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.
2016-09-01
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.
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.
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.
Krishnan, V R; Hui, C-Y
2009-05-01
We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates. PMID:19437055
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.
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.
On Dynamic Nonlinear Elasticity and Small Strain
NASA Astrophysics Data System (ADS)
Johnson, P. A.; Sutin, A.; Guyer, R. A.; Tencate, J. A.
2002-12-01
We are addressing the question of whether or not there is a threshold strain behavior where anomalous nonlinear fast dynamics (ANFD) commences in rock and other similar solids, or if the elastic nonlinearity persists to the smallest measurable values. In qualitative measures of many rock types and other materials that behave in the same manner, we have not observed a threshold; however the only careful, small strain level study conducted under controlled conditions that we are aware of is that of TenCate et al. in Berea sandstone (Phys. Rev. Lett. 85, 1020-1024 (2000)). This work indicates that in Berea sandstone, the elastic nonlinearity persists to the minimum measured strains of at least 10-8. Recently, we have begun controlled experiments in other materials that exhibit ANFD in order to see whether or not they behave as Berea sandstone does. We are employing Young's mode resonance to study resonance peak shift and amplitude variations as a function of drive level and detected strain level. In this type of experiment, the time average amplitude is recorded as the sample is driven by a continuous wave source from below to above the fundamental mode resonance. The drive level is increased, and the measurement is repeated progressively over larger and larger drive levels. Experiments are conducted at ambient pressure. Pure alumina ceramic is a material that is highly, elastically-nonlinear and nonporous, and therefore the significant influence of relative humidity on elastic nonlinear response that rock suffers is avoided. Temperature is carefully monitored. Measurements on pure alumina ceramic show that, like Berea sandstone, there is no threshold of elastic nonlinearity within our measurement capability. We are now studying other solids that exhibit ANFD including rock and mixed phase metal. These results indicate that elastic nonlinearity influences all elastic measurments on these solids including modulus and Q at ambient conditions. There appears to be no
The strain-based beam finite elements in multibody dynamics
NASA Astrophysics Data System (ADS)
Gams, M.; Planinc, I.; Saje, M.
2007-08-01
We present a strain-based finite-element formulation for the dynamic analysis of flexible elastic planar multibody systems, composed of planar beams. We consider finite displacements, rotations and strains. The discrete dynamic equations of motion are obtained by the collocation method. The strains are the basic interpolated variables, which makes the formulation different from other formulations. The further speciality of the formulation is the strong satisfaction of the cross-sectional constitutive conditions at collocation points. In order to avoid the nested integrations, a special algorithm for the numerical integration over the length of the finite element is proposed. The midpoint scheme is used for the time integration. The performance of the formulation is illustrated via numerical examples, including a stiff multibody system.
NASA Technical Reports Server (NTRS)
Bauld, N. R., Jr.; Goree, J. G.
1983-01-01
The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.
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.
Numerical solution of acoustic scattering by finite perforated elastic plates
NASA Astrophysics Data System (ADS)
Cavalieri, A. V. G.; Wolf, W. R.; Jaworski, J. W.
2016-04-01
We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates.
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.
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.
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.
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.
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.
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.
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.
Elastically relaxed free-standing strained-silicon nanomembranes.
Roberts, Michelle M; Klein, Levente J; Savage, Donald E; Slinker, Keith A; Friesen, Mark; Celler, George; Eriksson, Mark A; Lagally, Max G
2006-05-01
Strain plays a critical role in the properties of materials. In silicon and silicon-germanium, strain provides a mechanism for control of both carrier mobility and band offsets. In materials integration, strain is typically tuned through the use of dislocations and elemental composition. We demonstrate a versatile method to control strain by fabricating membranes in which the final strain state is controlled by elastic strain sharing, that is, without the formation of defects. We grow Si/SiGe layers on a substrate from which they can be released, forming nanomembranes. X-ray-diffraction measurements confirm a final strain predicted by elasticity theory. The effectiveness of elastic strain to alter electronic properties is demonstrated by low-temperature longitudinal Hall-effect measurements on a strained-silicon quantum well before and after release. Elastic strain sharing and film transfer offer an intriguing path towards complex, multiple-layer structures in which each layer's properties are controlled elastically, without the introduction of undesirable defects.
NASA Technical Reports Server (NTRS)
Gayda, J.; Srolovitz, D. J.
1989-01-01
This paper presents a specialized microstructural lattice model, MCFET (Monte Carlo finite element technique), which simulates microstructural evolution in materials in which strain energy has an important role in determining morphology. The model is capable of accounting for externally applied stress, surface tension, misfit, elastic inhomogeneity, elastic anisotropy, and arbitrary temperatures. The MCFET analysis was found to compare well with the results of analytical calculations of the equilibrium morphologies of isolated particles in an infinite 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.
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.
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.
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.
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:
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.
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.
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.
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.
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…
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
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.
Scaling Behavior and Strain Dependence of In-Plane Elastic Properties of Graphene.
Los, J H; Fasolino, A; Katsnelson, M I
2016-01-01
We show by atomistic simulations that, in the thermodynamic limit, the in-plane elastic moduli of graphene at finite temperature vanish with system size L as a power law L(-η(u)) with η(u)≃0.325, in agreement with the membrane theory. We provide explicit expressions for the size and strain dependence of graphene's elastic moduli, allowing comparison to experimental data. Our results explain the recently experimentally observed increase of the Young modulus by more than a factor of 2 for a tensile strain of only a few per mill. The difference of a factor of 2 between the measured asymptotic value of the Young modulus for tensilely strained systems and the value from ab initio calculations remains, however, unsolved. We also discuss the asymptotic behavior of the Poisson ratio, for which our simulations disagree with the predictions of the self-consistent screening approximation.
Painter Street Overcrossing: Linear-elastic finite element dynamic analysis
Salveson, M.W.
1991-08-01
Painter Street Overcrossing is a two span continuous box girder bridge Highway 101 near Rio Del, California. It has been heavily instrumented with strong motion accelerometers by the California Department of Mines and Geology Strong Motion Instrumentation Program. On 11/21/86, the response of the bridge to a magnitude 5.1 earthquake (epicentral distance 32 km) was measured. This report considers the data generated at stations six, seven, and eight, during this earthquake. Station six recorded the vertical accelerations at the midpoint of the long span. Station seven recorded the transverse accelerations at the top of the bent. Station eight recorded the vertical accelerations at the midpoint of the short span. Typically, seismic analysis is done with the aid of a linear-elastic finite element code. Damping is assumed to be viscous. This report summarizes the results of such an analysis using the commercial P.C. based program SAP90. This analysis conforms as closely as possible to a typical'' seismic analysis. It is intended to be used as basis for comparison against a non-linear analysis to be done using NIKE3D. This report contains detailed information about the models used to represent the bridge. The results of each analysis and discussions of the results are included. 2 refs., 37 figs.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Mangeri, John; Heinonen, Olle; Karpeyev, Dmitry; Nakhmanson, Serge
2015-07-01
Core-shell nanoparticle systems of Zn-ZnO and ZnO -TiO2 are studied computationally using finite-element methods. The inclusion of a surface free energy and the elastic mismatch of the core and shell create an imprinting effect within the shell structure that produces a wide variation of strains. Due to this diversity of strains, the sharp, direct, band-gap edges of the bulk semiconductor are observed to be broadened. We show that a variety of factors, such as particle size, core-to-shell volume ratio, applied hydrostatic pressure, shell microstructure, as well as the effect of elastic anisotropy, can influence the distribution of optical band-gap values throughout the particle.
Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity
NASA Astrophysics Data System (ADS)
Gourgiotis, P. A.; Georgiadis, H. G.
2009-11-01
The present study aims at determining the elastic stress and displacement fields around the tips of a finite-length crack in a microstructured solid under remotely applied plane-strain loading (mode I and II cases). The material microstructure is modeled through the Toupin-Mindlin generalized continuum theory of dipolar gradient elasticity. According to this theory, the strain-energy density assumes the form of a positive-definite function of the strain tensor (as in classical elasticity) and the gradient of the strain tensor (additional term). A simple but yet rigorous version of the theory is employed here by considering an isotropic linear expression of the elastic strain-energy density that involves only three material constants (the two Lamé constants and the so-called gradient coefficient). First, a near-tip asymptotic solution is obtained by the Knein-Williams technique. Then, we attack the complete boundary value problem in an effort to obtain a full-field solution. Hypersingular integral equations with a cubic singularity are formulated with the aid of the Fourier transform. These equations are solved by analytical considerations on Hadamard finite-part integrals and a numerical treatment. The results show significant departure from the predictions of standard fracture mechanics. In view of these results, it seems that the classical theory of elasticity is inadequate to analyze crack problems in microstructured materials. Indeed, the present results indicate that the stress distribution ahead of the crack tip exhibits a local maximum that is bounded. Therefore, this maximum value may serve as a measure of the critical stress level at which further advancement of the crack may occur. Also, in the vicinity of the crack tip, the crack-face displacement closes more smoothly as compared to the standard result and the strain field is bounded. Finally, the J-integral (energy release rate) in gradient elasticity was evaluated. A decrease of its value is noticed
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.
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
Medical ultrasound: imaging of soft tissue strain and elasticity.
Wells, Peter N T; Liang, Hai-Dong
2011-11-01
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.
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.
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
Prediction of the elastic strain limit of tendons.
Reyes, A M; Jahr, H; van Schie, H T M; Weinans, H; Zadpoor, A A
2014-02-01
The elastic strain limit (ESL) of tendons is the point where maximum elastic modulus is reached, after which micro-damage starts. Study of damage progression in tendons under repetitive (fatigue) loading requires a priori knowledge about ESL. In this study, we propose three different approaches for predicting ESL. First, one single value is assumed to represent the ESL of all tendon specimens. Second, different extrapolation curves are used for extrapolating the initial part of the stress-strain curve. Third, a method based on comparing the shape of the initial part of the stress-strain curve of specimens with a database of stress-strain curves is used. A large number of porcine tendon explants (97) were tested to examine the above-mentioned approaches. The variants of the third approach yielded significantly (p<0.05) smaller error values as compared to the other approaches. The mean absolute percentage error of the best-performing variant of the shape-based comparison was between 8.14±6.44% and 9.96±9.99% depending on the size of the initial part of the stress-strain curves. Interspecies generalizability of the best performing method was also studied by applying it for prediction of the ESL of horse tendons. The ESL of horse tendons was predicted with mean absolute percentage errors ranging between 10.53±7.6% and 19.16±14.31% depending on the size of the initial part of the stress-strain curves and the type of normalization. The results of this study suggest that both ESL and the shape of stress-strain curves may be highly different between different individuals and different anatomical locations.
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.
Lesion edge preserved direct average strain estimation for ultrasound elasticity imaging.
Hussain, Mohammad Arafat; Alam, Farzana; Rupa, Sharmin Akhtar; Awwal, Rayhana; Lee, Soo Yeol; Hasan, Md Kamrul
2014-01-01
Elasticity imaging techniques with built-in or regularization-based smoothing feature for ensuring strain continuity are not intelligent enough to prevent distortion or lesion edge blurring while smoothing. This paper proposes a novel approach with built-in lesion edge preservation technique for high quality direct average strain imaging. An edge detection scheme, typically used in diffusion filtering is modified here for lesion edge detection. Based on the extracted edge information, lesion edges are preserved by modifying the strain determining cost function in the direct-average-strain-estimation (DASE) method. The proposed algorithm demonstrates approximately 3.42-4.25 dB improvement in terms of edge-mean-square-error (EMSE) than the other reported regularized or average strain estimation techniques in finite-element-modeling (FEM) simulation with almost no sacrifice in elastographic-signal-to-noise-ratio (SNRe) and elastographic-contrast-to-noise-ratio (CNRe) metrics. The efficacy of the proposed algorithm is also tested for the experimental phantom data and in vivo breast data. The results reveal that the proposed method can generate a high quality strain image delineating the lesion edge more clearly than the other reported strain estimation techniques that have been designed to ensure strain continuity. The computational cost, however, is little higher for the proposed method than the simpler DASE and considerably higher than that of the 2D analytic minimization (AM2D) method.
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.
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.
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.
Sun, Wei; Sacks, Michael S
2005-11-01
Numerical simulations of the anisotropic mechanical properties of soft tissues and tissue-derived biomaterials using accurate constitutive models remain an important and challenging research area in biomechanics. While most constitutive modeling efforts have focused on the characterization of experimental data, only limited studies are available on the feasibility of utilizing those models in complex computational applications. An example is the widely utilized exponential constitutive model proposed by Fung. Although present in the biomechanics literature for several decades, implementation of this model into finite element (FE) simulations has been limited. A major reason for limited numerical implementations are problems associated with inherent numerical instability and convergence. To address this issue, we developed and applied two restrictions for a generalized Fung-elastic constitutive model necessary to achieve numerical stability. These are (1) convexity of the strain energy function, and (2) the condition number of material stiffness matrix set lower than a prescribed value. These constraints were implemented in the nonlinear regression used for constitutive model parameter estimation to the experimental biaxial mechanical data. We then implemented the generalized Fung-elastic model into a commercial FE code (ABAQUS, Pawtucket, RI, USA). Single element and multi-element planar biaxial test simulations were conducted to verify the accuracy and robustness of the implementation. Results indicated that numerical convergence and accurate FE implementation were consistently obtained. The present study thus presents an integrated framework for accurate and robust implementation of pseudo-elastic constitutive models for planar soft tissues. Moreover, since our approach is formulated within a general FE code, it can be straightforwardly adopted across multiple software platforms.
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
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.
Finite Element Prediction of Acoustic Scattering and Radiation from Submerged Elastic Structures
NASA Technical Reports Server (NTRS)
Everstine, G. C.; Henderson, F. M.; Lipman, R. R.
1984-01-01
A finite element formulation is derived for the scattering and radiation of acoustic waves from submerged elastic structures. The formulation uses as fundamental unknowns the displacement in the structure and a velocity potential in the field. Symmetric coefficient matrices result. The outer boundary of the fluid region is terminated with an approximate local wave-absorbing boundary condition which assumes that outgoing waves are locally planar. The finite element model is capable of predicting only the near-field acoustic pressures. Far-field sound pressure levels may be determined by integrating the surface pressures and velocities over the wet boundary of the structure using the Helmholtz integral. Comparison of finite element results with analytic results show excellent agreement. The coupled fluid-structure problem may be solved with general purpose finite element codes by using an analogy between the equations of elasticity and the wave equation of linear acoustics.
NASA Technical Reports Server (NTRS)
Abdul-Aziz, Ali; Kalluri, Sreeramesh
1991-01-01
The temperature-dependent engineering elastic constants of a directionally solidified nickel-base superalloy were estimated from the single-crystal elastic constants of nickel and MAR-MOO2 superalloy by using Wells' method. In this method, the directionally solidified (columnar-grained) nickel-base superalloy was modeled as a transversely isotropic material, and the five independent elastic constants of the transversely isotropic material were determined from the three independent elastic constants of a cubic single crystal. Solidification for both the single crystals and the directionally solidified superalloy was assumed to be along the (001) direction. Temperature-dependent Young's moduli in longitudinal and transverse directions, shear moduli, and Poisson's ratios were tabulated for the directionally solidified nickel-base superalloy. These engineering elastic constants could be used as input for performing finite element structural analysis of directionally solidified turbine engine components.
Heat-induced changes in the finite strain viscoelastic behavioir of a collaagenous tissue.
Baek, S; Wells, P B; Rajagopal, K R; Humphrey, J D
2005-08-01
Supra-physiological temperatures are increasingly being used to treat many different soft need for injuries. To identify improved clinical treatments, however, there is a need for better information on the effect of the mechanics on the thermal damage process as well as the effect of the incurred damage on the subsequent mechanical properties. In this paper we report the first biaxial data on the stress relaxation behavior of a collagenous tissue before and after thermal damage. Based on a two-dimensional finite strain viscoelastic model, which incorporates an exponential elastic response, it is shown that the thermal damage can significantly decrease the characteristic time for stress relaxation and the stress residual.
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.
Harmonic three-phase circular inclusions in finite elasticity
NASA Astrophysics Data System (ADS)
Wang, Xu; Schiavone, Peter
2015-09-01
We study the exterior stress field in a three-phase circular inclusion which is bonded to the surrounding matrix through an intermediate interphase layer. All three phases belong to a particular class of compressible hyperelastic materials of harmonic type. We focus on the design of a harmonic elastic inclusion which by definition, does not disturb the sum of the normal stresses in the surrounding matrix. We show that in order to make the coated inclusion harmonic, certain inequalities concerning the material and geometric parameters of the three-phase composite must first be satisfied. The corresponding remote loading parameters can then be uniquely determined while keeping the associated phase angles arbitrary. Our results allow for both uniform and non-uniform remote loading. We show that the stress field inside the inclusion is uniform when the remote loading is uniform.
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
Feng, Xiaobing
1996-12-31
A non-overlapping domain decomposition iterative method is proposed and analyzed for mixed finite element methods for a sequence of noncoercive elliptic systems with radiation boundary conditions. These differential systems describe the motion of a nearly elastic solid in the frequency domain. The convergence of the iterative procedure is demonstrated and the rate of convergence is derived for the case when the domain is decomposed into subdomains in which each subdomain consists of an individual element associated with the mixed finite elements. The hybridization of mixed finite element methods plays a important role in the construction of the discrete procedure.
NASA Astrophysics Data System (ADS)
Hansbo, Peter; Larson, Mats G.; Larsson, Fredrik
2015-07-01
We develop a finite element method for a large deformation membrane elasticity problem on meshed curved surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also applied to form finding problems.
A computational framework for polyconvex large strain elasticity for geometrically exact beam theory
NASA Astrophysics Data System (ADS)
Ortigosa, Rogelio; Gil, Antonio J.; Bonet, Javier; Hesch, Christian
2016-02-01
In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55-70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney-Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.
NASA Astrophysics Data System (ADS)
Chi, Heng; Lopez-Pamies, Oscar; Paulino, Glaucio H.
2016-02-01
This paper presents a new variational principle in finite elastostatics applicable to arbitrary elastic solids that may contain constitutively rigid spatial domains (e.g., rigid inclusions). The basic idea consists in describing the constitutive rigid behavior of a given spatial domain as a set of kinematic constraints over the boundary of the domain. From a computational perspective, the proposed formulation is shown to reduce to a set of algebraic constraints that can be implemented efficiently in terms of both single-field and mixed finite elements of arbitrary order. For demonstration purposes, applications of the proposed rigid-body-constraint formulation are illustrated within the context of elastomers, reinforced with periodic and random distributions of rigid filler particles, undergoing finite deformations.
Mixed finite element methods for linear elasticity with weakly imposed symmetry
NASA Astrophysics Data System (ADS)
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2007-12-01
In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a modified form of the Hellinger-Reissner variational principle that only weakly imposes the symmetry condition on the stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from the de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.
Finite element analysis of 3D elastic-plastic frictional contact problem for Cosserat materials
NASA Astrophysics Data System (ADS)
Zhang, S.; Xie, Z. Q.; Chen, B. S.; Zhang, H. W.
2013-06-01
The objective of this paper is to develop a finite element model for 3D elastic-plastic frictional contact problem of Cosserat materials. Because 3D elastic-plastic frictional contact problems belong to the unspecified boundary problems with nonlinearities in both material and geometric forms, a large number of calculations are needed to obtain numerical results with high accuracy. Based on the parametric variational principle and the corresponding quadratic programming method for numerical simulation of frictional contact problems, a finite element model is developed for 3D elastic-plastic frictional contact analysis of Cosserat materials. The problems are finally reduced to linear complementarity problems (LCP). Numerical examples show the feasibility and importance of the developed model for analyzing the contact problems of structures with materials which have micro-polar characteristics.
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.
A hybrid-stress finite element for linear anisotropic elasticity
NASA Technical Reports Server (NTRS)
Fly, Gerald W.; Oden, J. Tinsley; Pearson, Mark L.
1988-01-01
Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.
Effect of finite strain on clast-based vorticity gauges
NASA Astrophysics Data System (ADS)
Stahr, Donald W., III; Law, Richard D.
