <p>2015-04-14</p> <p>It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as <span class="hlt">finite</span>-difference method and <span class="hlt">finite</span>-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale <span class="hlt">Finite</span>-Element Method (GMsFEM) for <span class="hlt">elastic</span> wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional <span class="hlt">finite</span>-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the <span class="hlt">elastic</span> wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/pages/biblio/1221548-generalized-multiscale-finite-element-method-gmsfem-elastic-wave-propagation-heterogeneous-anisotropic-media','SCIGOV-DOEP'); return false;" href="http://www.osti.gov/pages/biblio/1221548-generalized-multiscale-finite-element-method-gmsfem-elastic-wave-propagation-heterogeneous-anisotropic-media"><span id="translatedtitle">Generalized multiscale <span class="hlt">finite</span>-element method (GMsFEM) for <span class="hlt">elastic</span> wave propagation in heterogeneous, anisotropic media</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGESBeta</a></p> <p>Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin</p> <p>2015-04-14</p> <p>It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as <span class="hlt">finite</span>-difference method and <span class="hlt">finite</span>-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale <span class="hlt">Finite</span>-Element Method (GMsFEM) for <span class="hlt">elastic</span> wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional <span class="hlt">finite</span>-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the <span class="hlt">elastic</span> wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/biblio/22465640','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/biblio/22465640"><span id="translatedtitle">Generalized Multiscale <span class="hlt">Finite</span>-Element Method (GMsFEM) for <span class="hlt">elastic</span> wave propagation in heterogeneous, anisotropic media</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin</p> <p>2015-08-15</p> <p>It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as <span class="hlt">finite</span>-difference method and <span class="hlt">finite</span>-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale <span class="hlt">Finite</span>-Element Method (GMsFEM) for <span class="hlt">elastic</span> wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional <span class="hlt">finite</span>-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the <span class="hlt">elastic</span> wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JChPh.142x4905L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JChPh.142x4905L"><span id="translatedtitle">Phase field modelling of <span class="hlt">strain</span> induced crystal growth in an <span class="hlt">elastic</span> matrix</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Laghmach, Rabia; Candau, Nicolas; Chazeau, Laurent; Munch, Etienne; Biben, Thierry</p> <p>2015-06-01</p> <p>When a crystal phase grows in an amorphous matrix, such as a crystallisable elastomer, containing cross-links and/or entanglements, these "topological constraints" need to be pushed away from the crystal phase to allow further crystallization. The accumulation of these topological constraints in the vicinity of the crystal interface may store <span class="hlt">elastic</span> energy and affect the phase transition. To evaluate the consequences of such mechanism, we introduce a phase field model based on the Flory theory of entropic <span class="hlt">elasticity</span>. We show that the growth process is indeed sensibly affected, in particular, an exponential increase of the surface energy with the displacement of the interface is induced. This explains the formation of stable nano-crystallites as it is observed in the <span class="hlt">Strain</span> Induced Crystallization (SIC) of natural rubber. Although simple, the model developed here is able to account for many interesting features of SIC, for instance, the crystallite shapes and their sizes which depend on the applied deformation.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li class="active"><span>10</span></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_10 --> <div id="page_11" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li class="active"><span>11</span></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="201"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/26133455','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/26133455"><span id="translatedtitle">Phase field modelling of <span class="hlt">strain</span> induced crystal growth in an <span class="hlt">elastic</span> matrix.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Laghmach, Rabia; Candau, Nicolas; Chazeau, Laurent; Munch, Etienne; Biben, Thierry</p> <p>2015-06-28</p> <p>When a crystal phase grows in an amorphous matrix, such as a crystallisable elastomer, containing cross-links and/or entanglements, these "topological constraints" need to be pushed away from the crystal phase to allow further crystallization. The accumulation of these topological constraints in the vicinity of the crystal interface may store <span class="hlt">elastic</span> energy and affect the phase transition. To evaluate the consequences of such mechanism, we introduce a phase field model based on the Flory theory of entropic <span class="hlt">elasticity</span>. We show that the growth process is indeed sensibly affected, in particular, an exponential increase of the surface energy with the displacement of the interface is induced. This explains the formation of stable nano-crystallites as it is observed in the <span class="hlt">Strain</span> Induced Crystallization (SIC) of natural rubber. Although simple, the model developed here is able to account for many interesting features of SIC, for instance, the crystallite shapes and their sizes which depend on the applied deformation. PMID:26133455</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016InvPr..32f5002B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016InvPr..32f5002B"><span id="translatedtitle">Isotropic realizability of a <span class="hlt">strain</span> field for the two‑dimensional incompressible <span class="hlt">elasticity</span> system</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Briane, M.</p> <p>2016-06-01</p> <p>In the paper we study the problem of the isotropic realizability in {{{R}}}2 of a regular <span class="hlt">strain</span> field e(U)=\\tfrac{1}{2}({DU}+{{DU}}T) for the incompressible <span class="hlt">elasticity</span> system, namely the existence of a positive shear modulus μ \\gt 0 solving the <span class="hlt">elasticity</span> system in {{{R}}}2 with the prescribed field e(U). We show that if e(U) does not vanish at some point, then the isotropic realizability holds in the neighborhood of that point. The global realizability in {{{R}}}2 or in the torus is much more delicate, since it involves the global existence of a regular solution to a semilinear wave equation, the coefficients of which depend on the derivatives of U. Using this semilinear wave equation we prove a small perturbation result: if DU is periodic and close enough to its average value for the C 4‑norm, then the associated <span class="hlt">strain</span> field is isotropically realizable in a given disk centered at the origin. On the other hand, a counterexample shows that the global realizability in {{{R}}}2 may hold without the realizability in the torus, and it is discussed in connection with the associated semilinear wave equation. The case where the <span class="hlt">strain</span> field vanishes is illustrated by an example. The singular case of a rank-one laminate field is also investigated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016PhRvE..94b3003M&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016PhRvE..94b3003M&link_type=ABSTRACT"><span id="translatedtitle">Hydrodynamic description of <span class="hlt">elastic</span> or viscoelastic composite materials: Relative <span class="hlt">strains</span> as macroscopic variables</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Menzel, Andreas M.</p> <p>2016-08-01</p> <p>One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)<span class="hlt">elastic</span> substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)<span class="hlt">elastic</span> composite materials. For this purpose, additional <span class="hlt">strain</span> variables reflect the state of the inclusions and their immediate environment. These additional <span class="hlt">strain</span> variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a macroscopic variable termed relative <span class="hlt">strains</span>. We analyze two simplified minimal example geometries as an illustration.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016MTDM...20..139Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MTDM...20..139Z"><span id="translatedtitle">Approximate analytical solution for the problem of an inclusion in a viscoelastic solid under <span class="hlt">finite</span> <span class="hlt">strains</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zingerman, K. M.; Shavyrin, D. A.</p> <p>2016-06-01</p> <p>The approximate analytical solution of a quasi-static plane problem of the theory of viscoelasticity is obtained under <span class="hlt">finite</span> <span class="hlt">strains</span>. This is the problem of the stress-<span class="hlt">strain</span> state in an infinite body with circular viscoelastic inclusion. The perturbation technique, Laplace transform, and complex Kolosov-Muskhelishvili's potentials are used for the solution. The numerical results are presented. The nonlinear effects and the effects of viscosity are estimated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/20634548','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/20634548"><span id="translatedtitle"><span class="hlt">Elastic</span> <span class="hlt">strain</span> tensor measurement using electron backscatter diffraction in the SEM.