Finite strain crack tip fields in soft incompressible elastic solids.
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
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.
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.
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.
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.
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.
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
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.
Beyond linear elasticity: jammed solids at finite shear strain and rate.
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
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.
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.
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
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
Models for elastic shells with incompatible strains
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
Tunable thermoelectric transport in nanomeshes via elastic strain engineering
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.
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.
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.
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.
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.
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.
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.
Influence of thermal residual stresses on the elastic phase-strain
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.
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.
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.
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.
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.
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.
Solution of elastic-plastic stress analysis problems by the P-version of the finite element method
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.
Development of the average lattice phase-strain and global elastic macro-strain in Al/TiC composites
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.
Elastic finite-difference method for irregular grids
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.
Stress-dependent finite growth in soft elastic tissues.
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
Finite element investigation of thermo-elastic and thermo-plastic consolidation
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.
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.
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.
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.
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.
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.
Atomistic modeling of diffusional phasetransformations with elastic strain
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.
Evidence for residual elastic strain in deformed natural quartz
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.
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:
Visualization of elastic wavefields computed with a finite difference code
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.
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.
Elastic Wave Radiation from a Line Source of Finite Length
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.
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.
Approaching the ideal elastic strain limit in silicon nanowires.
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
Approaching the ideal elastic strain limit in silicon nanowires
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
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.
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…
Internal elastic strains in an IF steel following changes in strain path
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.
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.
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.
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.
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.
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.
Medical ultrasound: imaging of soft tissue strain and elasticity
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
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.
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
Elastic strain relaxation in axial Si/Ge whisker heterostructures
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.
Controlling surface reactions with nanopatterned surface elastic strain.
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
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
Retaining Large and Adjustable Elastic Strains of Kilogram-Scale Nb Nanowires.
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
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.
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.
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.
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.
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
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.
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.
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.
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.
The Influence of Elastic Strain on Catalytic Activity in the Hydrogen Evolution Reaction.
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
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.
NASA Astrophysics Data System (ADS)
Renaud, G.; RivièRe, J.; Le Bas, P.-Y.; Johnson, P. A.
2013-02-01