2011-07-01
Clast-based vorticity gauges utilize orientations of grains assumed to have behaved as isolated rigid particles suspended in a flowing viscous matrix. A fundamental assumption behind use of the method is that sufficient strain has accumulated for high aspect ratio grains to rotate into positions approaching their stable sink orientation, and that clasts below a critical aspect ratio may be observed in any orientation relative to the flow plane. We constructed a numerical model to explore the effect of variable finite strain on development of the orientation distribution of a large population of rigid clasts embedded in a viscous medium for end-member pure and simple shear and for several distinct general shear flows. Our model predicts the technique will tend to produce vorticity overestimates for lower vorticity flows for a wide range of finite strain. The model also indicates that clast populations in moderate to high vortical flows tend to develop shape preferred orientations that closely resemble those expected for flows of lower vorticity. We conclude that clast-based methods are not effective for extracting detailed kinematic information from a mylonite deformed in a flow with arbitrary boundary conditions. In fact, it appears that most general shear flows continued long enough to develop moderate-high finite strains will tend to produce a clast orientation distribution that will yield a visual estimate of the critical aspect ratio that suggests approximately equal contributions of pure and simple shear components.
Elastic transducers incorporating finite-length optical paths
NASA Astrophysics Data System (ADS)
Peters, Kara J.; Washabaugh, Peter D.
1995-08-01
Frequently, when designing a structure to incorporate integrated sensors, one sacrifices the stiffness of the system to improve sensitivity. However, the use of interferometric displacement sensors that tessellate throughout the volume of a structure has the potential to allow the precision and range of the component measurement to scale with the geometry of the device rather than the maximum strain in the structure. The design of stiff structures that measure all six resultant-load components is described. In addition, an advanced torsion sensor and a linear acceleration transducer are also discussed. Finally, invariant paths are presented that allow the in situ integrity of a structural volume to be monitored with a single pair of displacement sensors.
Three-dimensional analysis of pore effect on composite elasticity by means of finite element method
NASA Astrophysics Data System (ADS)
Yoneda, A.
2015-12-01
A three-dimensional buffer-layer finite element method (FEM) model was developed to investigate the porosity effect on macroscopic elasticity. Using the three-dimensional model, the effect of pores on bulk effective elastic properties were systematically analyzed by changing the degree of porosity, the aspect ratio of the ellipsoidal pore, and the elasticity of the material. The present results in 3D space was compared with the previous ones in 2D space. Derivatives of normalized elastic stiffness constants with respect to needle-type porosity are integers, if the Poisson ratio of a matrix material is zero; those derivatives of normalized stiffness elastic constants for C33, C44, C11, and C66 converge to -1, -2, -3, and -4, respectively, at the corresponding condition. We proposed a criterion of R <~1/3, where the mutual interaction between pores becomes negligible for macroscopic composite elasticity. These derivatives are nearly constant below 5% porosity in the case of spherical pore, suggesting that the interaction between neighboring pores is insignificant if the representative size of the pore is less than one-third of the mean distance between neighboring pores. The relations we obtained in this work were successfully applied to invert bulk modulus and rigidity of Cmcm-CaIrO3 as a case study; the performance of the inverting scheme was confirmed through this assessment. Thus the present scheme is applicable to predict macroscopic elasticity of porous object as well.
Viscous Flutter of a Finite Elastic Membrane in Poiseuille Flow
NASA Astrophysics Data System (ADS)
Huang, L.
2001-10-01
Flow-induced vibration in a collapsible tube is relevant to many biomedical applications including the human respiratory system. This paper presents a linear analysis of the coupling between Poiseuille flow and a tensioned membrane of finite length using an eigenvalue approach. The undisturbed state of the channel flow is perfectly parallel. To some extent, this configuration bridges the gap between two types of theoretical models: one for the travelling-wave flutter in an infinite, flexible channel, and the other for the self-induced oscillation of a collapsing section of a Starling-resistor tube. In our study, we focus on the parameter range where the wall-to-fluid mass ratio is high (100), and the Reynolds number based on the maximum flow velocity in the channel is moderately high (200). Eigenmodes representing both static divergence and flutter are found. Particular attention is paid to the energetics of flutter modes. It is shown that energy transfer from the flow to the membrane occurs as a result of unstable, downstream-travelling waves, while the upstream-travelling waves are stable and release most of the transferred energy back to the flow. Coupling between different in vacuo modes offers another view of the origin of energy transfer. In addition, an energy conservation analysis similar to the one used in aeroacoustics is carried out. It is shown that terms directly proportional to fluid viscosity contribute most to the production of fluctuation energy, leading to a special type of dynamic instability which resembles both Tollmien-Schlichting instability in the sense that the fluid viscosity destabilises, and traditional travelling wave flutter since the structural damping plays the role of stabilising. Effects of the membrane mass, length and structural damping are also studied. The characteristics of the membrane flutter are found to depend crucially on the upstream and downstream boundary conditions.
Qiang, Bo; Greenleaf, James; Oyen, Michelle; Zhang, Xiaoming
2011-07-01
A two-step viscoelastic spherical indentation method is proposed to compensate for 1) material relaxation and 2) sample thickness. In the first step, the indenter is moved at a constant speed and the reaction force is measured. In the second step, the indenter is held at a constant position and the relaxation response of the material is measured. Then the relaxation response is fit with a multi-exponential function which corresponds to a three-branch general Maxwell model. The relaxation modulus is derived by correcting the finite ramp time introduced in the first step. The proposed model takes into account the sample thickness, which is important for applications in which the sample thickness is less than ten times the indenter radius. The model is validated numerically by finite element simulations. Experiments are carried out on a 10% gelatin phantom and a chicken breast sample with the proposed method. The results for both the gelatin phantom and the chicken breast sample agree with the results obtained from a surface wave method. Both the finite element simulations and experimental results show improved elasticity estimations by incorporating the sample thickness into the model. The measured shear elasticities of the 10% gelatin sample are 6.79 and 6.93 kPa by the proposed finite indentation method at sample thickness of 40 and 20 mm, respectively. The elasticity of the same sample is estimated to be 6.53 kPa by the surface wave method. For the chicken breast sample, the shear elasticity is measured to be 4.51 and 5.17 kPa by the proposed indentation method at sample thickness of 40 and 20 mm, respectively. Its elasticity is measured by the surface wave method to be 4.14 kPa.
Wu, Fu-Fa; Chan, K. C.; Jiang, Song-Shan; Chen, Shun-Hua; Wang, Gang
2014-01-01
Bulk metallic glasses exhibit high strength and large elastic strain limit but have no tensile ductility. However, bulk metallic glass composites reinforced by in-situ dendrites possess significantly improved toughness but at the expense of high strength and large elastic strain limit. Here, we report a bulk metallic glass composite with strong strain-hardening capability and large elastic strain limit. It was found that, by plastic predeformation, the bulk metallic glass composite can exhibit both a large elastic strain limit and high strength under tension. These unique elastic mechanical properties are attributed to the reversible B2↔B19′ phase transformation and the plastic-predeformation-induced complicated stress state in the metallic glass matrix and the second phase. These findings are significant for the design and application of bulk metallic glass composites with excellent mechanical properties. PMID:24931632
NASA Astrophysics Data System (ADS)
Thomases, Becca; Guy, Robert
2014-11-01
A computational model of finite-length undulatory swimmers is used to examine the physical origin of the effect of elasticity on swimming speed. We explore two distinct target swimming strokes, one derived from the motion of C. elegans, with large head undulations, and a contrasting stroke with large tail undulations. We show that both favorable stroke asymmetry and swimmer elasticity contribute to a speed-up, but a substantial boost results only when these two effects work together. We reproduce conflicting results from the literature simply by changing relevant physical parameters.
Thomases, Becca; Guy, Robert D
2014-08-29
A computational model of finite-length undulatory swimmers is used to examine the physical origin of the effect of elasticity on swimming speed. We explore two distinct target swimming strokes: one derived from the motion of Caenorhabditis elegans, with large head undulations, and a contrasting stroke with large tail undulations. We show that both favorable stroke asymmetry and swimmer elasticity contribute to a speed-up, but a substantial boost results only when these two effects work together. We reproduce conflicting results from the literature simply by changing relevant physical parameters. PMID:25216008
NASA Astrophysics Data System (ADS)
Thomases, Becca; Guy, Robert D.
2014-08-01
A computational model of finite-length undulatory swimmers is used to examine the physical origin of the effect of elasticity on swimming speed. We explore two distinct target swimming strokes: one derived from the motion of Caenorhabditis elegans, with large head undulations, and a contrasting stroke with large tail undulations. We show that both favorable stroke asymmetry and swimmer elasticity contribute to a speed-up, but a substantial boost results only when these two effects work together. We reproduce conflicting results from the literature simply by changing relevant physical parameters.
Numerical solution of an elastic and viscoelastic gravitational models by the finite element method
NASA Astrophysics Data System (ADS)
Arjona Almodóvar, A.; Chacón Rebollo, T.; Gómez Marmol, M.
2014-12-01
Volcanic areas present a lower effective viscosity than usually in the Earth's crust. Both the elastic-gravitational and the viscoelastic-gravitational models allow the computation of gravity, deformation, and gravitational potential changes in order to investigate crustal deformations of Earth (see for instance Battaglia & Segall, 2004; Fernández et al. 1999, 2001; Rundle 1980 and 1983). These models can be represented by a coupled system of linear parabolic (for the elastic deformations), hyperbolic (for the viscoelastic deformations) and elliptic partial differential equations (for gravitational potential changes) (see for instance Arjona et al. 2008 and 2010). The existence and uniqueness of weak solutions for both the elastic-gravitational and viscoelastic-gravitational problem was demonstrated in Arjona et al. (2008 and 2014). The stabilization to solutions of the associated stationary system was proved in Arjona and Díaz (2007). Here we consider the internal source as response to the effect of a pressurized magma reservoir into a multilayered, elastic-gravitational and viscoelastic-gravitational earth model. We introduce the numerical analysis of a simplified steady elastic-gravitational model, solved by means of the finite element method. We also present some numerical tests in realistic situations that confirm the predictions of theoretical order of convergence. Finally, we describe the methodology for both the elastic-gravitational and the viscoelastic-gravitational models using 2D and 3D test examples performed with FreeFEM++.
NASA Technical Reports Server (NTRS)
Kring, J.; Gyekenyesi, J.; Mendelson, A.
1977-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement fields in finite geometry bars containing central, surface, and double-edge cracks under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Normal stresses and the stress intensity factor variation along the crack periphery are calculated using the obtained displacement field. The reported results demonstrate the usefulness of this method in calculating stress intensity factors for commonly encountered crack geometries in finite solids.
NASA Astrophysics Data System (ADS)
Nestorović, M. D.; Triantafyllidis, N.
2004-04-01
A limiting factor in the design of fiber-reinforced composites is their failure under axial compression along the fiber direction. These critical axial stresses are significantly reduced in the presence of shear stresses. This investigation is motivated by the desire to study the onset of failure in fiber-reinforced composites under arbitrary multi-axial loading and in the absence of the experimentally inevitable imperfections and finite boundaries. By using a finite strain continuum mechanics formulation for the bifurcation (buckling) problem of a rate-independent, perfectly periodic (layered) solid of infinite extent, we are able to study the influence of load orientation, material properties and fiber volume fraction on the onset of instability in fiber-reinforced composites. Two applications of the general theory are presented in detail, one for a finitely strained elastic rubber composite and another for a graphite-epoxy composite, whose constitutive properties have been determined experimentally. For the latter case, extensive comparisons are made between the predictions of our general theory and the available experimental results as well as to the existing approximate structural theories. It is found that the load orientation, material properties and fiber volume fraction have substantial effects on the onset of failure stresses as well as on the type of the corresponding mode (local or global).
NASA Technical Reports Server (NTRS)
Rehfield, Lawrence W.; Pickings, Richard D.; Chang, Stephen; Holl, Michael
1991-01-01
Structural tailoring concepts were developed to create wings with elastically produced camber for the purpose of increasing lift during takeoff conditions. Simple models based upon enhancements to the thin walled composite beam theory of Rehfield were developed to investigate prospects for elastic tailoring of the chordwise deformation of wing structures. The purpose here is to provide a comparison of the theoretical results with a finite element model for the bending method of producing camber. Finite element correlation studies were completed for two cases: a bonded unstiffened structural box, and a bolted unstiffened structural box. Results from these studies show an error of less than one percent for the bonded case and less than six percent for the bolted case in predicting camber curvature for the structural box. Examination of the results shows that the theory is very accurate for the cases studied and will provide an excellent basis for conducting further tailoring studies.
Simple structures test for elastic-plastic strain acceptance criterion validation
Trimble, T.F.; Krech, G.R.
1997-11-01
A Simple Structures Test Program was performed where several cantilevered beam and fixed-end beam test specimens (fabricated from HY-80 steel) were subjected to a series of analytically predetermined rapidly applied transient dynamic input loads. The primary objective of the test program was to obtain dynamic nonlinear response for simple structures subjected to these load inputs. Data derived from these tests was subsequently used to correlate to analysis predictions to assess the capability to analytically predict elastic-plastic nonlinear material behavior in structures using typical time-dependent (transient) design methods and the ABAQUS finite element analysis code. The installation of a significant amount of instrumentation on these specimens and post-test measurements enabled the monitoring and recording of strain levels, displacements, accelerations, and permanent set. An assessment of modeling parameters such as the element type and mesh refinement was made using these test results. In addition, currently available material models and the incremental time step procedure used in the transient analyses were evaluated. Comparison of test data to analysis results shows that displacements, accelerations, and peak strain can be predicted with a reasonable level of accuracy using detailed solid models of the tested specimens. Permanent set is overpredicted by a factor of approximately two. However, the accuracy of the prediction of permanent set is being enhanced by updating material modeling in the ABAQUS code to account for effects of strain reversal in oscillatory behavior of dynamically loaded specimens.
NASA Technical Reports Server (NTRS)
Gyekenyesi, J. P.; Mendelson, A.; Kring, J.
1973-01-01
A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.
Barkaoui, Abdelwahed; Tlili, Brahim; Vercher-Martínez, Ana; Hambli, Ridha
2016-10-01
Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the elastic properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the elastic properties of the bone tissue in a multiscale approach including a sensitivity analysis of the elastic behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and finite elements method (FEM) analysis. The elastic properties are estimated using a neural network simulation that previously has been trained with the database results of the finite element models. In the results of this work, parametric analysis and averaged elastic constants for each length scale are provided. Likewise, the influence of the elastic constants of the tissue constituents is also depicted. Results highlight
Barkaoui, Abdelwahed; Tlili, Brahim; Vercher-Martínez, Ana; Hambli, Ridha
2016-10-01
Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the elastic properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the elastic properties of the bone tissue in a multiscale approach including a sensitivity analysis of the elastic behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and finite elements method (FEM) analysis. The elastic properties are estimated using a neural network simulation that previously has been trained with the database results of the finite element models. In the results of this work, parametric analysis and averaged elastic constants for each length scale are provided. Likewise, the influence of the elastic constants of the tissue constituents is also depicted. Results highlight
On the origin of elastic strain limit of bulk metallic glasses
NASA Astrophysics Data System (ADS)
Ding, J.; Cheng, Y. Q.; Ma, E.
2014-01-01
All bulk metallic glasses exhibit a large and almost universal elastic strain limit. Here, we show that the magnitude of the yield strain of the glass state can be quantitatively derived from a characteristic property of the flow state typical in running shear bands (the root cause of yielding). The strain in the shear flow is mostly plastic, but associated with it there is an effective elastic atomic strain. The latter is almost identical for very different model systems in our molecular dynamics simulations, such that the corresponding yield strain is universal at any given homologous temperature.
Variational integrators for the dynamics of thermo-elastic solids with finite speed thermal waves
Mata, Pablo
2014-01-15
This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the fact that the Green–Naghdi theory of type II for thermo-elastic solids has a Hamiltonian structure. Thus, standard techniques to construct variational integrators can be applied to finite element discretizations of the problem. The resulting discrete-in-time trajectories are then consistent with the laws of thermodynamics for these systems: for an isolated system, they exactly conserve the total entropy, and nearly exactly conserve the total energy over exponentially long periods of time. Moreover, linear and angular momenta are also exactly conserved whenever the exact system does. For definiteness, we construct an explicit second-order accurate algorithm for affine tetrahedral elements in two and three dimensions, and demonstrate its performance with numerical examples.
Vibration band gaps for elastic metamaterial rods using wave finite element method
NASA Astrophysics Data System (ADS)
Nobrega, E. D.; Gautier, F.; Pelat, A.; Dos Santos, J. M. C.
2016-10-01
Band gaps in elastic metamaterial rods with spatial periodic distribution and periodically attached local resonators are investigated. New techniques to analyze metamaterial systems are using a combination of analytical or numerical method with wave propagation. One of them, called here wave spectral element method (WSEM), consists of combining the spectral element method (SEM) with Floquet-Bloch's theorem. A modern methodology called wave finite element method (WFEM), developed to calculate dynamic behavior in periodic acoustic and structural systems, utilizes a similar approach where SEM is substituted by the conventional finite element method (FEM). In this paper, it is proposed to use WFEM to calculate band gaps in elastic metamaterial rods with spatial periodic distribution and periodically attached local resonators of multi-degree-of-freedom (M-DOF). Simulated examples with band gaps generated by Bragg scattering and local resonators are calculated by WFEM and verified with WSEM, which is used as a reference method. Results are presented in the form of attenuation constant, vibration transmittance and frequency response function (FRF). For all cases, WFEM and WSEM results are in agreement, provided that the number of elements used in WFEM is sufficient to convergence. An experimental test was conducted with a real elastic metamaterial rod, manufactured with plastic in a 3D printer, without local resonance-type effect. The experimental results for the metamaterial rod with band gaps generated by Bragg scattering are compared with the simulated ones. Both numerical methods (WSEM and WFEM) can localize the band gap position and width very close to the experimental results. A hybrid approach combining WFEM with the commercial finite element software ANSYS is proposed to model complex metamaterial systems. Two examples illustrating its efficiency and accuracy to model an elastic metamaterial rod unit-cell using 1D simple rod element and 3D solid element are
Bouvier, Adeline; Deleaval, Flavien; Doyley, Marvin M; Yazdani, Saami K; Finet, Gérard; Le Floc'h, Simon; Cloutier, Guy; Pettigrew, Roderic I; Ohayon, Jacques
2016-01-01
The peak cap stress (PCS) amplitude is recognized as a biomechanical predictor of vulnerable plaque (VP) rupture. However, quantifying PCS in vivo remains a challenge since the stress depends on the plaque mechanical properties. In response, an iterative material finite element (FE) elasticity reconstruction method using strain measurements has been implemented for the solution of these inverse problems. Although this approach could resolve the mechanical characterization of VPs, it suffers from major limitations since (i) it is not adapted to characterize VPs exhibiting high material discontinuities between inclusions, and (ii) does not permit real time elasticity reconstruction for clinical use. The present theoretical study was therefore designed to develop a direct material-FE algorithm for elasticity reconstruction problems which accounts for material heterogeneities. We originally modified and adapted the extended FE method (Xfem), used mainly in crack analysis, to model material heterogeneities. This new algorithm was successfully applied to six coronary lesions of patients imaged in vivo with intravascular ultrasound. The results demonstrated that the mean relative absolute errors of the reconstructed Young's moduli obtained for the arterial wall, fibrosis, necrotic core, and calcified regions of the VPs decreased from 95.3±15.56%, 98.85±72.42%, 103.29±111.86% and 95.3±10.49%, respectively, to values smaller than 2.6 × 10−8±5.7 × 10−8% (i.e. close to the exact solutions) when including modified-Xfem method into our direct elasticity reconstruction method. PMID:24240392
Power Output of Noise Sources Operating Near Elastic Scatterers of Finite Dimensions
NASA Astrophysics Data System (ADS)
TOMILINA, T. M.; BOBROVNITSKII, YU. I.; YASHKIN, V. B.; KOCHKIN, A. A.