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Dingley, David J; Wilkinson, Angus J; Meaden, Graham; Karamched, Phani S</p> <p>2010-08-01</p> <p>The established electron backscatter diffraction (EBSD) technique for obtaining crystallographic information in the SEM has been adapted to permit <span class="hlt">elastic</span> <span class="hlt">strain</span> measurement. Basically, the displacement of crystallographic features in an EBSD pattern, such as zone axes, which result from <span class="hlt">strain</span> in a crystal, is determined by comparing those same features as they appear in a pattern from an unstrained region of the crystal. The comparison is made by cross-correlation of selected regions in the two patterns. Tests show that the sensitivity to displacement measurement is 1 part in 10 000, which translates to a <span class="hlt">strain</span> sensitivity of 2 parts in 10 000. Eight components of the <span class="hlt">strain</span> tensor are determined directly and the ninth is calculated using the fact that the free surface of the sample is traction-free. Examples discussed are taken from studies of a lenticular fracture in germanium, the <span class="hlt">strain</span> distribution surrounding a carbide precipitate in a nickel base alloy and grain boundary studies in another nickel base alloy. PMID:20634548</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4816497','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4816497"><span id="translatedtitle">Dynamic <span class="hlt">finite-strain</span> modelling of the human left ventricle in health and disease using an immersed boundary-<span class="hlt">finite</span> element method</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Gao, Hao; Carrick, David; Berry, Colin; Griffith, Boyce E.; Luo, Xiaoyu</p> <p>2016-01-01</p> <p>Detailed models of the biomechanics of the heart are important both for developing improved interventions for patients with heart disease and also for patient risk stratification and treatment planning. For instance, stress distributions in the heart affect cardiac remodelling, but such distributions are not presently accessible in patients. Biomechanical models of the heart offer detailed three-dimensional deformation, stress and <span class="hlt">strain</span> fields that can supplement conventional clinical data. In this work, we introduce dynamic computational models of the human left ventricle (LV) that are derived from clinical imaging data obtained from a healthy subject and from a patient with a myocardial infarction (MI). Both models incorporate a detailed invariant-based orthotropic description of the passive <span class="hlt">elasticity</span> of the ventricular myocardium along with a detailed biophysical model of active tension generation in the ventricular muscle. These constitutive models are employed within a dynamic simulation framework that accounts for the inertia of the ventricular muscle and the blood that is based on an immersed boundary (IB) method with a <span class="hlt">finite</span> element description of the structural mechanics. The geometry of the models is based on data obtained non-invasively by cardiac magnetic resonance (CMR). CMR imaging data are also used to estimate the parameters of the passive and active constitutive models, which are determined so that the simulated end-diastolic and end-systolic volumes agree with the corresponding volumes determined from the CMR imaging studies. Using these models, we simulate LV dynamics from enddiastole to end-systole. The results of our simulations are shown to be in good agreement with subject-specific CMR-derived <span class="hlt">strain</span> measurements and also with earlier clinical studies on human LV <span class="hlt">strain</span> distributions. PMID:27041786</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19790008473','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790008473"><span id="translatedtitle">Three-dimensional <span class="hlt">finite</span>-element <span class="hlt">elastic</span> analysis of a thermally cycled single-edge wedge geometry specimen</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bizon, P. T.; Hill, R. J.; Guilliams, B. P.; Drake, S. K.; Kladden, J. L.</p> <p>1979-01-01</p> <p>An <span class="hlt">elastic</span> 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, <span class="hlt">strain</span>, and temperature results are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/5489817','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/5489817"><span id="translatedtitle">Comparison of experiment and theory for <span class="hlt">elastic</span>-plastic plane <span class="hlt">strain</span> crack growth</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Hermann, L; Rice, J R</p> <p>1980-02-01</p> <p>Recent theoretical results on <span class="hlt">elastic</span>-plastic plane <span class="hlt">strain</span> crack growth, and experimental results for crack growth in a 4140 steel in terms of the theoretical concepts are reviewed. The theory is based on a recent asymptotic analysis of crack surface opening and <span class="hlt">strain</span> distributions at a quasi-statically advancing crack tip in an ideally-plastic solid. The analysis is incomplete in that some of the parameters which appear in it are known only approximately, especially at large scale yielding. Nevertheless, it suffices to derive a relation between the imposed loading and amount of crack growth, prior to general yielding, based on the assumption that a geometrically similar near-tip crack profile is maintained during growth. The resulting predictions for the variation of J with crack growth are found to fit well to the experimental results obtained on deeply cracked compact specimens.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CompM..55..229K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CompM..55..229K"><span id="translatedtitle">Automatic implementation of <span class="hlt">finite</span> <span class="hlt">strain</span> anisotropic hyperelastic models using hyper-dual numbers</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kiran, Ravi; Khandelwal, Kapil</p> <p>2015-01-01</p> <p>The main aim of this paper is to automate the implementation of <span class="hlt">finite</span> <span class="hlt">strain</span> anisotropic hyperelastic models into a general <span class="hlt">finite</span> element framework. The automation presented in this paper enables the end-user to implement a hyperelastic model by programming its Helmholtz free energy function alone. The automation is achieved by employing hyper-dual number system to evaluate analytical quality derivatives. New perturbation techniques are introduced and are employed to extend the hyper-dual numbers system to evaluate tensor derivatives. The capability of the proposed automation scheme is demonstrated by implementing five <span class="hlt">finite</span> <span class="hlt">strain</span> anisotropic hyperelastic models. The merits and demerits of the proposed automation scheme are compared to an automation scheme based on the central difference method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19920005175','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19920005175"><span id="translatedtitle">A variational justification of the assumed natural <span class="hlt">strain</span> formulation of <span class="hlt">finite</span> elements</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Militello, Carmelo; Felippa, Carlos A.</p> <p>1991-01-01</p> <p>The objective is to study the assumed natural <span class="hlt">strain</span> (ANS) formulation of <span class="hlt">finite</span> elements from a variational standpoint. The study is based on two hybrid extensions of the Reissner-type functional that uses <span class="hlt">strains</span> and displacements as independent fields. One of the forms is a genuine variational principle that contains an independent boundary traction field, whereas the other one represents a restricted variational principle. Two procedures for element level elimination of the <span class="hlt">strain</span> field are discussed, and one of them is shown to be equivalent to the inclusion of incompatible displacement modes. Also, the 4-node C(exp 0) plate bending quadrilateral element is used to illustrate applications of this theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/25197258','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/25197258"><span id="translatedtitle">Cones of localized shear <span class="hlt">strain</span> in incompressible <span class="hlt">elasticity</span> with prestress: Green's function and integral representations.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Argani, L P; Bigoni, D; Capuani, D; Movchan, N V</p> <p>2014-09-01</p> <p>The infinite-body three-dimensional Green's function set (for incremental displacement and mean stress) is derived for the incremental deformation of a uniformly <span class="hlt">strained</span> incompressible, nonlinear <span class="hlt">elastic</span> body. Particular cases of the developed formulation are the Mooney-Rivlin <span class="hlt">elasticity</span> 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 <span class="hlt">elasticity</span>. 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</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012AcMSn..28...91N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012AcMSn..28...91N"><span id="translatedtitle">C 1 natural element method for <span class="hlt">strain</span> gradient linear <span class="hlt">elasticity</span> and its application to microstructures</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nie, Zhi-Feng; Zhou, Shen-Jie; Han, Ru-Jun; Xiao, Lin-Jing; Wang, Kai</p> <p>2012-02-01</p> <p>C 1 natural element method ( C 1 NEM) is applied to <span class="hlt">strain</span> gradient linear <span class="hlt">elasticity</span>, and size effects on microstructures are analyzed. The shape functions in C 1 NEM are built upon the natural neighbor interpolation (NNI), with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions (EBCs) can be imposed directly in a Galerkin scheme for partial differential equations (PDEs). In the present paper, C 1 NEM for <span class="hlt">strain</span> gradient linear <span class="hlt">elasticity</span> is constructed, and several typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor (SCF) are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006PhyD..217..153S&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006PhyD..217..153S&link_type=ABSTRACT"><span id="translatedtitle">Multi phase field model for solid state transformation with <span class="hlt">elastic</span> <span class="hlt">strain</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Steinbach, I.; Apel, M.</p> <p>2006-05-01</p> <p>A multi phase field model is presented for the investigation of the effect of transformation <span class="hlt">strain</span> on the transformation kinetics, morphology and thermodynamic stability in multi phase materials. The model conserves homogeneity of stress in the diffuse interface between <span class="hlt">elastically</span> inhomogeneous phases, in which respect it differs from previous models. The model is formulated consistently with the multi phase field model for diffusional and surface driven phase transitions [I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler, G.J. Schmitz, J.L.L. Rezende, A phase field concept for multiphase systems, Physica D 94 (1996) 135-147; J. Tiaden, B. Nestler, H.J. Diepers, I. Steinbach, The multiphase-field model with an integrated concept for modeling solute diffusion, Physica D 115 (1998) 73-86; I. Steinbach, F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D 134 (1999) 385] and gives a consistent description of interfacial tension, multi phase thermodynamics and <span class="hlt">elastic</span> stress balance in multiple junctions between an arbitrary number of grains and phases. Some aspects of the model are demonstrated with respect to numerical accuracy and the relation between transformation <span class="hlt">strain</span>, external stress and thermodynamic equilibrium.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004JSV...276..615P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004JSV...276..615P"><span id="translatedtitle">Stability of <span class="hlt">elastic</span> and viscoelastic plates in a gas flow taking into account shear <span class="hlt">strains</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Potapov, V. D.