1999-09-01
The problem of variation of the sound power output of noise sources due to reflecting boundaries and elastic scatterers is considered experimentally and numerically. In the laboratory experiment with a source of loudspeakers operating near a resonant scatterer, the increase in the radiated power obtained is about one hundred. An important role of the source near field in the power enhancement is shown. In computer simulation, a two-dimensional radiation problem for a circle vibrating near a finite elastic beam is studied. Most attention is paid to revealing physical mechanisms of the power output variations. It is shown that, for the source and elastic scatterer of finite dimensions, the radiated power can reach orders of magnitude of the free-field value. Especially, high-power amplification can be obtained at low frequencies for the sources that are poor radiators in free space, i.e., behave as multipoles of high order: presence of a scatterer or reflector makes such a source to be of monopole or dipole type. The results presented can be useful in better understanding sound generation mechanisms in complicated industrial noise sources.
NASA Astrophysics Data System (ADS)
Jaquet, Yoann; Duretz, Thibault; Schmalholz, Stefan M.
2016-02-01
We present two-dimensional numerical simulations for shortening a viscoelastoplastic lithosphere to quantify the impact of elasticity on strain localization due to thermal softening. The model conserves energy and mechanical work is converted into heat or stored as elastic strain energy. For a shear modulus G = 1010 Pa, a prominent lithospheric shear zone forms and elastic energy release increases the localization intensity (strain rate amplification). For G = 5 × 1010 Pa shear zones still form but deformation is less localized. For G = 1012 Pa, the lithosphere behaves effectively viscoplastic and no shear zones form during homogeneous thickening. Maximal shearing-related increase of surface heat flux is 15-25 mW m-2 and of temperature at lower crustal depth is ˜150 °C, whereby these peak values are transient (0.1-1 My). Elasticity and related energy release can significantly contribute to strain localization and plate-like behaviour of the lithosphere required for plate tectonics.
Mixed boundary conditions for FFT-based homogenization at finite strains
NASA Astrophysics Data System (ADS)
Kabel, Matthias; Fliegener, Sascha; Schneider, Matti
2016-02-01
In this article we introduce a Lippmann-Schwinger formulation for the unit cell problem of periodic homogenization of elasticity at finite strains incorporating arbitrary mixed boundary conditions. Such problems occur frequently, for instance when validating computational results with tensile tests, where the deformation gradient in loading direction is fixed, as is the stress in the corresponding orthogonal plane. Previous Lippmann-Schwinger formulations involving mixed boundary can only describe tensile tests where the vector of applied force is proportional to a coordinate direction. Utilizing suitable orthogonal projectors we develop a Lippmann-Schwinger framework for arbitrary mixed boundary conditions. The resulting fixed point and Newton-Krylov algorithms preserve the positive characteristics of existing FFT-algorithms. We demonstrate the power of the proposed methods with a series of numerical examples, including continuous fiber reinforced laminates and a complex nonwoven structure of a long fiber reinforced thermoplastic, resulting in a speed-up of some computations by a factor of 1000.
On the mechanism of bandgap formation in locally resonant finite elastic metamaterials
NASA Astrophysics Data System (ADS)
Sugino, Christopher; Leadenham, Stephen; Ruzzene, Massimo; Erturk, Alper
2016-10-01
Elastic/acoustic metamaterials made from locally resonant arrays can exhibit bandgaps at wavelengths much longer than the lattice size for various applications spanning from low-frequency vibration/sound attenuation to wave guiding and filtering in mechanical and electromechanical devices. For an effective use of such locally resonant metamaterial concepts in finite structures, it is required to bridge the gap between the lattice dispersion characteristics and modal behavior of the host structure with its resonators. To this end, we develop a novel argument for bandgap formation in finite-length elastic metamaterial beams, relying on the modal analysis and the assumption of infinitely many resonators. We show that the dual problem to wave propagation through an infinite periodic beam is the modal analysis of a finite beam with an infinite number of resonators. A simple formula that depends only on the resonator natural frequency and total mass ratio is derived for placing the bandgap in a desired frequency range, yielding an analytical insight and a rule of thumb for design purposes. A method for understanding the importance of a resonator location and mass is discussed in the context of a Riemann sum approximation of an integral, and a method for determining the optimal number of resonators for a given set of boundary conditions and target frequency is introduced. The simulations of the theoretical framework are validated by experiments for bending vibrations of a locally resonant cantilever beam.
NASA Technical Reports Server (NTRS)
Kim, H. Alicia; Hardie, Robert; Yamakov, Vesselin; Park, Cheol
2015-01-01
This paper is the second part of a two-part series where the first part presents a molecular dynamics model of a single Boron Nitride Nanotube (BNNT) and this paper scales up to multiple BNNTs in a polymer matrix. This paper presents finite element (FE) models to investigate the effective elastic and piezoelectric properties of (BNNT) nanocomposites. The nanocomposites studied in this paper are thin films of polymer matrix with aligned co-planar BNNTs. The FE modelling approach provides a computationally efficient way to gain an understanding of the material properties. We examine several FE models to identify the most suitable models and investigate the effective properties with respect to the BNNT volume fraction and the number of nanotube walls. The FE models are constructed to represent aligned and randomly distributed BNNTs in a matrix of resin using 2D and 3D hollow and 3D filled cylinders. The homogenisation approach is employed to determine the overall elastic and piezoelectric constants for a range of volume fractions. These models are compared with an analytical model based on Mori-Tanaka formulation suitable for finite length cylindrical inclusions. The model applies to primarily single-wall BNNTs but is also extended to multi-wall BNNTs, for which preliminary results will be presented. Results from the Part 1 of this series can help to establish a constitutive relationship for input into the finite element model to enable the modeling of multiple BNNTs in a polymer matrix.
Finite element model for aero-elastically tailored residential wind turbine blade design
NASA Astrophysics Data System (ADS)
Robinson, Eric Alan
Advances in passive wind turbine control systems have allowed wind turbines to achieve higher efficiencies and operate in wider inflow conditions than ever before. Within recent years, the adoption of aero-elastically tailored (bend-twist coupled) composite blades have been a pursued strategy. Unfortunately, for this strategy to be applied, traditional means of modeling, designing and manufacturing are no longer adequate. New parameters regarding non-linearities in deflections, stiffness, and aerodynamic loadings must now be implemented. To aid in the development of passive wind turbine system design, a finite element based aero-elastic program capable of computationally predicting blade deflection and twist under loading was constructed. The program was built around the idea of iteratively solving a blade composite structure to reach a maximum aero-elastic twist configuration under elevated wind speeds. Adopting a pre-existing blade geometry, from a pitch controlled small scale (3.5kW) turbine design, the program was tested to discover the geometry bend-twist coupling potential. This research would be a contributing factor in designing a passive pitch control replacement system for the turbine. A study of various model loading configurations was first performed to insure model validity. Then, a final model was used to analyze composite layups for selected spar configurations. Results characterize the aero-elastic twist properties for the selected configurations.
NASA Astrophysics Data System (ADS)
Nzodoum Fotsing, J. L.; Dietzel, D.; Chotikaprakhan, S.; Meckenstock, R.; Pelzl, J.; Cassette, S.
2005-06-01
In this contribution we report on combined investigations of hot areas in a high power high electron mobility transistor (HEMT) using a scanning thermo-elastic microscope and finite element simulations of the problem. The sample was a AlGaN/GaN-HEMT grown on sapphire substrate, with a gold coating for improved thermal management. The FE simulations were performed based on the ANSYS program version 5.7. The thermo-elastic response was detected with an Explorer AFM-head of Topometrix. To allow simultaneous detection of the topology and of the thermo-elastic expansion images, the explorer had been modified for AFM measurements in the DC mode and at the double frequency of the thermal sinus in AFM contact mode. The thermo-elastic image of the hot area of the HEMT recorded at 2f shows a bright line as the hot area which is located along the gate, between gate and drain. The absolute value of the vertical expansion has been calibrated from the measured diode signal by use of the microscope’s force-distance calibration curve. In order to obtain a reliable estimate of the maximum temperature on the hot line, the temperature image obtained by FE simulation is calibrated using the thermal expansion of the gold film of known thermal expansion coefficient.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1976-01-01
Some results of studies of convergence and accuracy of finite element approximations of certain nonlinear problems encountered in finite elasticity are presented. A general technique for obtaining error bounds is also described together with an existence theorem. Numerical results obtained by solving a representative problem are also included.
A fourth order accurate finite difference scheme for the computation of elastic waves
NASA Technical Reports Server (NTRS)
Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.
1986-01-01
A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.
NASA Astrophysics Data System (ADS)
Ponte Castañeda, P.; Tiberio, E.
2000-06-01
This work is concerned with the development of an analytical method for estimating the macroscopic behavior of heterogeneous elastic systems subjected to finite deformations. The objective is to generate variational estimates for the effective or homogenized stored-energy function of hyperelastic composites, which will be accomplished by means of a suitable generalization of the "second-order procedure" of Ponte Castañeda (Ponte Castañeda, P., 1996. J. Mech. Phys. Solids 44, 827-862). The key idea in this method is the introduction of an optimally chosen "linear thermoelastic comparison composite," which can then be used to convert available homogenization estimates for linear systems directly into new estimates for nonlinear composites. To illustrate the use of the method, an application is given for carbon-black filled elastomers and estimates analogous to the well-known Hashin-Shtrikman and self-consistent estimates for linear-elastic composites are generated.
Bönisch, Matthias; Calin, Mariana; van Humbeeck, Jan; Skrotzki, Werner; Eckert, Jürgen
2015-03-01
While the current research focus in the search for biocompatible low-modulus alloys is set on β-type Ti-based materials, the potential of fully martensitic Ti-based alloys remains largely unexplored. In this work, the influence of composition and pre-straining on the elastic properties of martensitic binary Ti-Nb alloys was studied. Additionally, the phase formation was compared in the as-cast versus the quenched state. The elastic moduli and hardness of the studied martensitic alloys are at a minimum of 16wt.% Nb and peak between 23.5 and 28.5wt.% Nb. The uniaxial deformation behavior of the alloys used is characterized by the absence of distinct yield points. Monotonic and cyclic (hysteretic) loading-unloading experiments were used to study the influence of Nb-content and pre-straining on the elastic moduli. Such experiments were also utilized to assess the recoverable elastic and anelastic deformations as well as hysteretic energy losses. Particular attention has been paid to the separation of non-linear elastic from anelastic strains, which govern the stress and strain limits to which a material can be loaded without deforming it plastically. It is shown that slight pre-straining of martensitic Ti-Nb alloys can lead to considerable reductions in their elastic moduli as well as increases in their total reversible strains.
An Elastic Plastic Contact Model with Strain Hardening for the LAMMPS Granular Package
Kuhr, Bryan; Brake, Matthew Robert; Lechman, Jeremy B.
2015-03-01
The following details the implementation of an analytical elastic plastic contact model with strain hardening for normal im pacts into the LAMMPS granular package. The model assumes that, upon impact, the co llision has a period of elastic loading followed by a period of mixed elastic plas tic loading, with contributions to each mechanism estimated by a hyperbolic seca nt weight function. This function is implemented in the LAMMPS source code as the pair style gran/ep/history. Preliminary tests, simulating the pouring of pure nickel spheres, showed the elastic/plastic model took 1.66x as long as similar runs using gran/hertz/history.
Buckling of an elastic fiber with finite length in a soft matrix.
Zhao, Yan; Li, Jing; Cao, Yan Ping; Feng, Xi-Qiao
2016-02-21
Elastic fibers embedded in a soft matrix are frequently encountered in nature and engineering across different length scales, ranging from microtubules in cytosol and filament networks to dissociative slender fish bones in muscles and fiber-reinforced soft composites. Fibers may buckle when the composite is subjected to compression; this study investigates this issue through a combination of experiments, finite-element simulations and theoretical analysis. Analysis reveals the important role of the interfacial shear forces and leads to an explicit solution to predict the occurrence of buckling for a slender fiber with finite length. The results reported in this paper will help understand the formation of shapes in some natural systems and provide guidelines for the design of soft biocomposites. PMID:26762701
On the influence of strain rate in acousto-elasticity : experimental results for Berea sandstone
NASA Astrophysics Data System (ADS)
Riviere, J. V.; Candela, T.; Scuderi, M.; Marone, C.; Guyer, R. A.; Johnson, P. A.
2013-12-01
Elastic nonlinear effects are pervasive in the Earth, including during strong ground motion, tidal forcing and earthquake slip processes. We study elastic nonlinear effects in the laboratory with the goal of developing new methods to probe elastic changes in the Earth, and to characterize and understand their origins. Here we report on nonlinear, frequency dispersion effects by applying a method termed dynamic acousto-elasticity (DAE), analogous to quasi-static acousto-elasticity. DAE allows one to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. We perform DAE on samples of Berea sandstone subject to 0.5 MPa uniaxial and biaxial loading conditions with oscillating loads at frequencies from 0.001 to 10 Hz and amplitudes of a few 100 kPa. We compare results to DAE measurements made in the kHz range. We observe that the average decrease in modulus due to nonlinear material softening increases with frequency, suggesting a frequency and/or a strain rate dependence. Previous quasi-static measurements (Claytor et al., GRL 2009) show that stress-strain nonlinear hysteretic behavior disappears when the experiment is performed at a very low strain-rate, implying that a rate dependent nonlinear elastic model would be useful (Gusev et al., PRB 2004). Our results also suggest that when elastic nonlinear Earth processes are studied, stress forcing frequency is an important consideration, and may lead to unexpected behaviors.
Directional anisotropy, finite size effect and elastic properties of hexagonal boron nitride
NASA Astrophysics Data System (ADS)
Thomas, Siby; Ajith, K. M.; Valsakumar, M. C.
2016-07-01
Classical molecular dynamics simulations have been performed to analyze the elastic and mechanical properties of two-dimensional (2D) hexagonal boron nitride (h-BN) using a Tersoff-type interatomic empirical potential. We present a systematic study of h-BN for various system sizes. Young’s modulus and Poisson’s ratio are found to be anisotropic for finite sheets whereas they are isotropic for the infinite sheet. Both of them increase with system size in accordance with a power law. It is concluded from the computed values of elastic constants that h-BN sheets, finite or infinite, satisfy Born’s criterion for mechanical stability. Due to the the strong in-plane sp2 bonds and the small mass of boron and nitrogen atoms, h-BN possesses high longitudinal and shear velocities. The variation of bending rigidity with system size is calculated using the Foppl–von Karman approach by coupling the in-plane bending and out-of-plane stretching modes of the 2D h-BN.
Finite-size scaling in the interfacial stiffness of rough elastic contacts.
Pastewka, Lars; Prodanov, Nikolay; Lorenz, Boris; Müser, Martin H; Robbins, Mark O; Persson, Bo N J
2013-06-01
The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of K on the applied squeezing pressure p are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of p, K rises linearly with p. Sublinear power-law scaling is observed at small p, but the simulations reveal that this is a finite-size effect. We derive accurate, analytical expressions for the exponents and prefactors of this low-pressure scaling of K by extending the contact mechanics theory of Persson to systems of finite size. In agreement with our simulations, these expressions show that the onset of the low-pressure scaling regime moves to lower pressure as the system size increases.
Elastic bending modulus of single-layer molybdenum disulfide (MoS2): finite thickness effect.
Jiang, Jin-Wu; Qi, Zenan; Park, Harold S; Rabczuk, Timon
2013-11-01
We derive, from an empirical interaction potential, an analytic formula for the elastic bending modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained elastic bending modulus of 9.61 eV in SLMoS2 is significantly higher than the bending modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory with experimentally obtained values for the elastic constants of SLMoS2. This increase in bending modulus as compared to monolayer graphene is attributed, through our analytic expression, to the finite thickness of SLMoS2. Specifically, while each monolayer of S atoms contributes 1.75 eV to the bending modulus, which is similar to the 1.4 eV bending modulus of monolayer graphene, the additional pairwise and angular interactions between out of plane Mo and S atoms contribute 5.84 eV to the bending modulus of SLMoS2. PMID:24084656
NASA Astrophysics Data System (ADS)
Palchik, V.
2013-03-01
The stress [crack damage stress ( σ cd) and uniaxial compressive strength ( σ c)] and strain characteristics [maximum total volumetric strain ( ɛ cd), axial failure strain ( ɛ af)], porosity ( n) and elastic constants [elastic modulus ( E) and Poisson's ratio ( ν)] and their ratios were coordinated with the existence of two different types (type 1 and type 2) of volumetric strain curve. Type 1 volumetric strain curve has a reversal point and, therefore, σ cd is less than the uniaxial compressive strength ( σ c). Type 2 has no reversal point, and the bulk volume of rock decreases until its failure occurs (i.e., σ cd = σ c). It is confirmed that the ratio between the elastic modulus ( E) and the parameter λ = n/ ɛ cd strongly affects the crack damage stress ( σ cd) for both type 1 and type 2 volumetric strain curves. It is revealed that heterogeneous carbonate rock samples exhibit different types of the volumetric strain curve even within the same rock formation, and the range of σ cd/ σ c = 0.54-1 for carbonate rocks is wider than the range (0.71 < σ cd/ σ c < 0.84) obtained by other researchers for granites, sandstones and quartzite. It is established that there is no connection between the type of the volumetric strain curve and values of n, E, σ cd, ν, E/(1 - 2 ν), M R = E/ σ c and E/ λ. On the other hand, the type of volumetric strain curve is connected with the values of λ and the ratio between the axial failure strain ( ɛ af) and the maximum total volumetric strain ( ɛ cd). It is argued that in case of small ɛ af/ ɛ cd-small λ, volumetric strain curve follows the type 2.
NASA Technical Reports Server (NTRS)
Sanfeliz, Jose G.
1993-01-01
Micromechanical modeling via elastic-plastic finite element analyses were performed to investigate the effects that the residual stresses and the degree of matrix work hardening (i.e., cold-worked, annealed) have upon the behavior of a 9 vol percent, unidirectional W/Cu composite, undergoing tensile loading. The inclusion of the residual stress-containing state as well as the simulated matrix material conditions proved to be significant since the Cu matrix material exhibited plastic deformation, which affected the subsequent tensile response of the composite system. The stresses generated during cooldown to room temperature from the manufacturing temperature were more of a factor on the annealed-matrix composite, since they induced the softened matrix to plastically flow. This event limited the total load-carrying capacity of this matrix-dominated, ductile-ductile type material system. Plastic deformation of the hardened-matrix composite during the thermal cooldown stage was not considerable, therefore, the composite was able to sustain a higher stress before showing any appreciable matrix plasticity. The predicted room temperature, stress-strain response, and deformation stages under both material conditions represented upper and lower bounds characteristic of the composite's tensile behavior. The initial deformation stage for the hardened material condition showed negligible matrix plastic deformation while for the annealed state, its initial deformation stage showed extensive matrix plasticity. Both material conditions exhibited a final deformation stage where the fiber and matrix were straining plastically. The predicted stress-strain results were compared to the experimental, room temperature, tensile stress-strain curve generated from this particular composite system. The analyses indicated that the actual thermal-mechanical state of the composite's Cu matrix, represented by the experimental data, followed the annealed material condition.
Nobakhti, Sabah; Limbert, Georges; Thurner, Philipp J
2014-01-01
Bone is multi-scale hierarchical composite material making the prediction of fragility, as well as pinning it to a certain cause, complicated. For proper mechanical simulation and reflection of bone properties in models, microscopic structural features of bone tissue need to be included. This study sets out to gain a mechanistic insight into the role of various microstructural features of bone tissue in particular cement lines and interlamellar areas. Further the hypothesis that compliant interlamellar areas and cement lines within osteonal bone act as strain amplifiers was explored. To this end, a series of experimentally-based micromechanical finite element models of bovine osteonal bone were developed. Different levels of detail for the bone microstructure were considered and combined with the results of physical three-point bending tests and an analytical composite model of a single osteon. The objective was to examine local and global effects of interface structures. The geometrical and microstructural characteristics of the bone samples were derived from microscopy imaging. Parametric finite element studies were conducted to determine optimal values of the elastic modulus of interstitial bone and interlamellar areas. The average isotropic elastic modulus of interfaces suggested in this study is 88.5MPa. Based on the modelling results, it is shown that interfaces are areas of accumulated strain in bone and are likely to act as potential paths for crack propagation. The strain amplification capability of interface structures in the order of 10 predicted by the models suggests a new explanation for the levels of strain required in bone homoeostasis for maintenance and adaptation.
Nobakhti, Sabah; Limbert, Georges; Thurner, Philipp J
2014-01-01
Bone is multi-scale hierarchical composite material making the prediction of fragility, as well as pinning it to a certain cause, complicated. For proper mechanical simulation and reflection of bone properties in models, microscopic structural features of bone tissue need to be included. This study sets out to gain a mechanistic insight into the role of various microstructural features of bone tissue in particular cement lines and interlamellar areas. Further the hypothesis that compliant interlamellar areas and cement lines within osteonal bone act as strain amplifiers was explored. To this end, a series of experimentally-based micromechanical finite element models of bovine osteonal bone were developed. Different levels of detail for the bone microstructure were considered and combined with the results of physical three-point bending tests and an analytical composite model of a single osteon. The objective was to examine local and global effects of interface structures. The geometrical and microstructural characteristics of the bone samples were derived from microscopy imaging. Parametric finite element studies were conducted to determine optimal values of the elastic modulus of interstitial bone and interlamellar areas. The average isotropic elastic modulus of interfaces suggested in this study is 88.5MPa. Based on the modelling results, it is shown that interfaces are areas of accumulated strain in bone and are likely to act as potential paths for crack propagation. The strain amplification capability of interface structures in the order of 10 predicted by the models suggests a new explanation for the levels of strain required in bone homoeostasis for maintenance and adaptation. PMID:24113298
Finite Element Modeling of the Behavior of Armor Materials Under High Strain Rates and Large Strains
NASA Astrophysics Data System (ADS)
Polyzois, Ioannis
For years high strength steels and alloys have been widely used by the military for making armor plates. Advances in technology have led to the development of materials with improved resistance to penetration and deformation. Until recently, the behavior of these materials under high strain rates and large strains has been primarily based on laboratory testing using the Split Hopkinson Pressure Bar apparatus. With the advent of sophisticated computer programs, computer modeling and finite element simulations are being developed to predict the deformation behavior of these metals for a variety of conditions similar to those experienced during combat. In the present investigation, a modified direct impact Split Hopkinson Pressure Bar apparatus was modeled using the finite element software ABAQUS 6.8 for the purpose of simulating high strain rate compression of specimens of three armor materials: maraging steel 300, high hardness armor (HHA), and aluminum alloy 5083. These armor materials, provided by the Canadian Department of National Defence, were tested at the University of Manitoba by others. In this study, the empirical Johnson-Cook visco-plastic and damage models were used to simulate the deformation behavior obtained experimentally. A series of stress-time plots at various projectile impact momenta were produced and verified by comparison with experimental data. The impact momentum parameter was chosen rather than projectile velocity to normalize the initial conditions for each simulation. Phenomena such as the formation of adiabatic shear bands caused by deformation at high strains and strain rates were investigated through simulations. It was found that the Johnson-Cook model can accurately simulate the behavior of body-centered cubic (BCC) metals such as steels. The maximum shear stress was calculated for each simulation at various impact momenta. The finite element model showed that shear failure first occurred in the center of the cylindrical specimen and
W.R. Solonick
2003-04-01
Rapidly applied transient dynamic loads produce stresses and deflections in structures that typically exceed those from static loading conditions. Previous acceptance criteria for structures designed for rapidly applied transient dynamic loading limited stresses to those determined from elastic analysis. Different stress limits were established for different grades of structure depending upon the amount of permanent set considered acceptable. Structure allowed to sustain very limited permanent set is designed to stress limits not significantly greater than yield stress. Greater permanent set in structure under rapidly applied transient dynamic loading conditions is permitted by establishing stress limits that are significantly greater than yield stress but still provide adequate safety margin (with respect to failure). This paper presents a strain-based elastic-plastic (i.e., inelastic) analysis criterion developed as an alternative to the more conservative stress-based elastic analysis stress criterion for structures subjected to rapidly applied transient dynamic loading. The strain limits established are based on material ductility considerations only and are set as a fraction of the strain at ultimate stress obtained from an engineering stress/strain curve of the material. Strains limits are categorized by type as membrane or surface and by region as general, local , or concentrated. The application of the elastic-plastic criterion provides a more accurate, less conservative design/analysis basis for structures than that used in elastic stress-based analysis criteria, while still providing adequate safety margins.
Solonick, W.
1996-11-01
Rapidly applied transient dynamic loads produce stresses and deflections in structures that typically exceed those from static loading conditions. Previous acceptance criteria for structures designed for rapidly applied transient dynamic loading limited stresses to those determined from elastic analysis. Different stress limits were established for different grades of structure depending upon the amount of permanent set considered acceptable. Structure allowed to sustain very limited permanent set is designed to stress limits not significantly greater than yield stress. Greater permanent set in structure under rapidly applied transient dynamic loading conditions is permitted by establishing stress limits that are significantly greater than yield stress but still provide adequate safety margin (with respect to failure). This paper presents a strain-based elastic-plastic (i.e., inelastic) analysis criterion developed as an alternative to the more conservative stress-based elastic analysis stress criterion for structures subjected to rapidly applied transient dynamic loading. The strain limits established are based on a fraction of the strain at ultimate stress obtained from an engineering stress/strain curve of the material. Strains limits are categorized by type as membrane or surface and by region as general, local, or concentrated. The application of the elastic-plastic criterion provides a more accurate, less conservative design/analysis basis for structures than that used in elastic stress-based analysis criteria, while still providing adequate safety margins.
NASA Astrophysics Data System (ADS)
Vohar, B.; Kegl, M.; Ren, Z.
2008-12-01
Theoretical and practical aspects of an absolute nodal coordinate formulation (ANCF) beam finite element implementation are considered in the context of dynamic transient response optimization of elastic manipulators. The proposed implementation is based on the introduction of new nodal degrees of freedom, which is achieved by an adequate nonlinear mapping between the original and new degrees of freedom. This approach preserves the mechanical properties of the ANCF beam, but converts it into a conventional finite element so that its nodal degrees of freedom are initially always equal to zero and never depend explicitly on the design variables. Consequently, the sensitivity analysis formulas can be derived in the usual manner, except that the introduced nonlinear mapping has to be taken into account. Moreover, the adjusted element can also be incorporated into general finite element analysis and optimization software in the conventional way. The introduced design variables are related to the cross-section of the beam, to the shape of the (possibly) skeletal structure of the manipulator and to the drive functions. The layered cross-section approach and the design element technique are utilized to parameterize the shape of individual elements and the whole structure. A family of implicit time integration methods is adopted for the response and sensitivity analysis. Based on this assumption, the corresponding sensitivity formulas are derived. Two numerical examples illustrate the performance of the proposed element implementation.
NASA Technical Reports Server (NTRS)
Levy, R.
1991-01-01
Post-processing algorithms are given to compute the vibratory elastic-rigid coupling matrices and the modal contributions to the rigid-body mass matrices and to the effective modal inertias and masses. Recomputation of the elastic-rigid coupling matrices for a change in origin is also described. A computational example is included. The algorithms can all be executed by using standard finite-element program eigenvalue analysis output with no changes to existing code or source programs.
Statistical model for the prediction of elastic wave scattering from finite complicated shells
NASA Astrophysics Data System (ADS)
He, Hua
This thesis develops a simple statistical model to estimate bistatic elastic scattering from finite complicated shells in the mid-frequency range, 3 < ka/ < 10. The model has three parts: (1) sound power injection into the shell; (2) coupling among the elastic waves in the shell and wave power equipartition (3) sound radiation from the shell. Within 30o of beam aspect, sound power injection into the shell is mainly caused by acoustic trace matching, and is estimated by using an infinitely long shell model. Once trace matched, the compressional and shear waves can couple to each other and to the subsonic flexural waves at shell discontinuities such as bulkheads and endcaps. Under extensive wave conversion, wave power, defined as energy density multiplied by axial group speed, is hypothesized to be equipartitioned among the elastic wave types. Numerical calculations are conducted and the results show that the wave power equipartition hypothesis is plausible for a finite endcapped shell with four heavy deep rings. Using the wave power equipartition hypothesis, the shell motion is then converted to sound pressure in the surrounding fluid using Green's theorem. The sound radiation is further extended to the time domain, using random phase realizations and a decay rate model, which considers various dissipation mechanisms in the shells. The predicted target strength is compared with measured data for the ringed shell and the internalled shell, with the internal structures resiliently mounted to the rings. In terms of the mean target strength over the frequency region 3 < ka/ < 10 and the observation region within 30o of beam aspect, the prediction differs from the measured data by less than 2.5 dB for the second and third roundtrip of the trace matched wave in the shells, as well as for a time integrated case. The ring influence on elastic wave speeds is also studied. Inclusion of the influence in the model does not generally yield a better agreement with the
Revealing ultralarge and localized elastic lattice strains in Nb nanowires embedded in NiTi matrix
Zang, Ketao; Mao, Shengcheng; Cai, Jixiang; Liu, Yinong; Li, Haixin; Hao, Shijie; Jiang, Daqiang; Cui, Lishan
2015-01-01
Freestanding nanowires have been found to exhibit ultra-large elastic strains (4 to 7%) and ultra-high strengths, but exploiting their intrinsic superior mechanical properties in bulk forms has proven to be difficult. A recent study has demonstrated that ultra-large elastic strains of ~6% can be achieved in Nb nanowires embedded in a NiTi matrix, on the principle of lattice strain matching. To verify this hypothesis, this study investigated the elastic deformation behavior of a Nb nanowire embedded in NiTi matrix by means of in situ transmission electron microscopic measurement during tensile deformation. The experimental work revealed that ultra-large local elastic lattice strains of up to 8% are induced in the Nb nanowire in regions adjacent to stress-induced martensite domains in the NiTi matrix, whilst other parts of the nanowires exhibit much reduced lattice strains when adjacent to the untransformed austenite in the NiTi matrix. These observations provide a direct evidence of the proposed mechanism of lattice strain matching, thus a novel approach to designing nanocomposites of superior mechanical properties. PMID:26625854
Nonlinear elastic response in solid helium: critical velocity or strain?
Day, James; Syshchenko, Oleksandr; Beamish, John
2010-02-19
Torsional oscillator experiments show evidence of mass decoupling in solid 4He. This decoupling is amplitude dependent, suggesting a critical velocity for supersolidity. We observe similar behavior in the elastic shear modulus. By measuring the shear modulus over a wide frequency range, we can distinguish between an amplitude dependence which depends on velocity and one which depends on some other parameter such as displacement. In contrast with the torsional oscillator behavior, the modulus depends on the magnitude of stress, not velocity. We interpret our results in terms of the motion of dislocations which are weakly pinned by 3He impurities but which break away when large stresses are applied.
Strain fluctuations and elastic moduli in disordered solids
NASA Astrophysics Data System (ADS)
Sussman, Daniel M.; Schoenholz, Samuel S.; Xu, Ye; Still, Tim; Yodh, A. G.; Liu, Andrea J.
2015-08-01
Recently there has been a surge in interest in using video-microscopy techniques to infer the local mechanical properties of disordered solids. One common approach is to minimize the difference between particle vibrational displacements in a local coarse-graining volume and the displacements that would result from a best-fit affine deformation. Effective moduli are then inferred under the assumption that the components of this best-fit affine deformation tensor have a Boltzmann distribution. In this paper, we combine theoretical arguments with experimental and simulation data to demonstrate that the above does not reveal information about the true elastic moduli of jammed packings and colloidal glasses.
Super-elastic graphene ripples for flexible strain sensors.
Wang, Yi; Yang, Rong; Shi, Zhiwen; Zhang, Lianchang; Shi, Dongxia; Wang, Enge; Zhang, Guangyu
2011-05-24
In this study, we report a buckling approach for graphene and graphene ribbons on stretchable elastomeric substrates. Stretched polydimethylsiloxane (PDMS) films with different prestrains were used to receive the transferred graphene, and nanoscale periodical buckling of graphene was spontaneously formed after strain release. The morphology and periodicity of the as-formed graphene ripples are dependent strongly on their original shapes and substrates' prestrains. Regular periodicity of the ripples preferred to form for narrow graphene ribbons, and both the amplitude and periodicity are reduced with the increase of prestrain on PDMS. The graphene ripples have the ability to afford large strain deformation, thus making it ideal for flexible electronic applications. It was demonstrated that both graphene ribbon and nanographene film ripples could be used for strain sensors, and their resistance changes upon different strains were studied. This simple and controllable process of buckled graphene provides a feasible fabrication for graphene flexible electronic devices and strain sensors due to its novel mechanical and electrical properties. PMID:21452882
NASA Technical Reports Server (NTRS)
Gyekenyesi, J. P.; Mendelson, A.
1975-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement distributions in various bodies containing cracks. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The results obtained show a considerable potential for using this method in the three-dimensional analysis of finite geometry solids and suggest a possible extension of this technique to nonlinear material behavior.
NASA Technical Reports Server (NTRS)
Gyekenyesi, J. P.; Mendelson, A.
1974-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement distributions in various bodies containing cracks. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The results obtained show a considerable potential for using this method in the three-dimensional analysis of finite geometry solids and suggest a possible extension of this technique to nonlinear material behavior.
NASA Astrophysics Data System (ADS)
DeLuca, R.
2006-03-01
Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected.
NASA Astrophysics Data System (ADS)
Lim, C. W.; Zhang, G.; Reddy, J. N.
2015-05-01
In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories. The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory. The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain. The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale. By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory. In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed. It is based on the nonlocal effects of the strain field and first gradient strain field. This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function. The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense. By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational
Application Of Elastic Perfectly Plastic Cyclic Analysis To Assessment Of Creep Strain
Carter, Peter; Jetter, Robert I; Sham, Sam
2012-01-01
A cyclic elastic-perfectly plastic analysis method is proposed which provides a conservative estimate to cyclic creep strain accumulation within the ratchet boundary. The method is to check for ratcheting based on an elastic-perfectly material with a temperature-dependent pseudo yield stress defined by temperature, time and stress to give 1% creep strain. It does not require stress classification and is also applicable to a full range of temperature above and below the creep regime. This simplified method could be used as a rapid screening calculation, with full time-dependent creep analysis used if necessary.
Application of equivalent elastic methods in three-dimensional finite element structural analysis
Jones, D.P.; Gordon, J.L.; Hutula, D.N.; Holliday, J.E.; Jandrasits, W.G.
1998-02-01
This paper describes use of equivalent solid (EQS) modeling to obtain efficient solutions to perforated material problems using three-dimensional finite element analysis (3D-FEA) programs. It is shown that the accuracy of EQS methods in 3D-FEA depends on providing sufficient equivalent elastic properties to allow the EQS material to respond according to the elastic symmetry of the pattern. Peak stresses and ligament stresses are calculated from the EQS stresses by an appropriate 3D-FEA submodel approach. The method is demonstrated on the problem of a transversely pressurized simply supported plate with a central divider lane separating two perforated regions with circular penetrations arranged in a square pattern. A 3D-FEA solution for a model that incorporates each penetration explicitly is used for comparison with results from an EQS solution for the plate. Results for deflection and stresses from the EQS solution are within 3% of results from the explicit 3D-FE model. A solution to the sample problem is also provided using the procedures in the ASME B and PV Code. The ASME B and PV Code formulas for plate deflection were shown to overestimate the stiffening effects of the divider lane and the outer stiffening ring.
Finite element simulation for damage detection of surface rust in steel rebars using elastic waves
NASA Astrophysics Data System (ADS)
Tang, Qixiang; Yu, Tzuyang
2016-04-01
Steel rebar corrosion reduces the integrity and service life of reinforced concrete (RC) structures and causes their gradual and sudden failures. Early stage detection of steel rebar corrosion can improve the efficiency of routine maintenance and prevent sudden failures from happening. In this paper, detecting the presence of surface rust in steel rebars is investigated by the finite element method (FEM) using surface-generated elastic waves. Simulated wave propagation mimics the sensing scheme of a fiber optic acoustic generator mounted on the surface of steel rebars. Formation of surface rust in steel rebars is modeled by changing material's property at local elements. In this paper, various locations of a fiber optic acoustic transducer and a receiver were considered. Megahertz elastic waves were used and different sizes of surface rust were applied. Transient responses of surface displacement and pressure were studied. It is found that surface rust is most detectable when the rust location is between the transducer and the receiver. Displacement response of intact steel rebar is needed in order to obtain background-subtracted response with a better signal-to-noise ratio. When the size of surface rust increases, reduced amplitude in displacement was obtained by the receiver.
Analytical phase-tracking-based strain estimation for ultrasound elasticity.
Yuan, Lili; Pedersen, Peder C
2015-01-01
A new strain estimator for quasi-static elastography is presented, based on tracking of the analytical signal phase as a function of the external force. Two implementations are introduced: zero-phase search with moving window (SMW) and zero-phase band tracking using connected component labeling (CCL). Low analytical signal amplitude caused by local destructive interference is associated with large error in the phase trajectories, and amplitude thresholding can thus be used to terminate the phase tracking along a particular path. Interpolation is then applied to estimate displacement in the eliminated path. The paper describes first a mathematical analysis based on 1-D multi-scatter modeling, followed by a statistical study of the displacement and strain error. Simulation and experiment with an inhomogeneous phantom indicate that SMW and CCL are capable of reliably estimating tissue displacement and strain over a larger range of deformation than standard timedomain cross-correlation (SCC). Results also show that SMW is roughly 40 times faster than SCC with comparable or even better accuracy. CCL is slower than SMW, but more noise robust. Simulation assessment at compression level 3% and 6% with SNR 20 dB demonstrates average strain error for SMW and CCL of 10%, whereas SCC achieves 18%. PMID:25585402
A new spectral finite volume method for elastic wave modelling on unstructured meshes
NASA Astrophysics Data System (ADS)
Zhang, Wensheng; Zhuang, Yuan; Chung, Eric T.
2016-07-01
In this paper, we consider a new spectral finite volume method (FVM) for the elastic wave equations. Our new FVM is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order FVM and the spectral FVM. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an overdetermined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard finite volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2-D problems, but the same methodology can be applied to 3-D.
Determination of Constant Strain Gradients of Elastically Bent Crystal Using X-ray Mirage Fringes
NASA Astrophysics Data System (ADS)
Jongsukswat, Sukswat; Fukamachi, Tomoe; Hirano, Kenji; Ju, Dongying; Negishi, Riichirou; Shimojo, Masayuki; Hirano, Keiichi; Kawamura, Takaaki
2012-07-01
Two experimental approaches are studied to determine a parameter of the strain gradient in an elastically bent crystal. In one approach, the parameter is determined by measuring the third peak of the X-ray mirage interference fringes and in the other, by measuring the region where no mirage diffraction beam reaches on the lateral surface of the crystal. Using the X-rays from synchrotron radiation, the mirage fringes have been observed in the 220 reflection of the Si crystal whose strain is controlled in cantilever bending. These two approaches both give accurate values of the parameter of the strain gradient, showing good agreement with the values calculated using elastic theory. In addition, the residual strain due to gravity is observed by measuring mirage fringes when the bending force becomes zero.
Efstathiou, C.; Boyce, D.E.; Park, J.-S.; Lienert, U.; Dawson, P.R.; Miller, M.P.
2010-11-30
This paper presents a method - based on high-energy synchrotron X-ray diffraction data and a crystal-based finite element simulation formulation - for understanding grain scale deformation behavior within a polycrystalline aggregate. We illustrate this method by using it to determine the single-crystal elastic moduli of {beta}21s, a body-centered cubic titanium alloy. We employed a polycrystalline sample. Using in situ loading and high-energy X-rays at the Advanced Photon Source beamline 1-ID-C, we measured components of the lattice strain tensor from four individual grains embedded within a polycrystalline specimen. We implemented an optimization routine that minimized the difference between the experiment and simulation lattice strains. Sensitivity coefficients needed in the optimization routine are generated numerically using the finite element model. The elastic moduli that we computed for the {beta}21s are C{sub 11} = 110 GPa, C{sub 12} = 74 GPa and C{sub 44} = 89 GPa. The resulting Zener anisotropic ratio is A = 5.
Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone
NASA Astrophysics Data System (ADS)
Rivière, Jacques; Pimienta, Lucas; Scuderi, Marco; Candela, Thibault; Shokouhi, Parisa; Fortin, Jérôme; Schubnel, Alexandre; Marone, Chris; Johnson, Paul A.
2016-04-01
Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static (f→0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2-3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. These findings can be used to improve theories relating the macroscopic elastic response to microstructural features.
Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels.
Nam, Sungmin; Hu, Kenneth H; Butte, Manish J; Chaudhuri, Ovijit
2016-05-17
The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction. PMID:27140623
A Unified Finite Element Method for Arbitrary Elastic and Acoustic Media
NASA Astrophysics Data System (ADS)
Karaoglu, H.; Bielak, J.
2011-12-01
This study reports on a mixed finite element formulation that overcomes certain limitations faced by low-order primal-based formulations. A primal-based formulation with displacement as the variable is a widely used method to solve wave-propagation problems. It has been observed, however, that its accuracy deteriorates badly with increasing contrast between the P- and S-wave velocities (a situation often referred to, inaccurately, as almost incompressible). The extreme case for this contrast is an ideal, compressible fluid medium with S-wave velocity equals to zero. This extreme case creates problems in the equations of compressible elasticity. By using a dual-based formulation, we develop a method that is robust within the entire range of an elastic solid with moderate contrast between the P- and S-wave velocities up to the limiting case of an acoustic medium for which the S-wave velocity is zero. By solving a constrained variational problem with the Lagrange-Multiplier Method, we developed the dual-based (mixed) formulation with pressure and displacement as the variables.This is similar to earlier mixed displacement-pressure formulations, except that we introduce the methodology as a global one applicable to different domains rather than being limited to certain extreme cases. The variational problem makes a wider range of interpolation functions permissible for pressure including discontinuous functions across element boundaries. We verify the method and illustrate the general principles with an application in Southern California of the 1994 Northridge earthquake. We also discuss the possible extension of the method to fluid-structure interaction problems with dry interface conditions.
NASA Astrophysics Data System (ADS)
Grilo, Tiago J.; Vladimirov, Ivaylo N.; Valente, Robertt A. F.; Reese, Stefanie
2016-06-01
In the present paper, a finite strain model for complex combined isotropic-kinematic hardening is presented. It accounts for finite elastic and finite plastic strains and is suitable for any anisotropic yield criterion. In order to model complex cyclic hardening phenomena, the kinematic hardening is described by several back stress components. To that end, a new procedure is proposed in which several multiplicative decompositions of the plastic part of the deformation gradient are considered. The formulation incorporates a completely general format of the yield function, which means that any yield function can by employed by following a procedure that ensures the principle of material frame indifference. The constitutive equations are derived in a thermodynamically consistent way and numerically integrated by means of a backward-Euler algorithm based on the exponential map. The performance of the constitutive model is assessed via numerical simulations of industry-relevant sheet metal forming processes (U-channel forming and draw/re-draw of a panel benchmarks), the results of which are compared to experimental data. The comparison between numerical and experimental results shows that the use of multiple back stress components is very advantageous in the description of springback. This holds in particular if one carries out a comparison with the results of using only one component. Moreover, the numerically obtained results are in excellent agreement with the experimental data.
Development of Ti-Nb-Zr alloys with high elastic admissible strain for temporary orthopedic devices.
Ozan, Sertan; Lin, Jixing; Li, Yuncang; Ipek, Rasim; Wen, Cuie
2015-07-01
A new series of beta Ti-Nb-Zr (TNZ) alloys with considerable plastic deformation ability during compression test, high elastic admissible strain, and excellent cytocompatibility have been developed for removable bone tissue implant applications. TNZ alloys with nominal compositions of Ti-34Nb-25Zr, Ti-30Nb-32Zr, Ti-28Nb-35.4Zr and Ti-24.8Nb-40.7Zr (wt.% hereafter) were fabricated using the cold-crucible levitation technique, and the effects of alloying element content on their microstructures, mechanical properties (tensile strength, yield strength, compressive yield strength, Young's modulus, elastic energy, toughness, and micro-hardness), and cytocompatibilities were investigated and compared. Microstructural examinations revealed that the TNZ alloys consisted of β phase. The alloy samples displayed excellent ductility with no cracking, or fracturing during compression tests. Their tensile strength, Young's modulus, elongation at rupture, and elastic admissible strain were measured in the ranges of 704-839 MPa, 62-65 GPa, 9.9-14.8% and 1.08-1.31%, respectively. The tensile strength, Young's modulus and elongation at rupture of the Ti-34Nb-25Zr alloy were measured as 839 ± 31.8 MPa, 62 ± 3.6 GPa, and 14.8 ± 1.6%, respectively; this alloy exhibited the elastic admissible strain of approximately 1.31%. Cytocompatibility tests indicated that the cell viability ratios (CVR) of the alloys are greater than those of the control group; thus the TNZ alloys possess excellent cytocompatibility.
Kakeshita, Tomoyuki; Xiao, Fei; Fukuda, Takashi
2016-08-13
A Fe-31.2Pd (at.%) alloy exhibits a weak first-order martensitic transformation from a cubic structure to a tetragonal structure near 230 K. This transformation is associated with significant softening of elastic constant C'. Because of the softening, the alloy shows a large elastic strain of more than 6% in the [001] direction. In addition, the alloy has a critical point and shows a high elastocaloric effect in a wide temperature range for both the parent and the martensite phases.This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'. PMID:27402932
Kakeshita, Tomoyuki; Xiao, Fei; Fukuda, Takashi
2016-08-13
A Fe-31.2Pd (at.%) alloy exhibits a weak first-order martensitic transformation from a cubic structure to a tetragonal structure near 230 K. This transformation is associated with significant softening of elastic constant C'. Because of the softening, the alloy shows a large elastic strain of more than 6% in the [001] direction. In addition, the alloy has a critical point and shows a high elastocaloric effect in a wide temperature range for both the parent and the martensite phases.This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'.
Eberle, Sebastian; Göttlinger, Michael; Augat, Peter
2013-09-01
In a previous study on subject-specific finite-element-models, we found that appropriate density-elasticity relationships to compute the mechanical behavior of femurs seem to be subject-specific. The purpose of this study was to test the hypothesis that the predictive error of a cohort of subject-specific finite element-models is lower with subject-specific density-elasticity relationships than with a cohort-specific density-elasticity relationship. Finite-element-analysis and inverse optimization based on response surface methodology were employed to test the hypothesis. Subject-specific FE-models of 17 human femurs and corresponding experimental data from biomechanical tests were taken from a previous study. A power function for the relation between radiological bone density and elastic modulus was set up with the optimization variables a and b: E(MPa)=aρqCT(b)(gK2HPO4/cm(3)). The goal of the optimization was to minimize the root-mean-square error in percent (RMSE%) between computational and experimental results. A Wilcoxon test (p=0.05) was performed on all absolute relative errors between the two groups (subject-specific functions vs. cohort-specific function). The subject-specific functions resulted in a 6% lower overall prediction error and a 6% lower RMSE% than the cohort-specific function (p<0.001). The determined subject-specific relations were mostly linear, with variable a ranging from 9307 to 15673 and variable b ranging from 0.68 to 1.40. For the cohort-specific relation, the following power law was obtained: E(MPa)=12486ρqCT(1.16)(gK2HPO4/cm(3)). We conclude that individual density-elasticity relationships improve the accuracy of subject-specific finite element models. Future subject-specific finite-element-analyses of bones should include the individuality of the elastic properties by a stochastic density-elasticity relationship with mean and standard deviation of a and b.
Validation of composite finite elements efficiently simulating elasticity of trabecular bone.
Schwen, Lars Ole; Wolfram, Uwe
2014-01-01
Patient-specific analyses of the mechanical properties of bones become increasingly important for the management of patients with osteoporosis. The potential of composite finite elements (CFEs), a novel FE technique, to assess the apparent stiffness of vertebral trabecular bone is investigated in this study. Segmented volumes of cylindrical specimens of trabecular bone are compared to measured volumes. Elasticity under uniaxial loading conditions is simulated; apparent stiffnesses are compared to experimentally determined values. Computational efficiency is assessed and recommendations for simulation parameters are given. Validating apparent uniaxial stiffnesses results in concordance correlation coefficients 0.69 ≤ r(c) ≤ 0.92 for resolutions finer than 168 μm, and an average error of 5.8% between experimental and numerical results at 24 μm resolution. As an application, the code was used to compute local, macroscopic stiffness tensors for the trabecular structure of a lumbar vertebra. The presented technique allows for computing stiffness using smooth FE meshes at resolutions that are well achievable in peripheral high resolution quantitative CT. Therefore, CFEs could be a valuable tool for the patient-specific assessment of bone stiffness.
Elastic strains at interfaces in InAs/AlSb multilayer structures for quantum cascade lasers
Nicolai, J.; Gatel, Ch.; Warot-Fonrose, B.; Ponchet, A.; Teissier, R.; Baranov, A. N.; Magen, C.
2014-01-20
InAs/AlSb multilayers similar to those used in quantum cascade lasers have been grown by molecular beam epitaxy on (001) InAs substrates. Elastic strain is investigated by high resolution transmission electron microscopy. Thin interfacial regions with lattice distortions significantly different from the strain of the AlSb layers themselves are revealed from the geometrical phase analysis. Strain profiles are qualitatively compared to the chemical contrast of high angle annular dark field images obtained by scanning transmission electron microscopy. The strain and chemical profiles are correlated with the growth sequences used to form the interfaces. Tensile strained AlAs-like interfaces tend to form predominantly due to the high thermal stability of AlAs. Strongly asymmetric interfaces, AlAs-rich and (Al, In)Sb, respectively, can also be achieved by using appropriate growth sequences.
Stress and strain distribution in demineralized enamel: A micro-CT based finite element study.
Neves, Aline Almeida; Coutinho, Eduardo; Alves, Haimon Diniz Lopes; de Assis, Joaquim Teixeira
2015-10-01
Physiological oral mechanical forces may play a role on the progression of enamel carious lesions to cavitation. Thus, the aim of this study was to describe, by 3D finite element analysis, stress, and strain patterns in sound and carious enamel after a simulated occlusal load. Micro-CT based models were created and meshed with tetrahedral elements (based on an extracted third molar), namely: a sound (ST) and a carious tooth (CT). For the CT, enamel material properties were assigned according to the micro-CT gray values. Below the threshold corresponding to the enamel lesion (2.5 g/cm(3) ) lower and isotropic elastic modulus was assigned (E = 18 GPa against E1 = 80 GPa, E2 = E3 = 20 GPa for sound enamel). Both models were imported into a FE solver where boundary conditions were assigned and a pressure load (500 MPa) was applied at the occlusal surface. A linear static analysis was performed, considering anisotropy in sound enamel. ST showed a more efficient transfer of maximum principal stress from enamel to the dentin layer, while for the CT, enamel layer was subjected to higher and concentrated loads. Maximum principal strain distributions were seen at the carious enamel surface, especially at the central fossa, correlating to the enamel cavity seen at the original micro-CT model. It is possible to conclude that demineralized enamel compromises appropriate stress transfer from enamel to dentin, contributing to the odds of fracture and cavitation. Enamel fracture over a dentin lesion may happen as one of the normal pathways to caries progression and may act as a confounding factor during clinical diagnostic decisions. PMID:26240030
Stress and strain distribution in demineralized enamel: A micro-CT based finite element study.
Neves, Aline Almeida; Coutinho, Eduardo; Alves, Haimon Diniz Lopes; de Assis, Joaquim Teixeira
2015-10-01
Physiological oral mechanical forces may play a role on the progression of enamel carious lesions to cavitation. Thus, the aim of this study was to describe, by 3D finite element analysis, stress, and strain patterns in sound and carious enamel after a simulated occlusal load. Micro-CT based models were created and meshed with tetrahedral elements (based on an extracted third molar), namely: a sound (ST) and a carious tooth (CT). For the CT, enamel material properties were assigned according to the micro-CT gray values. Below the threshold corresponding to the enamel lesion (2.5 g/cm(3) ) lower and isotropic elastic modulus was assigned (E = 18 GPa against E1 = 80 GPa, E2 = E3 = 20 GPa for sound enamel). Both models were imported into a FE solver where boundary conditions were assigned and a pressure load (500 MPa) was applied at the occlusal surface. A linear static analysis was performed, considering anisotropy in sound enamel. ST showed a more efficient transfer of maximum principal stress from enamel to the dentin layer, while for the CT, enamel layer was subjected to higher and concentrated loads. Maximum principal strain distributions were seen at the carious enamel surface, especially at the central fossa, correlating to the enamel cavity seen at the original micro-CT model. It is possible to conclude that demineralized enamel compromises appropriate stress transfer from enamel to dentin, contributing to the odds of fracture and cavitation. Enamel fracture over a dentin lesion may happen as one of the normal pathways to caries progression and may act as a confounding factor during clinical diagnostic decisions.
Effect of high-energy X-ray doses on bone elastic properties and residual strains.
Singhal, A; Deymier-Black, Alix C; Almer, J D; Dunand, D C
2011-11-01
Bone X-ray irradiation occurs during medical treatments, sterilization of allografts, space travel and in vitro studies. High doses are known to affect the post-yield properties of bone, but their effect on the bone elastic properties is unclear. The effect of such doses on the mineral-organic interface has also not been adequately addressed. Here, the evolution of elastic properties and residual strains with increasing synchrotron X-ray dose (5-3880 kGy) is examined on bovine cortical bone. It is found that these doses affect neither the degree of nanometer-level load transfer between the hydroxyapatite (HAP) platelets and the collagen up to stresses of -60 MPa nor the microscopic modulus of collagen fibrils (both measured by synchrotron X-ray scattering during repeated in situ loading and unloading). However, the residual elastic strains in the HAP phase decrease markedly with increased irradiation, indicating damage at the HAP-collagen interface. The HAP residual strain also decreases after repeated loading/unloading cycles. These observations can be explained by temporary de-bonding at the HAP/collagen interface (thus reducing the residual strain), followed by rapid re-bonding (so that load transfer capability is not affected).
NASA Astrophysics Data System (ADS)
Preston, R. V.; Shercliff, H. R.; Withers, P. J.; Hughes, D. J.; Smith, S. D.; Webster, P. J.
2006-12-01
Residual strains have been measured in a tungsten inert gas (TIG) butt-welded 2024 aluminum alloy plate using synchrotron X-ray diffraction. Novel two-dimensional strain maps spanning the entire plate reveal steep gradients in residual stress and provide detailed validation data for finite element (FE) analysis. Two variants of a FE model have been used to predict the residual strain distributions, incorporating different levels of plate constraint. The model uses decoupled thermal and elastic-plastic mechanical analyses and successfully predicts the longitudinal and transverse residual strain field over the entire weld. For butt weld geometries, the degree of transverse constraint is shown to be a significant boundary condition, compared to simpler bead-on-plate analyses. The importance of transverse residual strains for detailed model validation is highlighted, together with the need for care in selecting the location for line scans. The residual stress is largest in the heat-affected zone (HAZ), being equal to the local postweld yield stress, though the strength increases subsequently by natural aging. In addition, a halving of the diffraction line width has been observed local to the weld, and this correlates with the microstructural changes in the region.
Appelo, D; Petersson, N A
2007-12-17
The isotropic elastic wave equation governs the propagation of seismic waves caused by earthquakes and other seismic events. It also governs the propagation of waves in solid material structures and devices, such as gas pipes, wave guides, railroad rails and disc brakes. In the vast majority of wave propagation problems arising in seismology and solid mechanics there are free surfaces. These free surfaces have, in general, complicated shapes and are rarely flat. Another feature, characterizing problems arising in these areas, is the strong heterogeneity of the media, in which the problems are posed. For example, on the characteristic length scales of seismological problems, the geological structures of the earth can be considered piecewise constant, leading to models where the values of the elastic properties are also piecewise constant. Large spatial contrasts are also found in solid mechanics devices composed of different materials welded together. The presence of curved free surfaces, together with the typical strong material heterogeneity, makes the design of stable, efficient and accurate numerical methods for the elastic wave equation challenging. Today, many different classes of numerical methods are used for the simulation of elastic waves. Early on, most of the methods were based on finite difference approximations of space and time derivatives of the equations in second order differential form (displacement formulation), see for example [1, 2]. The main problem with these early discretizations were their inability to approximate free surface boundary conditions in a stable and fully explicit manner, see e.g. [10, 11, 18, 20]. The instabilities of these early methods were especially bad for problems with materials with high ratios between the P-wave (C{sub p}) and S-wave (C{sub s}) velocities. For rectangular domains, a stable and explicit discretization of the free surface boundary conditions is presented in the paper [17] by Nilsson et al. In summary
NASA Astrophysics Data System (ADS)
Chinta, Prashanth K.; Mayer, K.; Langenberg, K. J.
2012-05-01
Nondestructive Evaluation (NDE) of elastic anisotropic media is very complex because of directional dependency of elastic stiffness tensor. Modeling of elastic waves in such materials gives us intuitive knowledge about the propagation and scattering phenomena. The wave propagation in three dimensional space in anisotropic media gives us the deep insight of the transition of the different elastic wave modes i.e. mode conversion, and scattering of these waves because of inhomogeneities present in the material. The numerical tool Three Dimensional-Elastodynamic Finite Integration Technique (3D-EFIT) has been proved to be a very efficient tool for the modeling of elastic waves in very complex geometries. The 3D-EFIT is validated using the analytical approach based on the Radon transform. The simulation results of 3D-EFIT applied to inhomogeneous austenitic steel welds and wood structures are presented. In the first application the geometry consists of an austenitic steel weld that joins two isotropic steel blocks. The vertical transversal isotropic (VTI) austenitic steel is used. The convolutional perfectly matched layers are applied at the boundaries that are supported by isotropic steel. In the second application the wave propagation in the orthotropic wooden structure with an air cavity inside is investigated. The wave propagation results are illustrated using time domain elastic wave snapshots.
Groger, Roman1; Lockman, Turab; Saxena, Avadh
2008-01-01
In dislocation-free martensites the components of the elastic strain tensor are constrained by the Saint-Venant compatibility condition which guarantees continuity of the body during external loading. However, in dislocated materials the plastic part of the distortion tensor introduces a displacement mismatch that is removed by elastic relaxation. The elastic strains are then no longer compatible in the sense of the Saint-Venant law and the ensuing incompatibility tensor is shown to be proportional to the gradients of the Nye dislocation density tensor. We demonstrate that the presence of this incompatibility gives rise to an additional long-range contribution in the inhomogeneous part of the Landau energy functional and to the corresponding stress fields. Competition among the local and long-range interactions results in frustration in the evolving order parameter (elastic) texture. We show how the Peach-Koehler forces and stress fields for any distribution of dislocations in arbitrarily anisotropic media can be calculated and employed in a Fokker-Planck dynamics for the dislocation density. This approach represents a self-consistent scheme that yields the evolutions of both the order parameter field and the continuous dislocation density. We illustrate our method by studying the effects of dislocations on microstructure, particularly twinned domain walls, in an Fe-Pd alloy undergoing a martensitic transformation.
Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo
2016-07-01
The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an elastic plate is studied by experiment and finite element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The finite element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the elastic constants are demonstrated. PMID:27079489
Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo
2016-07-01
The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an elastic plate is studied by experiment and finite element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The finite element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the elastic constants are demonstrated.
A 3D Orthotropic Strain-Rate Dependent Elastic Damage Material Model.
English, Shawn Allen
2014-09-01
A three dimensional orthotropic elastic constitutive model with continuum damage and cohesive based fracture is implemented for a general polymer matrix composite lamina. The formulation assumes the possibility of distributed (continuum) damage followed b y localized damage. The current damage activation functions are simply partially interactive quadratic strain criteria . However, the code structure allows for changes in the functions without extraordinary effort. The material model formulation, implementation, characterization and use cases are presented.
Elastic Strain Energy Storage and Neighboring Organ Assistance for Fluid Propulsion
NASA Astrophysics Data System (ADS)
Arun, C. P.