</p> <p>2004-09-01</p> <p>It is well known that the internal friction in a material can have a considerable destabilizing effect on the stability of non-conservative systems. Apart from the Voigt model, the viscoelastic body model is sometimes utilized to describe material damping. This relates the stability problem for non-conservative <span class="hlt">elastic</span> systems with that for viscoelastic system. The Bubnov-Galerkin method is usually applied for solving the problems. In this case, the displacement functions are represented by series in terms of natural vibration modes ϕ i( x) of the <span class="hlt">elastic</span> system. To provide a high degree of accuracy for the solution, one should involve a fairly large number of modes. For a viscoelastic plate, the number of terms to be kept in the expansion of the deflection can be substantially more. One should bear in mind, however, that as the number of modes preserved in the expansion increases, the influence of shear <span class="hlt">strains</span> and rotational inertia on the behavior of the solution becomes more pronounced. In view of this, it is important to study the stability of non-conservative viscoelastic systems with the shear <span class="hlt">strain</span> and rotational inertia being taken into account. In the present paper this problem is solved for a viscoelastic plate in a supersonic gas flow.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3668218','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3668218"><span id="translatedtitle">Computational simulation of the bone remodeling using the <span class="hlt">finite</span> element method: an <span class="hlt">elastic</span>-damage theory for small displacements</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p></p> <p>2013-01-01</p> <p>Background The resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property. These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of <span class="hlt">elastic</span>-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior. Results The purpose of the present study is to simulate a two dimensional model of a proximal femur by taking into consideration <span class="hlt">elastic</span>-damage and mechanical stimulus. Here, we present a mathematical model based on a system of nonlinear ordinary differential equations and we develop the variational formulation for the mechanical problem. Then, we implement our mathematical model into the <span class="hlt">finite</span> element method algorithm to investigate the effect of the damage. Conclusion The results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading. PMID:23663260</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/2637','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/2637"><span id="translatedtitle">A Family of Uniform <span class="hlt">Strain</span> Tetrahedral Elements and a Method for Connecting Dissimilar <span class="hlt">Finite</span> Element Meshes</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.</p> <p>1999-01-01</p> <p>This report documents a collection of papers on a family of uniform <span class="hlt">strain</span> tetrahedral <span class="hlt">finite</span> elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral <span class="hlt">Finite</span> Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform <span class="hlt">strain</span> and enhanced uniform <span class="hlt">strain</span> formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/948345','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/948345"><span id="translatedtitle">On the Relationship between Stress and <span class="hlt">Elastic</span> <span class="hlt">Strain</span> for Porous and Fractured Rock</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Liu, Hui-Hai; Rutqvist, Jonny; Berryman, James G.</p> <p>2008-02-25</p> <p>Modeling the mechanical deformations of porous and fractured rocks requires a stress-<span class="hlt">strain</span> relationship. Experience with inherently heterogeneous earth materials suggests that different varieties of Hook's law should be applied within regions of the rock having significantly different stress-<span class="hlt">strain</span> behavior, e.g., such as solid phase and various void geometries. We apply this idea by dividing a rock body conceptually into two distinct parts. The natural <span class="hlt">strain</span> (volume change divided by rock volume at the current stress state), rather than the engineering <span class="hlt">strain</span> (volume change divided by the unstressed rock volume), should be used in Hooke's law for accurate modeling of the <span class="hlt">elastic</span> deformation of that part of the pore volume subject to a relatively large degree of relative deformation (i.e., cracks or fractures). This approach permits the derivation of constitutive relations between stress and a variety of mechanical and/or hydraulic rock properties. We show that the theoretical predictions of this method are generally consistent with empirical expressions (from field data) and also laboratory rock experimental data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PMag...96.1420L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PMag...96.1420L"><span id="translatedtitle">Transformation-rate maxima during lath martensite formation: plastic vs. <span class="hlt">elastic</span> shape <span class="hlt">strain</span> accommodation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Loewy, Sarah; Rheingans, Bastian; Mittemeijer, Eric J.</p> <p>2016-05-01</p> <p>Recently, a modulated formation behaviour of lath martensite in Fe-Ni(-based) alloys was observed, exhibiting a series of transformation-rate maxima. This peculiar transformation behaviour was explained on the basis of the hierarchical microstructure of lath martensite, minimising the net shape <span class="hlt">strain</span> associated with martensite formation, by a block-by-block formation of martensite packages occurring simultaneously in all packages. In the present work, the martensitic transformation upon slow cooling of two Fe-Ni alloys, containing 22 and 25 at.% of Ni, respectively, was investigated by high-resolution dilatometry with the aim of identifying the influence of alloy composition on the modulated transformation behaviour. The differences observed for the two alloys, a more rapid sequence of the transformation-rate maxima and a narrower temperature range in case of Fe-25 at.% Ni, can be explained consistently as a consequence of the lower transformation temperatures in Fe-25 at.% Ni, highlighting the role of temporary accommodation of the shape <span class="hlt">strain</span> during formation of the lath martensite microstructure: the depression of the transformation toward lower temperatures leads to a higher strength of the austenite, hence resulting in a more <span class="hlt">elastic</span> (less plastic) temporary accommodation of the shape <span class="hlt">strain</span> upon block formation and thereby in a more effective mutual compensation of the shape <span class="hlt">strain</span> by neighbouring blocks. A kinetic model on the basis of energy-change considerations is presented which is able to describe the observed modulated transformation behaviour.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011NatNa...6..788L&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011NatNa...6..788L&link_type=ABSTRACT"><span id="translatedtitle">Skin-like pressure and <span class="hlt">strain</span> sensors based on transparent <span class="hlt">elastic</span> films of carbon nanotubes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lipomi, Darren J.; Vosgueritchian, Michael; Tee, Benjamin C.-K.; Hellstrom, Sondra L.; Lee, Jennifer A.; Fox, Courtney H.; Bao, Zhenan</p> <p>2011-12-01</p> <p>Transparent, <span class="hlt">elastic</span> conductors are essential components of electronic and optoelectronic devices that facilitate human interaction and biofeedback, such as interactive electronics, implantable medical devices and robotic systems with human-like sensing capabilities. The availability of conducting thin films with these properties could lead to the development of skin-like sensors that stretch reversibly, sense pressure (not just touch), bend into hairpin turns, integrate with collapsible, stretchable and mechanically robust displays and solar cells, and also wrap around non-planar and biological surfaces such as skin and organs, without wrinkling. We report transparent, conducting spray-deposited films of single-walled carbon nanotubes that can be rendered stretchable by applying <span class="hlt">strain</span> along each axis, and then releasing this <span class="hlt">strain</span>. This process produces spring-like structures in the nanotubes that accommodate <span class="hlt">strains</span> of up to 150% and demonstrate conductivities as high as 2,200 S cm-1 in the stretched state. We also use the nanotube films as electrodes in arrays of transparent, stretchable capacitors, which behave as pressure and <span class="hlt">strain</span> sensors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/25173237','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/25173237"><span id="translatedtitle">Determination of the <span class="hlt">elastic</span> properties of rabbit vocal fold tissue using uniaxial tensile testing and a tailored <span class="hlt">finite</span> element model.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Latifi, Neda; Miri, Amir K; Mongeau, Luc</p> <p>2014-11-01</p> <p>The aim of the present study was to quantify the effects of the specimen shape on the accuracy of mechanical properties determined from a shape-specific model generation strategy. Digital images of five rabbit vocal folds (VFs) in their initial undeformed conditions were used to build corresponding specific solid models. The displacement field of the VFs under uniaxial tensile test was then measured over the visible portion of the surface using digital image correlation. A three-dimensional <span class="hlt">finite</span> element model was built, using ABAQUS, for each solid model, while imposing measured boundary conditions. An inverse-problem method was used, assuming a homogeneous isotropic linear <span class="hlt">elastic</span> constitutive model. Unknown <span class="hlt">elastic</span> properties were identified iteratively through an error minimization technique between simulated and measured force-time data. The longitudinal <span class="hlt">elastic</span> moduli of the five rabbit VFs were calculated and compared to values from a simple analytical method and those obtained by approximating the cross-section as elliptical. The use of shape-specific models significantly reduced the standard deviation of the Young׳s moduli of the tested specimens. However, a non-parametric statistical analysis test, i.e., the Friedman test, yielded no statistically significant differences between the shape-specific method and the elliptic cylindrical <span class="hlt">finite</span> element model. Considering the required procedures to reconstruct the shape-specific <span class="hlt">finite</span> element model for each tissue specimen, it might be expedient to use the simpler method when large numbers of tissue specimens are to be compared regarding their Young׳s moduli. PMID:25173237</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li class="active"><span>11</span></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_11 --> <div id="page_12" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li class="active"><span>12</span></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="221"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/24948642','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/24948642"><span id="translatedtitle">Tendon <span class="hlt">elastic</span> <span class="hlt">strain</span> energy in the human ankle plantar-flexors and its role with increased running speed.