2003-11-01
Storage of elastic strain energy by non-muscular structures such as tendons and ligaments, is a common scheme employed by jumping animals. Also, since skeletal muscle is attached to bone, mechanical advantage is obtained, allowing a burst of power that is unobtainable by muscle contraction alone. This is important at launch since force may be applied for only the brief period when the legs are in contact with the ground. Liquid propelling structures such as the urinary bladder and the heart face the similar problem of being able to impart force to the content only as long as the wall is in a stretched state. Using data from videocystometry and cardiac catheterisation we show that the means employed to achieve liquid propulsion appears to involve a combination of isometric contraction (contraction against a closed sphincter or valve) with hyperelastic stretch of the wall, elastic strain energy storage by the wall, overshoot past the undistended state and neighboring organ assistance (NOA). Thus, the heart, a partially collapsible thick muscular shell without the benefit of NOA manages an ejection fraction of about 70%. Using all of the above means, the collapsible urinary bladder is able to nearly always empty. Elastic strain energy storage and NOA appear to be important strategies for liquid propulsion employed by hollow viscera.
Unified ab initio formulation of flexoelectricity and strain-gradient elasticity
NASA Astrophysics Data System (ADS)
Stengel, Massimiliano
2016-06-01
The theory of flexoelectricity and that of nonlocal elasticity are closely related, and are often considered together when modeling strain-gradient effects in solids. Here I show, based on a first-principles lattice-dynamical analysis, that their relationship is much more intimate than previously thought, and their consistent simultaneous treatment is crucial for obtaining correct physical answers. In particular, I identify a gauge invariance in the theory, whereby the energies associated to strain-gradient elasticity and flexoelectrically induced electric fields are individually reference dependent, and only when summed up they yield a well-defined result. To illustrate this, I construct a minimal thermodynamic functional incorporating strain-gradient effects, and establish a formal link between the continuum description and ab initio phonon dispersion curves to calculate the relevant tensor quantities. As a practical demonstration, I apply such a formalism to bulk SrTiO3, where I find an unusually strong contribution of nonlocal elasticity, mediated by the interaction between the ferroelectric soft mode and the transverse acoustic branches. These results have important implications towards the construction of well-defined thermodynamic theories where flexoelectricity and ferroelectricity coexist. More generally, they open exciting new avenues for the implementation of hierarchical multiscale concepts in the first-principles simulation of crystalline insulators.
A comparison of strain calculation using digital image correlation and finite element software
NASA Astrophysics Data System (ADS)
Iadicola, M.; Banerjee, D.
2016-08-01
Digital image correlation (DIC) data are being extensively used for many forming applications and for comparisons with finite element analysis (FEA) simulated results. The most challenging comparisons are often in the area of strain localizations just prior to material failure. While qualitative comparisons can be misleading, quantitative comparisons are difficult because of insufficient information about the type of strain output. In this work, strains computed from DIC displacements from a forming limit test are compared to those from three commercial FEA software. Quantitative differences in calculated strains are assessed to determine if the scale of variations seen between FEA and DIC calculated strains constitute real behavior or just calculation differences.
Karimi, Alireza; Navidbakhsh, Mahdi; Alizadeh, Mansour; Razaghi, Reza
2014-10-01
There have been different stress-strain definitions to measure the elastic modulus of spongy materials, especially polyvinyl alcohol (PVA) sponge. However, there is no agreement as to which stress-strain definition should be implemented. This study was aimed to show how different results are given by the various definitions of stress-strain used, and to recommend a specific definition when testing spongy materials. A fabricated PVA sponge was subjected to a series of tensile tests in order to measure its mechanical properties. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were used to determine the elastic modulus. The results revealed that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and, as a result, may overestimate the elastic modulus at different stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress). The Green-St. Venant strain definition failed to address the non-linear stress-strain relation using different definitions of stress and invoked an underestimation of the elastic modulus values. Engineering stress and strain definitions were only valid for small strains and displacements, which make them impractical when analyzing spongy materials. The results showed that the effect of varying the stress definition on the maximum stress measurements was significant but not when calculating the elastic modulus. It is important to consider which stress-strain definition is employed when characterizing the mechanical properties of spongy materials. Although the true stress-true strain definition exhibits a non-linear relation, we favor it in spongy materials mechanics as it gives more accurate measurements of the material's response using the instantaneous values.
Finite element stress analysis of polymers at high strains
NASA Technical Reports Server (NTRS)
Durand, M.; Jankovich, E.
1973-01-01
A numerical analysis is presented for the problem of a flat rectangular rubber membrane with a circular rigid inclusion undergoing high strains due to the action of an axial load. The neo-hookean constitutive equations are introduced into the general purpose TITUS program by means of equivalent hookean constants and initial strains. The convergence is achieved after a few iterations. The method is not limited to any specific program. The results are in good agreement with those of a company sponsored photoelastic stress analysis. The theoretical and experimental deformed shapes also agree very closely with one another. For high strains it is demonstrated that using the conventional HOOKE law the stress concentration factor obtained is unreliable in the case of rubberlike material.
Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin
2015-04-14
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.
Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin
2015-08-15
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.
Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin
2015-04-14
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less
In vivo bone strain and finite element modeling of the mandible of Alligator mississippiensis
Porro, Laura B; Metzger, Keith A; Iriarte-Diaz, Jose; Ross, Callum F
2013-01-01
Forces experienced during feeding are thought to strongly influence the morphology of the vertebrate mandible; in vivo strain data are the most direct evidence for deformation of the mandible induced by these loading regimes. Although many studies have documented bone strains in the mammalian mandible, no information is available on strain magnitudes, orientations or patterns in the sauropsid lower jaw during feeding. Furthermore, strain gage experiments record the mechanical response of bone at a few locations, not across the entire mandible. In this paper, we present bone strain data recorded at various sites on the lower jaw of Alligator mississippiensis during in vivo feeding experiments. These data are used to understand how changes in loading regime associated with changes in bite location are related to changes in strain regime on the working and balancing sides of the mandible. Our results suggest that the working side mandible is bent dorsoventrally and twisted about its long-axis during biting, and the balancing side experiences primarily dorsoventral bending. Strain orientations are more variable on the working side than on the balancing side with changes in bite point and between experiments; the balancing side exhibits higher strain magnitudes. In the second part of this paper, we use principal strain orientations and magnitudes recorded in vivo to evaluate a finite element model of the alligator mandible. Our comparison demonstrates that strain orientations and mandibular deformation predicted by the model closely match in vivo results; however, absolute strain magnitudes are lower in the finite element model. PMID:23855772
Cardinale, G.F.; Medlin, D.L.; Mirkarimi, P.B.; McCarty, K.F.; Howitt, D.G.
1997-01-01
Using anisotropic elasticity theory, we analyze the relative thermodynamic stabilities of strained graphitic (hexagonal) BN and cubic BN (cBN) single-crystal structures for all orientations of biaxial stress and strain fields relative to the crystallographic directions. In hBN, the most thermodynamically stable orientation has the graphitic basal planes oriented roughly 45{degree} relative to either the plane of stress or strain. For cBN, the lowest-energy configuration differs for the constant stress or constant strain assumptions. Importantly, these most-stable orientations of hBN and cBN differ from those found experimentally for graphitic BN and cBN in polycrystalline BN films produced by energetic deposition processes. Therefore, the observed textures are not those that minimize elastic strain energy. We discuss possible origins other than elastic strain{endash}energy effects for the observed textures. {copyright} {ital 1997 American Vacuum Society.}
Development of Ti-Nb-Zr alloys with high elastic admissible strain for temporary orthopedic devices.
Ozan, Sertan; Lin, Jixing; Li, Yuncang; Ipek, Rasim; Wen, Cuie
2015-07-01
A new series of beta Ti-Nb-Zr (TNZ) alloys with considerable plastic deformation ability during compression test, high elastic admissible strain, and excellent cytocompatibility have been developed for removable bone tissue implant applications. TNZ alloys with nominal compositions of Ti-34Nb-25Zr, Ti-30Nb-32Zr, Ti-28Nb-35.4Zr and Ti-24.8Nb-40.7Zr (wt.% hereafter) were fabricated using the cold-crucible levitation technique, and the effects of alloying element content on their microstructures, mechanical properties (tensile strength, yield strength, compressive yield strength, Young's modulus, elastic energy, toughness, and micro-hardness), and cytocompatibilities were investigated and compared. Microstructural examinations revealed that the TNZ alloys consisted of β phase. The alloy samples displayed excellent ductility with no cracking, or fracturing during compression tests. Their tensile strength, Young's modulus, elongation at rupture, and elastic admissible strain were measured in the ranges of 704-839 MPa, 62-65 GPa, 9.9-14.8% and 1.08-1.31%, respectively. The tensile strength, Young's modulus and elongation at rupture of the Ti-34Nb-25Zr alloy were measured as 839 ± 31.8 MPa, 62 ± 3.6 GPa, and 14.8 ± 1.6%, respectively; this alloy exhibited the elastic admissible strain of approximately 1.31%. Cytocompatibility tests indicated that the cell viability ratios (CVR) of the alloys are greater than those of the control group; thus the TNZ alloys possess excellent cytocompatibility. PMID:25818950
Applications of meshless methods for damage computations with finite strains
NASA Astrophysics Data System (ADS)
Pan, Xiaofei; Yuan, Huang
2009-06-01
Material defects such as cavities have great effects on the damage process in ductile materials. Computations based on finite element methods (FEMs) often suffer from instability due to material failure as well as large distortions. To improve computational efficiency and robustness the element-free Galerkin (EFG) method is applied in the micro-mechanical constitute damage model proposed by Gurson and modified by Tvergaard and Needleman (the GTN damage model). The EFG algorithm is implemented in the general purpose finite element code ABAQUS via the user interface UEL. With the help of the EFG method, damage processes in uniaxial tension specimens and notched specimens are analyzed and verified with experimental data. Computational results reveal that the damage which takes place in the interior of specimens will extend to the exterior and cause fracture of specimens; the damage is a fast procedure relative to the whole tensing process. The EFG method provides more stable and robust numerical solution in comparing with the FEM analysis.
Wang, Huamiao; Clausen, Bjorn; Capolungo, Laurent; Beyerlein, Irene Jane; Wang, Jian; Tome, Carlos N.
2015-07-16
Continuous mechanical tests with strain holds (stress relaxation) and with stress holds (strain relaxation) are performed simultaneously with in-situ neutron measurements to analyze the mechanisms of stress and strain relaxation in Mg AZ31 rolled plate. A dislocation activity based constitutive model, accounting for internal stress statistical distributions, is proposed and implemented into an elastic viscoplastic self-consistent (EVPSC) framework to simultaneously describe both stress and strain relaxation. The model captures the experimental data in terms of macroscopic stress strain curves, evolution of stress and strain during holding, as well as evolution of the internal elastic strains. Model results indicate that themore » magnitude of the stress relaxed during strain holding is dependent on both, the magnitude of the flow stress and the spread of the resolved shear stress distribution. The magnitude of strain accumulated during stress holding is, on the other hand, dependent on the magnitude of the hardening rate and on the spread of the resolved shear stress distribution. Furthermore, the internal elastic strains are directly correlated with the stress state, and hence the stress relaxation during strain holds has a greater influence on the lattice strains than strain relaxation during stress holds.« less
Giant elastic tunability in strained BiFeO3 near an electrically induced phase transition
Yu, Pu; Vasudevan, Rama K.; Tselev, Alexander; Xue, Fei; Chen, Long -Qing; Maksymovych, Petro; Kalinin, Sergei V.; Balke, Nina; Li, Q.; Cao, Y.; et al
2015-01-01
Elastic anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation elastic/piezoresponse spectroscopy, we probed sub-MHz elastic dynamics of a tip bias-induced rhombohedral–tetragonal phase transition of strained (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ~103 nm3 sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with 2-3 folds enhancement of local piezoresponse. Coupled with phase-field modeling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (e.g., domain walls) on the kinetics ofmore » this phase transition, thereby providing fresh insights into the morphotropic phase boundary (MPB) in ferroelectrics. Moreover, the giant electrically tunable elastic stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on utilization of the soft modes underlying successive ferroelectric phase transitions.« less
Frequency, pressure and strain dependence of nonlinear elasticity in Berea Sandstone
Riviere, Jacques; Johnson, Paul Allan; Marone, Chris; Pimienta, Lucas; Scuderi, Marco; Candela, Thibault; Shokouhi, Parisa; Schubnel, Alexandre; Fortin, Jerome
2016-04-14
Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static ( f → 0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1fmore » appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. Furthermore, these findings can be used to improve theories relating the macroscopic elastic response to microstructural features.« less
Giant elastic tunability in strained BiFeO3 near an electrically induced phase transition
NASA Astrophysics Data System (ADS)
Li, Q.; Cao, Y.; Yu, P.; Vasudevan, R. K.; Laanait, N.; Tselev, A.; Xue, F.; Chen, L. Q.; Maksymovych, P.; Kalinin, S. V.; Balke, N.
2015-11-01
Elastic anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation elastic/piezoresponse spectroscopy, we probed sub-MHz elastic dynamics of a tip bias-induced rhombohedral-tetragonal phase transition of strained (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ~103 nm3 sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with two- to three-fold enhancement of local piezoresponse. Coupled with phase-field modelling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (for example, domain walls) on the kinetics of this phase transition, thereby providing fresh insights into the morphotropic phase boundary in ferroelectrics. Furthermore, the giant electrically tunable elastic stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on the utilization of the soft modes underlying successive ferroelectric phase transitions.
Giant elastic tunability in strained BiFeO3 near an electrically induced phase transition
Li, Q; Cao, Y.; Yu, P.; Vasudevan, R. K.; Laanait, N.; Tselev, A.; Xue, F.; Chen, L. Q.; Maksymovych, P.; Kalinin, S. V.; Balke, N.
2015-01-01
Elastic anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation elastic/piezoresponse spectroscopy, we probed sub-MHz elastic dynamics of a tip bias-induced rhombohedral−tetragonal phase transition of strained (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ∼103 nm3 sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with two- to three-fold enhancement of local piezoresponse. Coupled with phase-field modelling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (for example, domain walls) on the kinetics of this phase transition, thereby providing fresh insights into the morphotropic phase boundary in ferroelectrics. Furthermore, the giant electrically tunable elastic stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on the utilization of the soft modes underlying successive ferroelectric phase transitions. PMID:26597483
Coupling between elastic strain and interstitial fluid flow: ramifications for poroelastic imaging.
Leiderman, Ricardo; Barbone, Paul E; Oberai, Assad A; Bamber, Jeffrey C
2006-12-21
We study the effects of interstitial fluid flow and interstitial fluid drainage on the spatio-temporal response of soft tissue strain. The motivation stems from the ability to measure in vivo strain distributions in soft tissue via elastography, and the desire to explore the possibility of using such techniques to investigate soft tissue fluid flow. Our study is based upon a mathematical model for soft tissue mechanics from the literature. It is a simple generalization of biphasic theory that includes coupling between the fluid and solid phases of the soft tissue, and crucially, fluid exchange between the interstitium and the local microvasculature. We solve the mathematical equations in two dimensions by the finite element method (FEM). The finite element implementation is validated against an exact analytical solution that is derived in the appendix. Realistic input tissue properties from the literature are used in conjunction with FEM modelling to conduct several computational experiments. The results of these lead to the following conclusions: (i) different hypothetical flow mechanisms lead to different patterns of strain relaxation with time; (ii) representative tissue properties show fluid drainage into the local microvasculature to be the dominant flow-related stress/strain relaxation mechanism; (iii) the relaxation time of strain in solid tumours due to drainage into the microvasculature is on the order of 5-10 s; (iv) under realistic applied pressure magnitudes, the magnitude of the strain relaxation can be as high as approximately 0.4% strain (4000 microstrains), which is well within the range of strains measurable by elastography.
Kurutz, M; Oroszváry, L
2010-02-10
3D finite element models of human lumbar functional spinal units (FSU) were used for numerical analysis of weightbath hydrotraction therapy (WHT) applied for treating degenerative diseases of the lumbar spine. Five grades of age-related degeneration were modeled by material properties. Tensile material parameters of discs were obtained by parameter identification based on in vivo measured elongations of lumbar segments during regular WHT, compressive material constants were obtained from the literature. It has been proved numerically that young adults of 40-45 years have the most deformable and vulnerable discs, while the stability of segments increases with further aging. The reasons were found by analyzing the separated contrasting effects of decreasing incompressibility and increasing hardening of nucleus, yielding non-monotonous functions of stresses and deformations in terms of aging and degeneration. WHT consists of indirect and direct traction phases. Discs show a bilinear material behaviour with higher resistance in indirect and smaller in direct traction phase. Consequently, although the direct traction load is only 6% of the indirect one, direct traction deformations are 15-90% of the indirect ones, depending on the grade of degeneration. Moreover, the ratio of direct stress relaxation remains equally about 6-8% only. Consequently, direct traction controlled by extra lead weights influences mostly the deformations being responsible for the nerve release; while the stress relaxation is influenced mainly by the indirect traction load coming from the removal of the compressive body weight and muscle forces in the water. A mildly degenerated disc in WHT shows 0.15mm direct, 0.45mm indirect and 0.6mm total extension; 0.2mm direct, 0.6mm indirect and 0.8mm total posterior contraction. A severely degenerated disc exhibits 0.05mm direct, 0.05mm indirect and 0.1mm total extension; 0.05mm direct, 0.25mm indirect and 0.3mm total posterior contraction. These
Phase field modelling of strain induced crystal growth in an elastic matrix
NASA Astrophysics Data System (ADS)
Laghmach, Rabia; Candau, Nicolas; Chazeau, Laurent; Munch, Etienne; Biben, Thierry
2015-06-01
When a crystal phase grows in an amorphous matrix, such as a crystallisable elastomer, containing cross-links and/or entanglements, these "topological constraints" need to be pushed away from the crystal phase to allow further crystallization. The accumulation of these topological constraints in the vicinity of the crystal interface may store elastic energy and affect the phase transition. To evaluate the consequences of such mechanism, we introduce a phase field model based on the Flory theory of entropic elasticity. We show that the growth process is indeed sensibly affected, in particular, an exponential increase of the surface energy with the displacement of the interface is induced. This explains the formation of stable nano-crystallites as it is observed in the Strain Induced Crystallization (SIC) of natural rubber. Although simple, the model developed here is able to account for many interesting features of SIC, for instance, the crystallite shapes and their sizes which depend on the applied deformation.
NASA Technical Reports Server (NTRS)
Bizon, P. T.; Hill, R. J.; Guilliams, B. P.; Drake, S. K.; Kladden, J. L.
1979-01-01
An elastic stress analysis was performed on a wedge specimen (prismatic bar with single-wedge cross section) subjected to thermal cycles in fluidized beds. Seven different combinations consisting of three alloys (NASA TAZ-8A, 316 stainless steel, and A-286) and four thermal cycling conditions were analyzed. The analyses were performed as a joint effort of two laboratories using different models and computer programs (NASTRAN and ISO3DQ). Stress, strain, and temperature results are presented.
Menzel, Andreas M
2016-08-01
One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a macroscopic variable termed relative strains. We analyze two simplified minimal example geometries as an illustration. PMID:27627384
NASA Astrophysics Data System (ADS)
Menzel, Andreas M.
2016-08-01
One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a macroscopic variable termed relative strains. We analyze two simplified minimal example geometries as an illustration.
NASA Astrophysics Data System (ADS)
Zingerman, K. M.; Shavyrin, D. A.
2016-06-01
The approximate analytical solution of a quasi-static plane problem of the theory of viscoelasticity is obtained under finite strains. This is the problem of the stress-strain state in an infinite body with circular viscoelastic inclusion. The perturbation technique, Laplace transform, and complex Kolosov-Muskhelishvili's potentials are used for the solution. The numerical results are presented. The nonlinear effects and the effects of viscosity are estimated.
Gao, Hao; Carrick, David; Berry, Colin; Griffith, Boyce E.; Luo, Xiaoyu
2016-01-01
Detailed models of the biomechanics of the heart are important both for developing improved interventions for patients with heart disease and also for patient risk stratification and treatment planning. For instance, stress distributions in the heart affect cardiac remodelling, but such distributions are not presently accessible in patients. Biomechanical models of the heart offer detailed three-dimensional deformation, stress and strain fields that can supplement conventional clinical data. In this work, we introduce dynamic computational models of the human left ventricle (LV) that are derived from clinical imaging data obtained from a healthy subject and from a patient with a myocardial infarction (MI). Both models incorporate a detailed invariant-based orthotropic description of the passive elasticity of the ventricular myocardium along with a detailed biophysical model of active tension generation in the ventricular muscle. These constitutive models are employed within a dynamic simulation framework that accounts for the inertia of the ventricular muscle and the blood that is based on an immersed boundary (IB) method with a finite element description of the structural mechanics. The geometry of the models is based on data obtained non-invasively by cardiac magnetic resonance (CMR). CMR imaging data are also used to estimate the parameters of the passive and active constitutive models, which are determined so that the simulated end-diastolic and end-systolic volumes agree with the corresponding volumes determined from the CMR imaging studies. Using these models, we simulate LV dynamics from enddiastole to end-systole. The results of our simulations are shown to be in good agreement with subject-specific CMR-derived strain measurements and also with earlier clinical studies on human LV strain distributions. PMID:27041786
2013-01-01
Background The resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property. These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of elastic-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior. Results The purpose of the present study is to simulate a two dimensional model of a proximal femur by taking into consideration elastic-damage and mechanical stimulus. Here, we present a mathematical model based on a system of nonlinear ordinary differential equations and we develop the variational formulation for the mechanical problem. Then, we implement our mathematical model into the finite element method algorithm to investigate the effect of the damage. Conclusion The results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading. PMID:23663260
Latifi, Neda; Miri, Amir K; Mongeau, Luc
2014-11-01
The aim of the present study was to quantify the effects of the specimen shape on the accuracy of mechanical properties determined from a shape-specific model generation strategy. Digital images of five rabbit vocal folds (VFs) in their initial undeformed conditions were used to build corresponding specific solid models. The displacement field of the VFs under uniaxial tensile test was then measured over the visible portion of the surface using digital image correlation. A three-dimensional finite element model was built, using ABAQUS, for each solid model, while imposing measured boundary conditions. An inverse-problem method was used, assuming a homogeneous isotropic linear elastic constitutive model. Unknown elastic properties were identified iteratively through an error minimization technique between simulated and measured force-time data. The longitudinal elastic moduli of the five rabbit VFs were calculated and compared to values from a simple analytical method and those obtained by approximating the cross-section as elliptical. The use of shape-specific models significantly reduced the standard deviation of the Young׳s moduli of the tested specimens. However, a non-parametric statistical analysis test, i.e., the Friedman test, yielded no statistically significant differences between the shape-specific method and the elliptic cylindrical finite element model. Considering the required procedures to reconstruct the shape-specific finite element model for each tissue specimen, it might be expedient to use the simpler method when large numbers of tissue specimens are to be compared regarding their Young׳s moduli. PMID:25173237
Extremely Elastic Wearable Carbon Nanotube Fiber Strain Sensor for Monitoring of Human Motion.
Ryu, Seongwoo; Lee, Phillip; Chou, Jeffrey B; Xu, Ruize; Zhao, Rong; Hart, Anastasios John; Kim, Sang-Gook
2015-06-23
The increasing demand for wearable electronic devices has made the development of highly elastic strain sensors that can monitor various physical parameters an essential factor for realizing next generation electronics. Here, we report an ultrahigh stretchable and wearable device fabricated from dry-spun carbon nanotube (CNT) fibers. Stretching the highly oriented CNT fibers grown on a flexible substrate (Ecoflex) induces a constant decrease in the conductive pathways and contact areas between nanotubes depending on the stretching distance; this enables CNT fibers to behave as highly sensitive strain sensors. Owing to its unique structure and mechanism, this device can be stretched by over 900% while retaining high sensitivity, responsiveness, and durability. Furthermore, the device with biaxially oriented CNT fiber arrays shows independent cross-sensitivity, which facilitates simultaneous measurement of strains along multiple axes. We demonstrated potential applications of the proposed device, such as strain gauge, single and multiaxial detecting motion sensors. These devices can be incorporated into various motion detecting systems where their applications are limited to their strain. PMID:26038807
Extremely Elastic Wearable Carbon Nanotube Fiber Strain Sensor for Monitoring of Human Motion.
Ryu, Seongwoo; Lee, Phillip; Chou, Jeffrey B; Xu, Ruize; Zhao, Rong; Hart, Anastasios John; Kim, Sang-Gook
2015-06-23
The increasing demand for wearable electronic devices has made the development of highly elastic strain sensors that can monitor various physical parameters an essential factor for realizing next generation electronics. Here, we report an ultrahigh stretchable and wearable device fabricated from dry-spun carbon nanotube (CNT) fibers. Stretching the highly oriented CNT fibers grown on a flexible substrate (Ecoflex) induces a constant decrease in the conductive pathways and contact areas between nanotubes depending on the stretching distance; this enables CNT fibers to behave as highly sensitive strain sensors. Owing to its unique structure and mechanism, this device can be stretched by over 900% while retaining high sensitivity, responsiveness, and durability. Furthermore, the device with biaxially oriented CNT fiber arrays shows independent cross-sensitivity, which facilitates simultaneous measurement of strains along multiple axes. We demonstrated potential applications of the proposed device, such as strain gauge, single and multiaxial detecting motion sensors. These devices can be incorporated into various motion detecting systems where their applications are limited to their strain.
Implementation of a strain energy-based nonlinear finite element in the object-oriented environment
NASA Astrophysics Data System (ADS)
Wegner, Tadeusz; Pęczak, Andrzej
2010-03-01
The objective of the paper is to describe a novel finite element computational method based on a strain energy density function and to implement it in the object-oriented environment. The original energy-based finite element was put into the known standard framework of classes and handled in a different manner. The nonlinear properties of material are defined with a modified strain energy density function. The local relaxation procedure proposed as a method used to resolve a nonlinear problem is implemented in C++ language. The hexahedral element with eight nodes as well as the adaptation of the nonlinear finite element is introduced. The chosen numerical model is made of nearly incompressible hyperelastic material. The application of the proposed element is shown on the example of a rectangular parallelepiped with a hollow port.
Argani, L. P.; Bigoni, D.; Capuani, D.; Movchan, N. V.
2014-01-01
The infinite-body three-dimensional Green's function set (for incremental displacement and mean stress) is derived for the incremental deformation of a uniformly strained incompressible, nonlinear elastic body. Particular cases of the developed formulation are the Mooney–Rivlin elasticity and the J2-deformation theory of plasticity. These Green's functions are used to develop a boundary integral equation framework, by introducing an ad hoc potential, which paves the way for a boundary element formulation of three-dimensional problems of incremental elasticity. Results are used to investigate the behaviour of a material deformed near the limit of ellipticity and to reveal patterns of shear failure. In fact, within the investigated three-dimensional framework, localized deformations emanating from a perturbation are shown to be organized in conical geometries rather than in planar bands, so that failure is predicted to develop through curved and thin surfaces of intense shearing, as can for instance be observed in the cup–cone rupture of ductile metal bars. PMID:25197258
NASA Astrophysics Data System (ADS)
Kim, Jeong Soo; Kyum Kim, Moon
2012-08-01
In this study, finite element analysis of beam on elastic foundation, which received great attention of researchers due to its wide applications in engineering, is performed for estimating dynamic responses of shallow foundation using exact stiffness matrix. First, element stiffness matrix based on the closed solution of beam on elastic foundation is derived. Then, we performed static finite element analysis included exact stiffness matrix numerically, comparing results from the analysis with some exact analysis solutions well known for verification. Finally, dynamic finite element analysis is performed for a shallow foundation structure under rectangular pulse loading using trapezoidal method. The dynamic analysis results exist in the reasonable range comparing solution of single degree of freedom problem under a similar condition. The results show that finite element analysis using exact stiffness matrix is evaluated as a good tool of estimating the dynamic response of structures on elastic foundation.
Multi phase field model for solid state transformation with elastic strain
NASA Astrophysics Data System (ADS)
Steinbach, I.; Apel, M.
2006-05-01
A multi phase field model is presented for the investigation of the effect of transformation strain on the transformation kinetics, morphology and thermodynamic stability in multi phase materials. The model conserves homogeneity of stress in the diffuse interface between elastically inhomogeneous phases, in which respect it differs from previous models. The model is formulated consistently with the multi phase field model for diffusional and surface driven phase transitions [I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler, G.J. Schmitz, J.L.L. Rezende, A phase field concept for multiphase systems, Physica D 94 (1996) 135-147; J. Tiaden, B. Nestler, H.J. Diepers, I. Steinbach, The multiphase-field model with an integrated concept for modeling solute diffusion, Physica D 115 (1998) 73-86; I. Steinbach, F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D 134 (1999) 385] and gives a consistent description of interfacial tension, multi phase thermodynamics and elastic stress balance in multiple junctions between an arbitrary number of grains and phases. Some aspects of the model are demonstrated with respect to numerical accuracy and the relation between transformation strain, external stress and thermodynamic equilibrium.
Harrison, Simon M; Whitton, R Chris; Kawcak, Chris E; Stover, Susan M; Pandy, Marcus G
2010-12-01
Storage and utilization of strain energy in the elastic tissues of the distal forelimb of the horse is thought to contribute to the excellent locomotory efficiency of the animal. However, the structures that facilitate elastic energy storage may also be exposed to dangerously high forces, especially at the fastest galloping speeds. In the present study, experimental gait data were combined with a musculoskeletal model of the distal forelimb of the horse to determine muscle and joint contact loading and muscle-tendon work during the stance phase of walking, trotting and galloping. The flexor tendons spanning the metacarpophalangeal (MCP) joint - specifically, the superficial digital flexor (SDF), interosseus muscle (IM) and deep digital flexor (DDF) - experienced the highest forces. Peak forces normalized to body mass for the SDF were 7.3±2.1, 14.0±2.5 and 16.7±1.1 N kg(-1) in walking, trotting and galloping, respectively. The contact forces transmitted by the MCP joint were higher than those acting at any other joint in the distal forelimb, reaching 20.6±2.8, 40.6±5.6 and 45.9±0.9 N kg(-1) in walking, trotting and galloping, respectively. The tendons of the distal forelimb (primarily SDF and IM) contributed between 69 and 90% of the total work done by the muscles and tendons, depending on the type of gait. The tendons and joints that facilitate storage of elastic strain energy in the distal forelimb also experienced the highest loads, which may explain the high frequency of injuries observed at these sites.
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.
1999-01-01
This report documents a collection of papers on a family of uniform strain tetrahedral finite elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral Finite Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform strain and enhanced uniform strain formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.
Simple formulas for strain-energy release rates with higher order and singular finite elements
NASA Technical Reports Server (NTRS)
Raju, I. S.
1986-01-01
A general finite element procedure for obtaining strain-energy release rates for crack growth in isotropic materials is presented. The procedure is applicable to two-dimensional finite element analyses and uses the virtual crack-closure method. The procedure was applied to non-singular 4-noded (linear), 8-noded (parabolic), and 12-noded (cubic) elements and to quarter-point and cubic singularity elements. Simple formulas for strain-energy release rates were obtained with this procedure for both non-singular and singularity elements. The formulas were evaluated by applying them to two mode I and two mixed mode problems. Comparisons with results from the literature for these problems showed that the formulas give accurate strain-energy release rates.
Calculation of strain-energy release rates with higher order and singular finite elements
NASA Technical Reports Server (NTRS)
Raju, I. S.
1987-01-01
A general finite element procedure for obtaining strain-energy release rates for crack growth in isotropic materials is presented. The procedure is applicable to two-dimensional finite element analyses and uses the virtual crack-closure method. The procedure was applied to nonsingular 4-noded (linear), 8-noded (parabolic), and 12-noded (cubic) elements and to quarter-point and cubic singularity elements. Simple formulas for strain-energy release rates were obtained with this procedure for both nonsingular and singularity elements. The formulas were evaluated by applying them to two mode I and two mixed mode problems. Comparisons with results from the literature for these problems showed that the formulas give accurate strain-energy release rates.
THz elastic dynamics in finite-size CoFeB-MgO phononic superlattices
NASA Astrophysics Data System (ADS)
Ulrichs, Henning; Meyer, Dennis; Müller, Markus; Wittrock, Steffen; Mansurova, Maria; Walowski, Jakob; Münzenberg, Markus
2016-10-01
In this article, we present the observation of coherent elastic dynamics in a nano-scale phononic superlattice, which consists of only 4 bilayers. We demonstrate how ultra-short light pulses with a length of 40 fs can be utilized to excite a coherent elastic wave at 0.535 THz, which persist over about 20 ps. In later steps of the elastic dynamics, modes with frequency of 1.7 THz and above appear. All these modes are related to acoustic band gaps. Thus, the periodicity strongly manifests in the wave physics, although the system under investigation has only a small number of spatial periods. To further illustrate this, we show how by breaking the translational invariance of the superlattice, these features can be suppressed. Discussed in terms of phonon blocking and radiation, we elucidate in how far our structures can be considered as useful building blocks for phononic devices.
On the Relationship between Stress and Elastic Strain for Porous and Fractured Rock
Liu, Hui-Hai; Rutqvist, Jonny; Berryman, James G.
2008-02-25
Modeling the mechanical deformations of porous and fractured rocks requires a stress-strain relationship. Experience with inherently heterogeneous earth materials suggests that different varieties of Hook's law should be applied within regions of the rock having significantly different stress-strain behavior, e.g., such as solid phase and various void geometries. We apply this idea by dividing a rock body conceptually into two distinct parts. The natural strain (volume change divided by rock volume at the current stress state), rather than the engineering strain (volume change divided by the unstressed rock volume), should be used in Hooke's law for accurate modeling of the elastic deformation of that part of the pore volume subject to a relatively large degree of relative deformation (i.e., cracks or fractures). This approach permits the derivation of constitutive relations between stress and a variety of mechanical and/or hydraulic rock properties. We show that the theoretical predictions of this method are generally consistent with empirical expressions (from field data) and also laboratory rock experimental data.
Skin-like pressure and strain sensors based on transparent elastic films of carbon nanotubes
NASA Astrophysics Data System (ADS)
Lipomi, Darren J.; Vosgueritchian, Michael; Tee, Benjamin C.-K.; Hellstrom, Sondra L.; Lee, Jennifer A.; Fox, Courtney H.; Bao, Zhenan
2011-12-01
Transparent, elastic conductors are essential components of electronic and optoelectronic devices that facilitate human interaction and biofeedback, such as interactive electronics, implantable medical devices and robotic systems with human-like sensing capabilities. The availability of conducting thin films with these properties could lead to the development of skin-like sensors that stretch reversibly, sense pressure (not just touch), bend into hairpin turns, integrate with collapsible, stretchable and mechanically robust displays and solar cells, and also wrap around non-planar and biological surfaces such as skin and organs, without wrinkling. We report transparent, conducting spray-deposited films of single-walled carbon nanotubes that can be rendered stretchable by applying strain along each axis, and then releasing this strain. This process produces spring-like structures in the nanotubes that accommodate strains of up to 150% and demonstrate conductivities as high as 2,200 S cm-1 in the stretched state. We also use the nanotube films as electrodes in arrays of transparent, stretchable capacitors, which behave as pressure and strain sensors.
Lai, Adrian; Schache, Anthony G; Lin, Yi-Chung; Pandy, Marcus G
2014-09-01
The human ankle plantar-flexors, the soleus and gastrocnemius, utilize tendon elastic strain energy to reduce muscle fiber work and optimize contractile conditions during running. However, studies to date have considered only slow to moderate running speeds up to 5 m s(-1). Little is known about how the human ankle plantar-flexors utilize tendon elastic strain energy as running speed is advanced towards maximum sprinting. We used data obtained from gait experiments in conjunction with musculoskeletal modeling and optimization techniques to calculate muscle-tendon unit (MTU) work, tendon elastic strain energy and muscle fiber work for the ankle plantar-flexors as participants ran at five discrete steady-state speeds ranging from jogging (~2 m s(-1)) to sprinting (≥8 m s(-1)). As running speed progressed from jogging to sprinting, the contribution of tendon elastic strain energy to the positive work generated by the MTU increased from 53% to 74% for the soleus and from 62% to 75% for the gastrocnemius. This increase was facilitated by greater muscle activation and the relatively isometric behavior of the soleus and gastrocnemius muscle fibers. Both of these characteristics enhanced tendon stretch and recoil, which contributed to the bulk of the change in MTU length. Our results suggest that as steady-state running speed is advanced towards maximum sprinting, the human ankle plantar-flexors continue to prioritize the storage and recovery of tendon elastic strain energy over muscle fiber work.
NASA Astrophysics Data System (ADS)
Petersson, N. Anders; Sjögreen, Björn
2015-10-01
We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The proposed method discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. We also generalize and evaluate the super-grid far-field technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. As a result, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.
Petersson, N. Anders; Sjogreen, Bjorn
2015-07-20
We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less
Petersson, N. Anders; Sjogreen, Bjorn
2015-07-20
We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-field technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.
Xian, Cory J.
2015-01-01
Osteocytes, the major type of bone cells which reside in their lacunar and canalicular system within the bone matrix, function as biomechanosensors and biomechanotransducers of the bone. Although biomechanical behaviour of the osteocyte-lacunar-canalicular system has been investigated in previous studies mostly using computational 2-dimensional (2D) geometric models, only a few studies have used the 3-dimensional (3D) finite element (FE) model. In the current study, a 3D FE model was used to predict the responses of strain distributions of osteocyte-lacunar-canalicular system analyzed under static and cyclic loads. The strain amplification factor was calculated for all simulations. Effects on the strain of the osteocyte system were investigated under 500, 1500, 2000, and 3000 microstrain loading magnitudes and 1, 5, 10, 40, and 100 Hz loading frequencies. The maximum strain was found to change with loading magnitude and frequency. It was observed that maximum strain under 3000-microstrain loading was higher than those under 500, 1500, and 2000 microstrains. When the loading strain reached the maximum magnitude, the strain amplification factor of 100 Hz was higher than those of the other frequencies. Data from this 3D FE model study suggests that the strain amplification factor of the osteocyte-lacunar-canalicular system increases with loading frequency and loading strain increasing. PMID:25664319
Wrinkling of a stiff thin film bonded to a pre-strained, compliant substrate with finite thickness
NASA Astrophysics Data System (ADS)
Ma, Yinji; Xue, Yeguang; Jang, Kyung-In; Feng, Xue; Rogers, John A.; Huang, Yonggang
2016-08-01
A stiff thin film bonded to a pre-strained, compliant substrate wrinkles into a sinusoidal form upon release of the pre-strain. Many analytical models developed for the critical pre-strain for wrinkling assume that the substrate is semi-infinite. This critical pre-strain is actually much smaller than that for a substrate with finite thickness (Ma Y et al. 2016 Adv. Funct. Mater. (doi:10.1002/adfm.201600713)). An analytical solution of the critical pre-strain for a system of a stiff film bonded to a pre-strained, finite-thickness, compliant substrate is obtained, and it agrees well with the finite-element analysis. The finite-thickness effect is significant when the substrate tensile stiffness cannot overwhelm the film tensile stiffness.
The Elastic Behaviour of Sintered Metallic Fibre Networks: A Finite Element Study by Beam Theory
Bosbach, Wolfram A.
2015-01-01
Background The finite element method has complimented research in the field of network mechanics in the past years in numerous studies about various materials. Numerical predictions and the planning efficiency of experimental procedures are two of the motivational aspects for these numerical studies. The widespread availability of high performance computing facilities has been the enabler for the simulation of sufficiently large systems. Objectives and Motivation In the present study, finite element models were built for sintered, metallic fibre networks and validated by previously published experimental stiffness measurements. The validated models were the basis for predictions about so far unknown properties. Materials and Methods The finite element models were built by transferring previously published skeletons of fibre networks into finite element models. Beam theory was applied as simplification method. Results and Conclusions The obtained material stiffness isn’t a constant but rather a function of variables such as sample size and boundary conditions. Beam theory offers an efficient finite element method for the simulated fibre networks. The experimental results can be approximated by the simulated systems. Two worthwhile aspects for future work will be the influence of size and shape and the mechanical interaction with matrix materials. PMID:26569603
Evaluation Of Elastic Strain Accumulation In The Southern Indian Peninsula By GPS-Geodesy
NASA Astrophysics Data System (ADS)
Narayanababu, R.; Ec, M.; Tummala, C.