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Lai, Adrian; Schache, Anthony G; Lin, Yi-Chung; Pandy, Marcus G</p> <p>2014-09-01</p> <p>The human ankle plantar-flexors, the soleus and gastrocnemius, utilize tendon <span class="hlt">elastic</span> <span class="hlt">strain</span> energy to reduce muscle fiber work and optimize contractile conditions during running. However, studies to date have considered only slow to moderate running speeds up to 5 m s(-1). Little is known about how the human ankle plantar-flexors utilize tendon <span class="hlt">elastic</span> <span class="hlt">strain</span> energy as running speed is advanced towards maximum sprinting. We used data obtained from gait experiments in conjunction with musculoskeletal modeling and optimization techniques to calculate muscle-tendon unit (MTU) work, tendon <span class="hlt">elastic</span> <span class="hlt">strain</span> energy and muscle fiber work for the ankle plantar-flexors as participants ran at five discrete steady-state speeds ranging from jogging (~2 m s(-1)) to sprinting (≥8 m s(-1)). As running speed progressed from jogging to sprinting, the contribution of tendon <span class="hlt">elastic</span> <span class="hlt">strain</span> energy to the positive work generated by the MTU increased from 53% to 74% for the soleus and from 62% to 75% for the gastrocnemius. This increase was facilitated by greater muscle activation and the relatively isometric behavior of the soleus and gastrocnemius muscle fibers. Both of these characteristics enhanced tendon stretch and recoil, which contributed to the bulk of the change in MTU length. Our results suggest that as steady-state running speed is advanced towards maximum sprinting, the human ankle plantar-flexors continue to prioritize the storage and recovery of tendon <span class="hlt">elastic</span> <span class="hlt">strain</span> energy over muscle fiber work. PMID:24948642</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19790004293','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790004293"><span id="translatedtitle"><span class="hlt">Elastic</span>-Plastic <span class="hlt">Finite</span> Element Analysis of Fatigue Crack Growth in Mode 1 and Mode 2 Conditions</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Nakagaki, M.; Atluri, S. N.</p> <p>1978-01-01</p> <p>Presented is an alternate cost-efficient and accurate <span class="hlt">elastic</span>-plastic <span class="hlt">finite</span> element procedure to analyze fatigue crack closure and its effects under general spectrum loading. Both Modes 1 and 2 type cycling loadings are considered. Also presented are the results of an investigation, using the newly developed procedure, of various factors that cause crack growth acceleration or retardation and delay effects under high-to-low, low-to-high, single overload, and constant amplitude type cyclic loading in a Mode 1 situation. Further, the results of an investigation of a centercracked panel under external pure shear (Mode 2) cyclic loading, of constant amplitude, are reported.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4312579','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4312579"><span id="translatedtitle"><span class="hlt">Strain</span> Amplification Analysis of an Osteocyte under Static and Cyclic Loading: A <span class="hlt">Finite</span> Element Study</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Xian, Cory J.</p> <p>2015-01-01</p> <p>Osteocytes, the major type of bone cells which reside in their lacunar and canalicular system within the bone matrix, function as biomechanosensors and biomechanotransducers of the bone. Although biomechanical behaviour of the osteocyte-lacunar-canalicular system has been investigated in previous studies mostly using computational 2-dimensional (2D) geometric models, only a few studies have used the 3-dimensional (3D) <span class="hlt">finite</span> element (FE) model. In the current study, a 3D FE model was used to predict the responses of <span class="hlt">strain</span> distributions of osteocyte-lacunar-canalicular system analyzed under static and cyclic loads. The <span class="hlt">strain</span> amplification factor was calculated for all simulations. Effects on the <span class="hlt">strain</span> of the osteocyte system were investigated under 500, 1500, 2000, and 3000 microstrain loading magnitudes and 1, 5, 10, 40, and 100 Hz loading frequencies. The maximum <span class="hlt">strain</span> was found to change with loading magnitude and frequency. It was observed that maximum <span class="hlt">strain</span> under 3000-microstrain loading was higher than those under 500, 1500, and 2000 microstrains. When the loading <span class="hlt">strain</span> reached the maximum magnitude, the <span class="hlt">strain</span> amplification factor of 100 Hz was higher than those of the other frequencies. Data from this 3D FE model study suggests that the <span class="hlt">strain</span> amplification factor of the osteocyte-lacunar-canalicular system increases with loading frequency and loading <span class="hlt">strain</span> increasing. PMID:25664319</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/22319376','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/22319376"><span id="translatedtitle">The effect of tensile hysteresis and contact resistance on the performance of <span class="hlt">strain</span>-resistant <span class="hlt">elastic</span>-conductive webbing.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Shyr, Tien-Wei; Shie, Jing-Wen; Jhuang, Yan-Er</p> <p>2011-01-01</p> <p>To use e-textiles as a <span class="hlt">strain</span>-resistance sensor they need to be both <span class="hlt">elastic</span> and conductive. Three kinds of <span class="hlt">elastic</span>-conductive webbings, including flat, tubular, and belt webbings, made of Lycra fiber and carbon coated polyamide fiber, were used in this study. The <span class="hlt">strain</span>-resistance properties of the webbings were evaluated in stretch-recovery tests and measured within 30% <span class="hlt">strain</span>. It was found that tensile hysteresis and contact resistance significantly influence the tensile <span class="hlt">elasticity</span> and the resistance sensitivity of the webbings. The results showed that the webbing structure definitely contributes to the tensile hysteresis and contact resistance. The smaller the friction is among the yarns in the belt webbing, the smaller the tensile hysteresis loss. However the close proximity of the conductive yarns in flat and tubular webbings results in a lower contact resistance. PMID:22319376</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3274011','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3274011"><span id="translatedtitle">The Effect of Tensile Hysteresis and Contact Resistance on the Performance of <span class="hlt">Strain</span>-Resistant <span class="hlt">Elastic</span>-Conductive Webbing</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Shyr, Tien-Wei; Shie, Jing-Wen; Jhuang, Yan-Er</p> <p>2011-01-01</p> <p>To use e-textiles as a <span class="hlt">strain</span>-resistance sensor they need to be both <span class="hlt">elastic</span> and conductive. Three kinds of <span class="hlt">elastic</span>-conductive webbings, including flat, tubular, and belt webbings, made of Lycra fiber and carbon coated polyamide fiber, were used in this study. The <span class="hlt">strain</span>-resistance properties of the webbings were evaluated in stretch-recovery tests and measured within 30% <span class="hlt">strain</span>. It was found that tensile hysteresis and contact resistance significantly influence the tensile <span class="hlt">elasticity</span> and the resistance sensitivity of the webbings. The results showed that the webbing structure definitely contributes to the tensile hysteresis and contact resistance. The smaller the friction is among the yarns in the belt webbing, the smaller the tensile hysteresis loss. However the close proximity of the conductive yarns in flat and tubular webbings results in a lower contact resistance. PMID:22319376</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004AGUFM.G21A0108N&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004AGUFM.G21A0108N&link_type=ABSTRACT"><span id="translatedtitle">Evaluation Of <span class="hlt">Elastic</span> <span class="hlt">Strain</span> Accumulation In The Southern Indian Peninsula By GPS-Geodesy</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Narayanababu, R.; Ec, M.; Tummala, C.</p> <p>2004-12-01</p> <p>The computed <span class="hlt">elastic</span> <span class="hlt">strain</span> accumulation in the southern Indian peninsula from the GPS derived velocity fields of the global network of GPS stations, in and around the Indian plate which includes Maitri, Indian Antarctic Station, show a significant departure from rigid plate behaviour in a manner consistent with the mapped intra plate stress field, observations of deformations and seismicity in the region. Our results of intraplate <span class="hlt">strain</span> accumulation within Antarctica Plate covering three sites MAIT, CAS1 and DAV1 are 1.8x10-9yr-1, 1.6x10-9yr-1 and 1.1x10-9yr-1, respectively. Similarly, the estimates of interplate <span class="hlt">strain</span> accumulation between Antarctica and other plates Somalia (SEY1), Africa (HARO), Australia (YAR1), and diffuse plate boundary between India and Australia (COCO) are found to be 1.1x10-9yr-1, 1.0x10-10yr-1, 1.27x10-8yr-1 and 1.18x10-8yr-1, respectively. These estimates are in good agreement with the earlier studies on estimation of global <span class="hlt">strain</span> rate. The combined GPS and seismic analysis confirm the emergence of diffuse plate boundary between India and Australia and relates to the late Miocene Himalayan uplift. The calculated stress field in the West of the Indian Peninsula has a roughly N-S directed tensional and E-W oriented compressional character and the velocity vectors of all other sites throw a significant insight into the plausible causes of the <span class="hlt">strain</span> accumulation processes in the Indian Ocean and the northward movement of Indian plate.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JMPSo..78...94G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JMPSo..78...94G"><span id="translatedtitle">The stability of <span class="hlt">elastically</span> <span class="hlt">strained</span> nanorings and the formation of quantum dot molecules</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gill, Simon P. A.</p> <p>2015-05-01</p> <p>Self-assembled nanorings have recently been identified in a number of heteroepitaxially <span class="hlt">strained</span> material systems. Under some circumstances these rings have been observed to break up into ring-shaped quantum dot molecules. A general non-linear model for the <span class="hlt">elastic</span> <span class="hlt">strain</span> energy of non-axisymmetric epitaxially <span class="hlt">strained</span> nanostructures beyond the small slope assumption is developed. This model is then used to investigate the stability of <span class="hlt">strained</span> nanorings evolving via surface diffusion subject to perturbations around their circumference. An expression for the fastest growing mode is determined and related to experimental observations. The model predicts a region of stability for rings below a critical radius, and also a region for larger rings which have a proportionally small thickness. The predictions of the model are shown to be consistent with the available results. For the heteroepitaxial InP on In0.5Ga0.5P system investigated by Jevasuwan et al. (2013), the nanorings are found to be stable below a certain critical size. This is in good quantitative agreement with the model predictions. At larger sizes, the rings are unstable. The number of dots in the resulting quantum dot molecule is similar to the mode number for the fastest growing mode. Second order terms show that the number of dots is expected to reduce as the height of the ring increases in proportion to its thickness. The <span class="hlt">strained</span> In0.4Ga0.6As on GaAs nanorings of Hanke et al. (2007) are always stable and this is in accordance with the findings of the analysis. The Au nanorings of Ruffino et al. (2011) are stable as well, even as they expand during annealing. This observation is also shown to be consistent with the proposed model, which is expected to be useful in the design and tailoring of heteroepitaxial systems for the self-organisation of quantum dot molecules.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/755313','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/755313"><span id="translatedtitle">An <span class="hlt">elastic</span>-perfectly plastic flow model for <span class="hlt">finite</span> element analysis of perforated materials</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Jones, D.P.; Gordon, J.L.; Hutula, D.N.; Banas, D.; Newman, J.B.</p> <p>1999-02-01</p> <p>This paper describes the formulation of an <span class="hlt">elastic</span>-perfectly plastic flow theory applicable to equivalent solid [EQS] modeling of perforated materials. An equilateral triangular array of circular penetrations is considered. The usual assumptions regarding geometry and loading conditions applicable to the development of <span class="hlt">elastic</span> constants for EQS modeling of perforated plates are considered to apply here. An <span class="hlt">elastic</span>-perfectly plastic [EPP] EQS model is developed for a collapse surface that includes fourth-order stress terms. The fourth order yield function has been shown to be appropriate for plates with a triangular array of circular holes. A complete flow model is formulated using the consistent tangent modulus approach based on the fourth order yield function.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PMag...96.1643G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PMag...96.1643G"><span id="translatedtitle">Stored energy in metallic glasses due to <span class="hlt">strains</span> within the <span class="hlt">elastic</span> limit</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Greer, A. L.; Sun, Y. H.</p> <p>2016-06-01</p> <p>Room temperature loading of metallic glasses, at stresses below the macroscopic yield stress, raises their enthalpy and causes creep. Thermal cycling of metallic glasses between room temperature and 77 K also raises their enthalpy. In both cases, the enthalpy increases are comparable to those induced by heavy plastic deformation, but, as we show, the origins must be quite different. For plastic deformation, the enthalpy increase is a fraction (<10%) of the work done (WD) (and, in this sense, the behaviour is similar to that of conventional polycrystalline metals and alloys). In contrast, the room temperature creep and the thermal cycling involve small <span class="hlt">strains</span> well within the <span class="hlt">elastic</span> limit; in these cases, the enthalpy increase in the glass exceeds the WD, by as much as three orders of magnitude. We argue that the increased enthalpy can arise only from an endothermic disordering process drawing heat from the surroundings. We examine the mechanisms of this process. The increased enthalpy ('stored energy') is a measure of rejuvenation and appears as an exothermic heat of relaxation on heating the glass. The profile of this heat release (the 'relaxation spectrum') is analysed for several metallic glasses subjected to various treatments. Thus, the effects of the small-<span class="hlt">strain</span> processing (creep and thermal cycling) can be better understood, and we can explore the potential for improving properties, in particular the plasticity, of metallic glasses. Metallic glasses can exhibit a wide range of enthalpy at a given temperature, and small-<span class="hlt">strain</span> processing may assist in accessing this for practical purposes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/17227094','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/17227094"><span id="translatedtitle"><span class="hlt">Finite</span> element modeling for <span class="hlt">strain</span> rate dependency of fracture resistance in compact bone.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Charoenphan, S; Polchai, A</p> <p>2007-02-01</p> <p>Crack growths in compact bones driven by various <span class="hlt">strain</span> rate levels were studied using <span class="hlt">finite</span> element modeling. The energy resistance curves in bovine femur cortical bones were characterized, whereas the orthotropic viscoelasticity in bone materials was accounted for to assess the effect of <span class="hlt">strain</span> rate on the energy resistance curve. The models were also used to justify the anticipated plane <span class="hlt">strain</span> response as a result of rather thick specimens used in experiments. Similarities were found between the experimental and model results when crack resistance ability exhibited in bones with slow loading rates, while unstable crack growth existed in bones with rapid loading rates. The critical energy release rates slightly decreased with the increase in <span class="hlt">strain</span> rates. The hybrid experimental and computational method introduced in this study could be beneficial for application in fracture study in which standard experiments cannot be validly performed. PMID:17227094</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1044892','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1044892"><span id="translatedtitle">An explicit <span class="hlt">finite</span> element formulation for dynamic <span class="hlt">strain</span> localization and damage evolution in metals</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Mourad, Hashem M; Bronkhorst, Curt A; Addessio, Francis L</p> <p>2010-12-16</p> <p>An explicit <span class="hlt">finite</span> element formulation, used to study the behavior and failure mechanisms of metallic materials under high <span class="hlt">strain</span> rate loading, is presented. The formulation is based on the assumed-<span class="hlt">strain</span> approach of Fish and Belytschko [1988], which allows localization bands to be embedded within an element, thereby alleviating mesh sensitivity and reducing the required computational effort. The behavior of the material outside localization bands (and of the virgin material prior to the onset of <span class="hlt">strain</span> localization) is represented using a Gurson-type coupled plasticity-damage model based on the work of Johnson and Addessio [1988]. Assuming adiabatic conditions, the response of the localization band material is represented by a set of constitutive equations for large elasticviscoplastic deformations in metals at high <span class="hlt">strain</span> rates and high homologous temperatures (see Brown et al. [1989]). Computational results are compared to experimental data for different metallic alloys to illustrate the advantages of the proposed modeling strategy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1228004','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1228004"><span id="translatedtitle">Wave propagation in anisotropic <span class="hlt">elastic</span> materials and curvilinear coordinates using a summation-by-parts <span class="hlt">finite</span> difference method</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Petersson, N. Anders; Sjogreen, Bjorn</p> <p>2015-07-20</p> <p>We develop a fourth order accurate <span class="hlt">finite</span> difference method for solving the three-dimensional <span class="hlt">elastic</span> 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 <span class="hlt">elastic</span> wave equation in second order formulation, using a node centered <span class="hlt">finite</span> 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-field 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.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/pages/biblio/1228004-wave-propagation-anisotropic-elastic-materials-curvilinear-coordinates-using-summation-parts-finite-difference-method','SCIGOV-DOEP'); return false;" href="http://www.osti.gov/pages/biblio/1228004-wave-propagation-anisotropic-elastic-materials-curvilinear-coordinates-using-summation-parts-finite-difference-method"><span id="translatedtitle">Wave propagation in anisotropic <span class="hlt">elastic</span> materials and curvilinear coordinates using a summation-by-parts <span class="hlt">finite</span> difference method</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGESBeta</a></p> <p>Petersson, N. Anders; Sjogreen, Bjorn</p> <p>2015-07-20</p> <p>We develop a fourth order accurate <span class="hlt">finite</span> difference method for solving the three-dimensional <span class="hlt">elastic</span> 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 <span class="hlt">elastic</span> wave equation in second order formulation, using a node centered <span class="hlt">finite</span> 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</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19840009553','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19840009553"><span id="translatedtitle">A <span class="hlt">finite</span> difference scheme for the equilibrium equations of <span class="hlt">elastic</span> bodies</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Phillips, T. N.; Rose, M. E.</p> <p>1984-01-01</p> <p>A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an <span class="hlt">elastic</span> body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009OptLE..47..352N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009OptLE..47..352N"><span id="translatedtitle">Mesoscopic <span class="hlt">strain</span> fields in woven composites: Experiments vs. <span class="hlt">finite</span> element modeling</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nicoletto, Gianni; Anzelotti, Giancarlo; Riva, Enrica</p> <p>2009-03-01</p> <p>Detailed determination of <span class="hlt">strain</span> in woven composite materials is fundamental for understanding their mechanics and for validating sophisticated computational models. The digital image correlation technique is briefly presented and applied to the full-field <span class="hlt">strain</span> determination in a twill-weave carbon-fiber-reinforced-plastic (CFRP) composite under in-plane loading. The experimental results are used to assess companion results obtained with an ad hoc <span class="hlt">finite</span> element-based model. The DIC vs. FEM comparison is carried out at the mesoscopic scale.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/26192949','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/26192949"><span id="translatedtitle">Evaluation of Axonal <span class="hlt">Strain</span> as a Predictor for Mild Traumatic Brain Injuries Using <span class="hlt">Finite</span> Element Modeling.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Giordano, Chiara; Kleiven, Svein</p> <p>2014-11-01</p> <p><span class="hlt">Finite</span> element (FE) models are often used to study the biomechanical effects of traumatic brain injury (TBI). Measures based on mechanical responses, such as principal <span class="hlt">strain</span> or invariants of the <span class="hlt">strain</span> tensor, are used as a metric to predict the risk of injury. However, the reliability of inferences drawn from these models depends on the correspondence between the mechanical measures and injury data, as well as the establishment of accurate thresholds of tissue injury. In the current study, a validated anisotropic FE model of the human head is used to evaluate the hypothesis that <span class="hlt">strain</span> in the direction of fibers (axonal <span class="hlt">strain</span>) is a better predictor of TBI than maximum principal <span class="hlt">strain</span> (MPS), anisotropic equivalent <span class="hlt">strain</span> (AESM) and cumulative <span class="hlt">strain</span> damage measure (CSDM). An analysis of head kinematics-based metrics, such as head injury criterion (HIC) and brain injury criterion (BrIC), is also provided. Logistic regression analysis is employed to compare binary injury data (concussion/no concussion) with continuous <span class="hlt">strain</span>/kinematics data. The threshold corresponding to 50% of injury probability is determined for each parameter. The predictive power (area under the ROC curve, AUC) is calculated from receiver operating characteristic (ROC) curve analysis. The measure with the highest AUC is considered to be the best predictor of mTBI. Logistic regression shows a statistical correlation between all the mechanical predictors and injury data for different regions of the brain. Peaks of axonal <span class="hlt">strain</span> have the highest AUC and determine a <span class="hlt">strain</span> threshold of 0.07 for corpus callosum and 0.15 for the brainstem, in agreement with previously experimentally derived injury thresholds for reversible axonal injury. For a data set of mild TBI from the national football league, the <span class="hlt">strain</span> in the axonal direction is found to be a better injury predictor than MPS, AESM, CSDM, BrIC and HIC. PMID:26192949</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20050185211','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20050185211"><span id="translatedtitle">Structural Health Monitoring Using High-Density Fiber Optic <span class="hlt">Strain</span> Sensor and Inverse <span class="hlt">Finite</span> Element Methods</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Vazquez, Sixto L.; Tessler, Alexander; Quach, Cuong C.; Cooper, Eric G.; Parks, Jeffrey; Spangler, Jan L.</p> <p>2005-01-01</p> <p>In an effort to mitigate accidents due to system and component failure, NASA s Aviation Safety has partnered with industry, academia, and other governmental organizations to develop real-time, on-board monitoring capabilities and system performance models for early detection of airframe structure degradation. NASA Langley is investigating a structural health monitoring capability that uses a distributed fiber optic <span class="hlt">strain</span> system and an inverse <span class="hlt">finite</span> element method for measuring and modeling structural deformations. This report describes the constituent systems that enable this structural monitoring function and discusses results from laboratory tests using the fiber <span class="hlt">strain</span> sensor system and the inverse <span class="hlt">finite</span> element method to demonstrate structural deformation estimation on an instrumented test article</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016JMPSo..88..204L&link_type=ABSTRACT','NASAADS'); return false;" href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2016JMPSo..88..204L&link_type=ABSTRACT"><span id="translatedtitle">Molecular simulation guided constitutive modeling on <span class="hlt">finite</span> <span class="hlt">strain</span> viscoelasticity of elastomers</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Li, Ying; Tang, Shan; Kröger, Martin; Liu, Wing Kam</p> <p>2016-03-01</p> <p>Viscoelasticity characterizes the most important mechanical behavior of elastomers. Understanding the viscoelasticity, especially <span class="hlt">finite</span> <span class="hlt">strain</span> viscoelasticity, of elastomers is the key for continuation of their dedicated use in industrial applications. In this work, we present a mechanistic and physics-based constitutive model to describe and design the <span class="hlt">finite</span> <span class="hlt">strain</span> viscoelastic behavior of elastomers. Mathematically, the viscoelasticity of elastomers has been decomposed into hyperelastic and viscous parts, which are attributed to the nonlinear deformation of the cross-linked polymer network and the diffusion of free chains, respectively. The hyperelastic deformation of a cross-linked polymer network is governed by the cross-linking density, the molecular weight of the polymer strands between cross-linkages, and the amount of entanglements between different chains, which we observe through large scale molecular dynamics (MD) simulations. Moreover, a recently developed non-affine network model (Davidson and Goulbourne, 2013) is confirmed in the current work to be able to capture these key physical mechanisms using MD simulation. The energy dissipation during a loading and unloading process of elastomers is governed by the diffusion of free chains, which can be understood through their reptation dynamics. The viscous stress can be formulated using the classical tube model (Doi and Edwards, 1986); however, it cannot be used to capture the energy dissipation during <span class="hlt">finite</span> deformation. By considering the tube deformation during this process, as observed from the MD simulations, we propose a modified tube model to account for the <span class="hlt">finite</span> deformation behavior of free chains. Combing the non-affine network model for hyperelasticity and modified tube model for viscosity, both understood by molecular simulations, we develop a mechanism-based constitutive model for <span class="hlt">finite</span> <span class="hlt">strain</span> viscoelasticity of elastomers. All the parameters in the proposed constitutive model have</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1132568','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1132568"><span id="translatedtitle">Spectral Modeling of Residual Stress and Stored <span class="hlt">Elastic</span> <span class="hlt">Strain</span> Energy in Thermal Barrier Coatings</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Donegan, Sean; Rolett, Anthony</p> <p>2013-12-31</p> <p>Solutions to the thermoelastic problem are important for characterizing the response under temperature change of refractory systems. This work extends a spectral fast Fourier transform (FFT) technique to analyze the thermoelastic behavior of thermal barrier coatings (TBCs), with the intent of probing the local origins of failure in TBCs. The thermoelastic FFT (teFFT) approach allows for the characterization of local thermal residual stress and <span class="hlt">strain</span> fields, which constitute the origins of failure in TBC systems. A technique based on statistical extreme value theory known as peaks-over-threshold (POT) is developed to quantify the extreme values ("hot spots") of stored <span class="hlt">elastic</span> <span class="hlt">strain</span> energy (i.e., <span class="hlt">elastic</span> energy density, or EED). The resolution dependence of the teFFT method is assessed through a sensitivity study of the extreme values in EED. The sensitivity study is performed both for the local (point-by-point) eld distributions as well as the grain scale eld distributions. A convergence behavior to a particular distribution shape is demonstrated for the local elds. The grain scale fields are shown to exhibit a possible convergence to a maximum level of EED. To apply the teFFT method to TBC systems, 3D synthetic microstructures are created to approximate actual TBC microstructures. The morphology of the grains in each constituent layer as well as the texture is controlled. A variety of TBC materials, including industry standard materials and potential future materials, are analyzed using the teFFT. The resulting hot spots are quantified using the POT approach. A correlation between hot spots in EED and interface rumpling between constituent layers is demonstrated, particularly for the interface between the bond coat (BC) and the thermally grown oxide (TGO) layer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4646616','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4646616"><span id="translatedtitle">The <span class="hlt">Elastic</span> Behaviour of Sintered Metallic Fibre Networks: A <span class="hlt">Finite</span> Element Study by Beam Theory</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Bosbach, Wolfram A.</p> <p>2015-01-01</p> <p>Background The <span class="hlt">finite</span> element method has complimented research in the field of network mechanics in the past years in numerous studies about various materials. Numerical predictions and the planning efficiency of experimental procedures are two of the motivational aspects for these numerical studies. The widespread availability of high performance computing facilities has been the enabler for the simulation of sufficiently large systems. Objectives and Motivation In the present study, <span class="hlt">finite</span> element models were built for sintered, metallic fibre networks and validated by previously published experimental stiffness measurements. The validated models were the basis for predictions about so far unknown properties. Materials and Methods The <span class="hlt">finite</span> element models were built by transferring previously published skeletons of fibre networks into <span class="hlt">finite</span> element models. Beam theory was applied as simplification method. Results and Conclusions The obtained material stiffness isn’t a constant but rather a function of variables such as sample size and boundary conditions. Beam theory offers an efficient <span class="hlt">finite</span> element method for the simulated fibre networks. The experimental results can be approximated by the simulated systems. Two worthwhile aspects for future work will be the influence of size and shape and the mechanical interaction with matrix materials. PMID:26569603</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li class="active"><span>12</span></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_12 --> <div id="page_13" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li class="active"><span>13</span></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="241"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1238736','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1238736"><span id="translatedtitle">Direct synchrotron x-ray measurements of local <span class="hlt">strain</span> fields in <span class="hlt">elastically</span> and plastically bent metallic glasses</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Wu, Yuan; Stoica, Alexandru Dan; Ren, Yang; Ma, Dong; Gao, Yanfei F.; Bei, Hongbin</p> <p>2015-09-03</p> <p><i>In situ</i> high-energy synchrotron X-ray diffraction was conducted on <span class="hlt">elastically</span> and plastically bent bulk metallic glass (BMG) thin plates, from which distinct local <span class="hlt">elastic</span> <span class="hlt">strain</span> fields were mapped spatially. These directly measured residual <span class="hlt">strain</span> fields can be nicely interpreted by our stress analysis, and also validate a previously proposed indirect residual-stress-measurement method by relating nanoindentation hardness to residual stresses. Local shear <span class="hlt">strain</span> variations on the cross sections of these thin plates were found in the plastically bent BMG, which however cannot be determined from the indirect indentation method. As a result, this study has important implications in designing and manipulating internal <span class="hlt">strain</span> fields in BMGs for the purpose of ductility enhancement.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/pages/biblio/1238736-direct-synchrotron-ray-measurements-local-strain-fields-elastically-plastically-bent-metallic-glasses','SCIGOV-DOEP'); return false;" href="http://www.osti.gov/pages/biblio/1238736-direct-synchrotron-ray-measurements-local-strain-fields-elastically-plastically-bent-metallic-glasses"><span id="translatedtitle">Direct synchrotron x-ray measurements of local <span class="hlt">strain</span> fields in <span class="hlt">elastically</span> and plastically bent metallic glasses</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGESBeta</a></p> <p>Wu, Yuan; Stoica, Alexandru Dan; Ren, Yang; Ma, Dong; Gao, Yanfei F.; Bei, Hongbin</p> <p>2015-09-03</p> <p>In situ high-energy synchrotron X-ray diffraction was conducted on <span class="hlt">elastically</span> and plastically bent bulk metallic glass (BMG) thin plates, from which distinct local <span class="hlt">elastic</span> <span class="hlt">strain</span> fields were mapped spatially. These directly measured residual <span class="hlt">strain</span> fields can be nicely interpreted by our stress analysis, and also validate a previously proposed indirect residual-stress-measurement method by relating nanoindentation hardness to residual stresses. Local shear <span class="hlt">strain</span> variations on the cross sections of these thin plates were found in the plastically bent BMG, which however cannot be determined from the indirect indentation method. As a result, this study has important implications in designing and manipulatingmore » internal <span class="hlt">strain</span> fields in BMGs for the purpose of ductility enhancement.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/24001928','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/24001928"><span id="translatedtitle">Validation of density-<span class="hlt">elasticity</span> relationships for <span class="hlt">finite</span> element modeling of human pelvic bone by modal analysis.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Scholz, Roger; Hoffmann, Falk; von Sachsen, Sandra; Drossel, Welf-Guntram; Klöhn, Carsten; Voigt, Christian</p> <p>2013-10-18</p> <p>In total hip arthroplasty and particularly in revision surgery, computer assisted pre-operative prediction of the best possible anchorage strategy for implant fixation would be a great help to the surgeon. Computer simulation relies on validated numerical models. In the current study, three density-<span class="hlt">elasticity</span> relationships (No. 1-3) from the literature for inhomogeneous material parameter assignment from CT data in automated <span class="hlt">finite</span> element (FE) modeling of long bones were evaluated for their suitability for FE modeling of human pelvic bone. Numerical modal analysis was conducted on 10 FE models of hemipelvic bone specimens and compared to the gold standard provided by experimental modal analysis results from a previous in-vitro study on the same specimens. Overall, calculated resonance frequencies came out lower than measured values. Magnitude of mean relative deviation of numerical resonance frequencies with regard to measured values is lowest for the density-<span class="hlt">elasticity</span> relationship No. 3 (-15.9%) and considerably higher for both density-<span class="hlt">elasticity</span> relationships No. 1 (-41.1%) and No. 2 (-45.0%). Mean MAC values over all specimens amount to 77.8% (No. 1), 78.5% (No. 2), and 83.0% (No. 3). MAC results show, that mode shapes are only slightly influenced by material distribution. Calculated resonance frequencies are generally lower than measured values, which indicates, that numerical models lack stiffness. Even when using the best suited (No. 3) out of three investigated density-<span class="hlt">elasticity</span> relationships, in FE modeling of pelvic bone a considerable underestimation of model stiffness has to be taken into account. PMID:24001928</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.ncbi.nlm.nih.gov/pubmed/21783112','PUBMED'); return false;" href="http://www.ncbi.nlm.nih.gov/pubmed/21783112"><span id="translatedtitle">The effect of <span class="hlt">strain</span> rate on fracture toughness of human cortical bone: a <span class="hlt">finite</span> element study.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ural, Ani; Zioupos, Peter; Buchanan, Drew; Vashishth, Deepak</p> <p>2011-10-01</p> <p>Evaluating the mechanical response of bone under high loading rates is crucial to understanding fractures in traumatic accidents or falls. In the current study, a computational approach based on cohesive <span class="hlt">finite</span> element modeling was employed to evaluate the effect of <span class="hlt">strain</span> rate on fracture toughness of human cortical bone. Two-dimensional compact tension specimen models were simulated to evaluate the change in initiation and propagation fracture toughness with increasing <span class="hlt">strain</span> rate (range: 0.08-18 s(-1)). In addition, the effect of porosity in combination with <span class="hlt">strain</span> rate was assessed using three-dimensional models of micro-computed tomography-based compact tension specimens. The simulation results showed that bone's resistance against the propagation of a crack decreased sharply with increase in <span class="hlt">strain</span> rates up to 1 s(-1) and attained an almost constant value for <span class="hlt">strain</span> rates larger than 1 s(-1). On the other hand, initiation fracture toughness exhibited a more gradual decrease throughout the <span class="hlt">strain</span> rates. There was a significant positive correlation between the experimentally measured number of microcracks and the fracture toughness found in the simulations. Furthermore, the simulation results showed that the amount of porosity did not affect the way initiation fracture toughness decreased with increasing <span class="hlt">strain</span> rates, whereas it exacerbated the same <span class="hlt">strain</span> rate effect when propagation fracture toughness was considered. These results suggest that <span class="hlt">strain</span> rates associated with falls lead to a dramatic reduction in bone's resistance against crack propagation. The compromised fracture resistance of bone at loads exceeding normal activities indicates a sharp reduction and/or absence of toughening mechanisms in bone during high <span class="hlt">strain</span> conditions associated with traumatic fracture. PMID:21783112</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3143384','PMC'); return false;" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3143384"><span id="translatedtitle">THE EFFECT OF <span class="hlt">STRAIN</span> RATE ON FRACTURE TOUGHNESS OF HUMAN CORTICAL BONE: A <span class="hlt">FINITE</span> ELEMENT STUDY</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Ural, Ani; Zioupos, Peter; Buchanan, Drew; Vashishth, Deepak</p> <p>2011-01-01</p> <p>Evaluating the mechanical response of bone under high loading rates is crucial to understanding fractures in traumatic accidents or falls. In the current study, a computational approach based on cohesive <span class="hlt">finite</span> element modeling was employed to evaluate the effect of <span class="hlt">strain</span> rate on fracture toughness of human cortical bone. Two-dimensional compact tension specimen models were simulated to evaluate the change in initiation and propagation fracture toughness with increasing <span class="hlt">strain</span> rate (range: 0.08 to 18 s−1). In addition, the effect of porosity in combination with <span class="hlt">strain</span> rate was assessed using three-dimensional models of microcomputed tomography-based compact tension specimens. The simulation results showed that bone’s resistance against the propagation of fracture decreased sharply with increase in <span class="hlt">strain</span> rates up to 1 s−1 and attained an almost constant value for <span class="hlt">strain</span> rates larger than 1 s−1. On the other hand, initiation fracture toughness exhibited a more gradual decrease throughout the <span class="hlt">strain</span> rates. There was a significant positive correlation between the experimentally measured number of microcracks and the fracture toughness found in the simulations. Furthermore, the simulation results showed that the amount of porosity did not affect the way initiation fracture toughness decreased with increasing <span class="hlt">strain</span> rates, whereas it exacerbated the same <span class="hlt">strain</span> rate effect when propagation fracture toughness was considered. These results suggest that <span class="hlt">strain</span> rates associated with falls lead to a dramatic reduction in bone’s resistance against crack propagation. The compromised fracture resistance of bone at loads exceeding normal activities indicates a sharp reduction and/or absence of toughening mechanisms in bone during high <span class="hlt">strain</span> conditions associated with traumatic fracture. PMID:21783112</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19840015853','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19840015853"><span id="translatedtitle">CLFE2D: A generalized plane <span class="hlt">strain</span> <span class="hlt">finite</span> element program laminated composites subject to mechanical and hygrothermal loading</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Buczek, M. B.; Gregory, M. A.; Herakovich, C. T.</p> <p>1983-01-01</p> <p>CLFE2D is a two dimensional generalized plane <span class="hlt">strain</span> <span class="hlt">finite</span> element code, using a linear, four node, general quadrilateral, isoparametric element. The program is developed to calculate the displacements, <span class="hlt">strains</span>, stresses, and <span class="hlt">strain</span> energy densities in a <span class="hlt">finite</span> width composite laminate. CLFE2D offers any combination of the following load types: nodal displacements, nodal forces, uniform normal <span class="hlt">strain</span>, or hygrothermal. The program allows the user to input one set of three dimensional orthotropic material properties. The user can then specify the angle of material principal orientation for each element in the mesh. Output includes displacements, stresses, <span class="hlt">strains</span> and <span class="hlt">strain</span> densities at points selected by the user. An option is also available to plot the underformed and deformed <span class="hlt">finite</span> element meshes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/pages/biblio/1259578-finite-element-simulation-ray-microdiffraction-study-strain-partitioning-layered-nanocomposite','SCIGOV-DOEP'); return false;" href="http://www.osti.gov/pages/biblio/1259578-finite-element-simulation-ray-microdiffraction-study-strain-partitioning-layered-nanocomposite"><span id="translatedtitle"><span class="hlt">Finite</span> Element Simulation and X-Ray Microdiffraction Study of <span class="hlt">Strain</span> Partitioning in a Layered Nanocomposite</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGESBeta</a></p> <p>Barabash, R. I.; Agarwal, V.; Koric, S.; Jasiuk, I.; Tischler, J. Z.</p> <p>2016-01-01</p> <p>Tmore » he depth-dependent <span class="hlt">strain</span> partitioning across the interfaces in the growth direction of the NiAl/Cr(Mo) nanocomposite between the Cr and NiAl lamellae was directly measured experimentally and simulated using a <span class="hlt">finite</span> element method (FEM). Depth-resolved X-ray microdiffraction demonstrated that in the as-grown state both Cr and NiAl lamellae grow along the 111 direction with the formation of as-grown distinct residual ~0.16% compressive <span class="hlt">strains</span> for Cr lamellae and ~0.05% tensile <span class="hlt">strains</span> for NiAl lamellae.hree-dimensional simulations were carried out using an implicit FEM. First simulation was designed to study residual <span class="hlt">strains</span> in the composite due to cooling resulting in formation of crystals. <span class="hlt">Strains</span> in the growth direction were computed and compared to those obtained from the microdiffraction experiments. Second simulation was conducted to understand the combined <span class="hlt">strains</span> resulting from cooling and mechanical indentation of the composite. Numerical results in the growth direction of crystal were compared to experimental results confirming the experimentally observed trends.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003PhDT.......212S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003PhDT.......212S"><span id="translatedtitle">High pressure and high <span class="hlt">strain</span> rate behavior of cementitious materials: Experiments and <span class="hlt">elastic</span>/viscoplastic modeling</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Schmidt, Martin Jeffrey</p> <p></p> <p> response as the quasistatic tests conducted at the same level of confinement. A decrease in <span class="hlt">strain</span> rate sensitivity with increasing confining pressure was observed. A new <span class="hlt">elastic</span>/viscoplastic model that captures compressibility and dilatancy, as well as <span class="hlt">strain</span> rate effects has been developed for concrete. (Abstract shortened by UMI.)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/6860496','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/6860496"><span id="translatedtitle">Numerical implementation of inelastic time dependent and time independent, <span class="hlt">finite</span> <span class="hlt">strain</span> constitutive equtions in solids</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Key, S.W.; Krieg, R.D.</p> <p>1980-01-01</p> <p>A number of complex issues are addressed which will allow the incorporation of <span class="hlt">finite</span> <span class="hlt">strain</span>, inelastic material behavior into the piecewise numerical construction of solutions in solid mechanics. Without recourse to extensive continuum mechanics preliminaries, an elementary time independent plasticity model, an elementary time dependent creep model, and a viscoelastic model are introduced as examples of constitutive equations which are routinely used in engineering calculations. The constitutive equations are all suitable for problems involving large deformations and <span class="hlt">finite</span> <span class="hlt">strains</span>. The plasticity and creep models are in rate form and use the symmetric part of the velocity gradient or the stretching to compute the co-rotational time derivative of the Cauchy stress. The viscoelastic model computes the current value of the Cauchy stress from a hereditary integral of a materially invariant form of the stretching history. The current configuration is selected for evaluation of equilibrium as opposed to either the reference configuration or the last established equilibrium configuration. The process of <span class="hlt">strain</span> incrementation is examined in some depth and the stretching evaluated at the midinterval multiplied by the time step is identified as the appropriate <span class="hlt">finite</span> <span class="hlt">strain</span> increment to use with the selected form of the constitutive equations. Discussed is the conversion of rotation rates based on the spin into incremental orthogonal rotations which are then used to update stresses and state variables due to rigid body rotation during the load increment. Comments and references to the literature are directed at numerical integration of the constitutive equations with an emphasis on doing this accurately, if not exactly, for any time step and stretching. This material taken collectively provides an approach to numerical implementation which is marked by its simplicity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014AGUFM.T21B4590H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014AGUFM.T21B4590H"><span id="translatedtitle">Basal shear stress below <span class="hlt">elastic</span> crust of the Tibetan plateau inferred from three-dimensional <span class="hlt">finite</span> element modeling</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>He, J.; Xiao, J.; Pan, Z.</p> <p>2014-12-01</p> <p>Associated with northward convergence of the India continent, the surface motion of the Tibetan plateau, documented mainly by dense geodetic GPS measurements, changes greatly both on magnitude and on direction in different tectonic units. The most remarkable discordance of surface motion is around the eastern Himalayan syntaxis, where GPS velocity field is rotated gradually to oppositional direction near the southeastern Tibetan plateau with respect to the northward convergence of the India continent. Such a velocity field could be result from lateral boundary conditions, since the strength of lithosphere is probably weaker in the Tibetan plateau than in the surrounding regions. However, whether the surface motion of the Tibetan plateau is affected by basal shear at base of the <span class="hlt">elastic</span> crust, that could exist if the coupling condition between the <span class="hlt">elastic</span> and the viscous crust were changed, is unclear. Here, we developed a large-scale three-dimensional <span class="hlt">finite</span> element model to explore the possible existence of basal shear below the Tibetan plateau and the surrounding regions. In the model, the lateral boundaries are specified with far-field boundary condition; the blocks surrounding the Tibetan plateaulike the Tarim, the Ordos, and the South China are treat as rigid blocks; and the mean thickness of <span class="hlt">elastic</span> crust is assumed about 25km. Then, the magnitude and distribution of basal shear stress is automatically searchedin numerical calculation to fit surface (GPS) motion of the Tibetan plateau. We find that to better fit surface motion of the Tibetan plateau, negligible basal shear stress on the base of <span class="hlt">elastic</span> crust is needed below majority of the western and the central Tibetan plateau; Whereas, around the eastern and the southeastern Tibetan plateau, especially between the Xianshuhestrike-slip fault and the eastern Himalayan syntaxis, at least ~1.5-3.0 Mpaof basal shear stress is needed to cause rotational surface motion as GPS measurements documented. This</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li class="active"><span>13</span></li> <li><a href="#" onclick='return showDiv("page_13");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_13 --> <center> <div class="footer-extlink text-muted"><small>Some links on this page may take you to non-federal websites. Their policies may differ from this site.</small> </div> </center> <div id="footer-wrapper"> <div class="footer-content"> <div id="footerOSTI" class=""> <div class="row"> <div class="col-md-4 text-center col-md-push-4 footer-content-center"><small><a href="http://www.science.gov/disclaimer.html">Privacy and Security</a></small> <div class="visible-sm visible-xs push_footer"></div> </div> <div class="col-md-4 text-center col-md-pull-4 footer-content-left"> <img src="http://www.osti.gov/images/DOE_SC31.png" alt="U.S. Department of Energy" usemap="#doe" height="31" width="177"><map style="display:none;" name="doe" id="doe"><area shape="rect" coords="1,3,107,30" href="http://www.energy.gov" alt="U.S. Deparment of Energy"><area shape="rect" coords="114,3,165,30" href="http://www.science.energy.gov" alt="Office of Science"></map> <a ref="http://www.osti.gov" style="margin-left: 15px;"><img src="http://www.osti.gov/images/footerimages/ostigov53.png" alt="Office of Scientific and Technical Information" height="31" width="53"></a> <div class="visible-sm visible-xs push_footer"></div> </div> <div class="col-md-4 text-center footer-content-right"> <a href="http://www.osti.gov/nle"><img src="http://www.osti.gov/images/footerimages/NLElogo31.png" alt="National Library of Energy" height="31" width="79"></a> <a href="http://www.science.gov"><img src="http://www.osti.gov/images/footerimages/scigov77.png" alt="science.gov" height="31" width="98"></a> <a href="http://worldwidescience.org"><img src="http://www.osti.gov/images/footerimages/wws82.png" alt="WorldWideScience.org" height="31" width="90"></a> </div> </div> </div> </div> </div> <p><br></p> </div><!-- container --> </body> </html>