2004-12-01
The computed elastic strain accumulation in the southern Indian peninsula from the GPS derived velocity fields of the global network of GPS stations, in and around the Indian plate which includes Maitri, Indian Antarctic Station, show a significant departure from rigid plate behaviour in a manner consistent with the mapped intra plate stress field, observations of deformations and seismicity in the region. Our results of intraplate strain accumulation within Antarctica Plate covering three sites MAIT, CAS1 and DAV1 are 1.8x10-9yr-1, 1.6x10-9yr-1 and 1.1x10-9yr-1, respectively. Similarly, the estimates of interplate strain accumulation between Antarctica and other plates Somalia (SEY1), Africa (HARO), Australia (YAR1), and diffuse plate boundary between India and Australia (COCO) are found to be 1.1x10-9yr-1, 1.0x10-10yr-1, 1.27x10-8yr-1 and 1.18x10-8yr-1, respectively. These estimates are in good agreement with the earlier studies on estimation of global strain rate. The combined GPS and seismic analysis confirm the emergence of diffuse plate boundary between India and Australia and relates to the late Miocene Himalayan uplift. The calculated stress field in the West of the Indian Peninsula has a roughly N-S directed tensional and E-W oriented compressional character and the velocity vectors of all other sites throw a significant insight into the plausible causes of the strain accumulation processes in the Indian Ocean and the northward movement of Indian plate.
Stored energy in metallic glasses due to strains within the elastic limit
NASA Astrophysics Data System (ADS)
Greer, A. L.; Sun, Y. H.
2016-06-01
Room temperature loading of metallic glasses, at stresses below the macroscopic yield stress, raises their enthalpy and causes creep. Thermal cycling of metallic glasses between room temperature and 77 K also raises their enthalpy. In both cases, the enthalpy increases are comparable to those induced by heavy plastic deformation, but, as we show, the origins must be quite different. For plastic deformation, the enthalpy increase is a fraction (<10%) of the work done (WD) (and, in this sense, the behaviour is similar to that of conventional polycrystalline metals and alloys). In contrast, the room temperature creep and the thermal cycling involve small strains well within the elastic limit; in these cases, the enthalpy increase in the glass exceeds the WD, by as much as three orders of magnitude. We argue that the increased enthalpy can arise only from an endothermic disordering process drawing heat from the surroundings. We examine the mechanisms of this process. The increased enthalpy ('stored energy') is a measure of rejuvenation and appears as an exothermic heat of relaxation on heating the glass. The profile of this heat release (the 'relaxation spectrum') is analysed for several metallic glasses subjected to various treatments. Thus, the effects of the small-strain processing (creep and thermal cycling) can be better understood, and we can explore the potential for improving properties, in particular the plasticity, of metallic glasses. Metallic glasses can exhibit a wide range of enthalpy at a given temperature, and small-strain processing may assist in accessing this for practical purposes.
Mourad, Hashem M; Bronkhorst, Curt A; Addessio, Francis L
2010-12-16
An explicit finite element formulation, used to study the behavior and failure mechanisms of metallic materials under high strain rate loading, is presented. The formulation is based on the assumed-strain approach of Fish and Belytschko [1988], which allows localization bands to be embedded within an element, thereby alleviating mesh sensitivity and reducing the required computational effort. The behavior of the material outside localization bands (and of the virgin material prior to the onset of strain localization) is represented using a Gurson-type coupled plasticity-damage model based on the work of Johnson and Addessio [1988]. Assuming adiabatic conditions, the response of the localization band material is represented by a set of constitutive equations for large elasticviscoplastic deformations in metals at high strain rates and high homologous temperatures (see Brown et al. [1989]). Computational results are compared to experimental data for different metallic alloys to illustrate the advantages of the proposed modeling strategy.
Nonlinear visco-elastic finite element analysis of different porcelain veneers configuration.
Sorrentino, Roberto; Apicella, Davide; Riccio, Carlo; Gherlone, Enrico; Zarone, Fernando; Aversa, Raffaella; Garcia-Godoy, Franklin; Ferrari, Marco; Apicella, Antonio
2009-11-01
This study is aimed at evaluating the biomechanical behavior of feldspathic versus alumina porcelain veneers. A 3D numerical model of a maxillary central incisor, with the periodontal ligament (PDL) and the alveolar bone was generated. Such model was made up of four main volumes: dentin, enamel, cement layer and veneer. Incisors restored with alumina and feldspathic porcelain veneers were compared with a natural sound tooth (control). Enamel, cementum, cancellous and cortical bone were considered as isotropic elastic materials; on the contrary, the tubular structure of dentin was designed as elastic orthotropic. The nonlinear visco-elatic behavior of the PDL was considered. The veneer volumes were coupled with alumina and feldspathic porcelain mechanical properties. The adhesive layers were modeled in the FE environment using spring elements. A 50N load applied at 60 degrees angle with tooth longitudinal axis was applied and validated. Compressive stresses were concentrated on the external surface of the buccal side of the veneer close to the incisal margin; such phenomenon was more evident in the presence of alumina. Tensile stresses were negligible when compared to compressive ones. Alumina and feldspathic ceramic were characterized by a different biomechanical behavior in terms of elastic deformations and stress distributions. The ultimate strength of both materials was not overcome in the performed analysis.
Finite-Element Modeling of Viscoelastic Cells During High-Frequency Cyclic Strain
Milner, Jaques S.; Grol, Matthew W.; Beaucage, Kim L.; Dixon, S. Jeffrey; Holdsworth, David W.
2012-01-01
Mechanotransduction refers to the mechanisms by which cells sense and respond to local loads and forces. The process of mechanotransduction plays an important role both in maintaining tissue viability and in remodeling to repair damage; moreover, it may be involved in the initiation and progression of diseases such as osteoarthritis and osteoporosis. An understanding of the mechanisms by which cells respond to surrounding tissue matrices or artificial biomaterials is crucial in regenerative medicine and in influencing cellular differentiation. Recent studies have shown that some cells may be most sensitive to low-amplitude, high-frequency (i.e., 1–100 Hz) mechanical stimulation. Advances in finite-element modeling have made it possible to simulate high-frequency mechanical loading of cells. We have developed a viscoelastic finite-element model of an osteoblastic cell (including cytoskeletal actin stress fibers), attached to an elastomeric membrane undergoing cyclic isotropic radial strain with a peak value of 1,000 µstrain. The results indicate that cells experience significant stress and strain amplification when undergoing high-frequency strain, with peak values of cytoplasmic strain five times higher at 45 Hz than at 1 Hz, and peak Von Mises stress in the nucleus increased by a factor of two. Focal stress and strain amplification in cells undergoing high-frequency mechanical stimulation may play an important role in mechanotransduction. PMID:24956525
Mesoscopic strain fields in woven composites: Experiments vs. finite element modeling
NASA Astrophysics Data System (ADS)
Nicoletto, Gianni; Anzelotti, Giancarlo; Riva, Enrica
2009-03-01
Detailed determination of strain in woven composite materials is fundamental for understanding their mechanics and for validating sophisticated computational models. The digital image correlation technique is briefly presented and applied to the full-field strain determination in a twill-weave carbon-fiber-reinforced-plastic (CFRP) composite under in-plane loading. The experimental results are used to assess companion results obtained with an ad hoc finite element-based model. The DIC vs. FEM comparison is carried out at the mesoscopic scale.
Numerical models of diapiric structures - analysis of the finite strain distribution
NASA Astrophysics Data System (ADS)
Fuchs*, L.; Schmeling, H.
2012-04-01
In gravity driven tectonic structures finite strain is a key parameter to understand the evolution of the underlying dynamic processes. In the study conducted here, the strain was analyzed numerically for two different diapiric models, the model of a classical Rayleigh-Taylor instability [1], which is mainly important for magmatic diapirs, and the down-building model [2], which is especially important for salt diapirs where the rise is driven by differential sediment loading. The equations of conservation of mass, momentum, and composition are solved by a 2D finite difference code (FDCON) based on a stream function formulation in combination with a marker approach based on a predictor-corrector Runge-Kutta 4th order scheme. The finite deformation was determined using the algorithm of McKenzie [3] calculated centered in time and in space, where the information of the deformation matrix is advected with the markers in the model. Two series of different viscosity contrasts m = ηbuoyant ηtop and different thicknesses were calculated for each hbuoyant of a Rayleigh-Taylor like instability with both no slip and free slip boundary conditions at the top and bottom. In the case of the down-building models we present two model series with different viscosity regimes: one with a stiff subsiding sediment layer, with the result of high deformation within the salt and negligible deformation in the ambient sediments and another with relatively weak sediments, in which the deformation is partitioned between the salt and the sediments. In addition to the local analysis of the strains in each layer, the strain partitioning is considered on the entire volume of the two layers. Therefore the maximum shear strain [4] is integrated in each layer and forms the ratio Sr between the integrated values of the upper and lower layer. This ratio provides information on how the strain is distributed between the two layers. For the RTI models the maximum values of the finite deformation inside
NASA Technical Reports Server (NTRS)
Vazquez, Sixto L.; Tessler, Alexander; Quach, Cuong C.; Cooper, Eric G.; Parks, Jeffrey; Spangler, Jan L.
2005-01-01
In an effort to mitigate accidents due to system and component failure, NASA s Aviation Safety has partnered with industry, academia, and other governmental organizations to develop real-time, on-board monitoring capabilities and system performance models for early detection of airframe structure degradation. NASA Langley is investigating a structural health monitoring capability that uses a distributed fiber optic strain system and an inverse finite element method for measuring and modeling structural deformations. This report describes the constituent systems that enable this structural monitoring function and discusses results from laboratory tests using the fiber strain sensor system and the inverse finite element method to demonstrate structural deformation estimation on an instrumented test article
Molecular simulation guided constitutive modeling on finite strain viscoelasticity of elastomers
NASA Astrophysics Data System (ADS)
Li, Ying; Tang, Shan; Kröger, Martin; Liu, Wing Kam
2016-03-01
Viscoelasticity characterizes the most important mechanical behavior of elastomers. Understanding the viscoelasticity, especially finite strain viscoelasticity, of elastomers is the key for continuation of their dedicated use in industrial applications. In this work, we present a mechanistic and physics-based constitutive model to describe and design the finite strain viscoelastic behavior of elastomers. Mathematically, the viscoelasticity of elastomers has been decomposed into hyperelastic and viscous parts, which are attributed to the nonlinear deformation of the cross-linked polymer network and the diffusion of free chains, respectively. The hyperelastic deformation of a cross-linked polymer network is governed by the cross-linking density, the molecular weight of the polymer strands between cross-linkages, and the amount of entanglements between different chains, which we observe through large scale molecular dynamics (MD) simulations. Moreover, a recently developed non-affine network model (Davidson and Goulbourne, 2013) is confirmed in the current work to be able to capture these key physical mechanisms using MD simulation. The energy dissipation during a loading and unloading process of elastomers is governed by the diffusion of free chains, which can be understood through their reptation dynamics. The viscous stress can be formulated using the classical tube model (Doi and Edwards, 1986); however, it cannot be used to capture the energy dissipation during finite deformation. By considering the tube deformation during this process, as observed from the MD simulations, we propose a modified tube model to account for the finite deformation behavior of free chains. Combing the non-affine network model for hyperelasticity and modified tube model for viscosity, both understood by molecular simulations, we develop a mechanism-based constitutive model for finite strain viscoelasticity of elastomers. All the parameters in the proposed constitutive model have
Spectral Modeling of Residual Stress and Stored Elastic Strain Energy in Thermal Barrier Coatings
Donegan, Sean; Rolett, Anthony
2013-12-31
Solutions to the thermoelastic problem are important for characterizing the response under temperature change of refractory systems. This work extends a spectral fast Fourier transform (FFT) technique to analyze the thermoelastic behavior of thermal barrier coatings (TBCs), with the intent of probing the local origins of failure in TBCs. The thermoelastic FFT (teFFT) approach allows for the characterization of local thermal residual stress and strain fields, which constitute the origins of failure in TBC systems. A technique based on statistical extreme value theory known as peaks-over-threshold (POT) is developed to quantify the extreme values ("hot spots") of stored elastic strain energy (i.e., elastic energy density, or EED). The resolution dependence of the teFFT method is assessed through a sensitivity study of the extreme values in EED. The sensitivity study is performed both for the local (point-by-point) eld distributions as well as the grain scale eld distributions. A convergence behavior to a particular distribution shape is demonstrated for the local elds. The grain scale fields are shown to exhibit a possible convergence to a maximum level of EED. To apply the teFFT method to TBC systems, 3D synthetic microstructures are created to approximate actual TBC microstructures. The morphology of the grains in each constituent layer as well as the texture is controlled. A variety of TBC materials, including industry standard materials and potential future materials, are analyzed using the teFFT. The resulting hot spots are quantified using the POT approach. A correlation between hot spots in EED and interface rumpling between constituent layers is demonstrated, particularly for the interface between the bond coat (BC) and the thermally grown oxide (TGO) layer.
Giordano, Chiara; Kleiven, Svein
2014-11-01
Finite element (FE) models are often used to study the biomechanical effects of traumatic brain injury (TBI). Measures based on mechanical responses, such as principal strain or invariants of the strain tensor, are used as a metric to predict the risk of injury. However, the reliability of inferences drawn from these models depends on the correspondence between the mechanical measures and injury data, as well as the establishment of accurate thresholds of tissue injury. In the current study, a validated anisotropic FE model of the human head is used to evaluate the hypothesis that strain in the direction of fibers (axonal strain) is a better predictor of TBI than maximum principal strain (MPS), anisotropic equivalent strain (AESM) and cumulative strain damage measure (CSDM). An analysis of head kinematics-based metrics, such as head injury criterion (HIC) and brain injury criterion (BrIC), is also provided. Logistic regression analysis is employed to compare binary injury data (concussion/no concussion) with continuous strain/kinematics data. The threshold corresponding to 50% of injury probability is determined for each parameter. The predictive power (area under the ROC curve, AUC) is calculated from receiver operating characteristic (ROC) curve analysis. The measure with the highest AUC is considered to be the best predictor of mTBI. Logistic regression shows a statistical correlation between all the mechanical predictors and injury data for different regions of the brain. Peaks of axonal strain have the highest AUC and determine a strain threshold of 0.07 for corpus callosum and 0.15 for the brainstem, in agreement with previously experimentally derived injury thresholds for reversible axonal injury. For a data set of mild TBI from the national football league, the strain in the axonal direction is found to be a better injury predictor than MPS, AESM, CSDM, BrIC and HIC.
Giordano, Chiara; Kleiven, Svein
2014-11-01
Finite element (FE) models are often used to study the biomechanical effects of traumatic brain injury (TBI). Measures based on mechanical responses, such as principal strain or invariants of the strain tensor, are used as a metric to predict the risk of injury. However, the reliability of inferences drawn from these models depends on the correspondence between the mechanical measures and injury data, as well as the establishment of accurate thresholds of tissue injury. In the current study, a validated anisotropic FE model of the human head is used to evaluate the hypothesis that strain in the direction of fibers (axonal strain) is a better predictor of TBI than maximum principal strain (MPS), anisotropic equivalent strain (AESM) and cumulative strain damage measure (CSDM). An analysis of head kinematics-based metrics, such as head injury criterion (HIC) and brain injury criterion (BrIC), is also provided. Logistic regression analysis is employed to compare binary injury data (concussion/no concussion) with continuous strain/kinematics data. The threshold corresponding to 50% of injury probability is determined for each parameter. The predictive power (area under the ROC curve, AUC) is calculated from receiver operating characteristic (ROC) curve analysis. The measure with the highest AUC is considered to be the best predictor of mTBI. Logistic regression shows a statistical correlation between all the mechanical predictors and injury data for different regions of the brain. Peaks of axonal strain have the highest AUC and determine a strain threshold of 0.07 for corpus callosum and 0.15 for the brainstem, in agreement with previously experimentally derived injury thresholds for reversible axonal injury. For a data set of mild TBI from the national football league, the strain in the axonal direction is found to be a better injury predictor than MPS, AESM, CSDM, BrIC and HIC. PMID:26192949
Wu, Yuan; Stoica, Alexandru Dan; Ren, Yang; Ma, Dong; Gao, Yanfei F.; Bei, Hongbin
2015-09-03
In situ high-energy synchrotron X-ray diffraction was conducted on elastically and plastically bent bulk metallic glass (BMG) thin plates, from which distinct local elastic strain fields were mapped spatially. These directly measured residual strain fields can be nicely interpreted by our stress analysis, and also validate a previously proposed indirect residual-stress-measurement method by relating nanoindentation hardness to residual stresses. Local shear strain variations on the cross sections of these thin plates were found in the plastically bent BMG, which however cannot be determined from the indirect indentation method. As a result, this study has important implications in designing and manipulatingmore » internal strain fields in BMGs for the purpose of ductility enhancement.« less
Wu, Yuan; Stoica, Alexandru Dan; Ren, Yang; Ma, Dong; Gao, Yanfei F.; Bei, Hongbin
2015-09-03
In situ high-energy synchrotron X-ray diffraction was conducted on elastically and plastically bent bulk metallic glass (BMG) thin plates, from which distinct local elastic strain fields were mapped spatially. These directly measured residual strain fields can be nicely interpreted by our stress analysis, and also validate a previously proposed indirect residual-stress-measurement method by relating nanoindentation hardness to residual stresses. Local shear strain variations on the cross sections of these thin plates were found in the plastically bent BMG, which however cannot be determined from the indirect indentation method. As a result, this study has important implications in designing and manipulating internal strain fields in BMGs for the purpose of ductility enhancement.
Finite Element Modeling of Plane Strain Toughness for 7085 Aluminum Alloy
NASA Astrophysics Data System (ADS)
Karabin, M. E.; Barlat, F.; Shuey, R. T.
2009-02-01
In this work, the constitutive model for 7085-T7X (overaged) aluminum alloy plate samples with controlled microstructures was developed. Different lengths of 2nd step aging times produced samples with similar microstructure but different stress-strain curves ( i.e., different nanostructure). A conventional phenomenological strain-hardening law with no strain gradient effects was proposed to capture the peculiar hardening behavior of the material samples investigated in this work. The classical Gurson-Tvergaard potential, which includes the influence of void volume fraction (VVF) on the plastic flow behavior, as well as an extension proposed by Leblond et al.,[3] were considered. Unlike the former, the latter is able to account for the influence of strain hardening on the VVF growth. All the constitutive coefficients used in this work were based on experimental stress-strain curves obtained in uniaxial tension and on micromechanical modeling results of a void embedded in a matrix. These material models were used in finite element (FE) simulations of a compact tension (CT) specimen. An engineering criterion based on the instability of plastic flow at a crack tip was used for the determination of plane strain toughness K Ic . The influence of the microstructure was lumped into a single state variable, the initial void volume fraction. The simulation results showed that the strain-hardening behavior has a significant influence on K Ic .
NASA Astrophysics Data System (ADS)
Galipeau, Evan; Ponte Castañeda, Pedro
2013-04-01
This paper is concerned with the development of constitutive models for a class of magnetoelastic composites consisting of stiff, aligned cylindrical fibers of a magnetizable material that are embedded firmly in a soft elastomeric matrix. The fibers have elliptical cross section and their (transverse) in-plane axes are also aligned, but their distribution is random and characterized by "elliptical" two-point correlations. Estimates are obtained for the macroscopic response and stability of this new type of magnetorheological elastomer (MRE) under combined in-plane mechanical and magnetic loading by means of the finite-strain homogenization framework and "partial decoupling approximation" of Ponte Castañeda and Galipeau (2011). The resulting macroscopic magnetoelastic constitutive model accounts for the microstructure of the composite and its evolution under finite strains and rotations, as well as for the nonlinear magnetic behavior of the fibers, including the effect of magnetic saturation. When the loading directions are not aligned with the fiber axes, the model predicts magnetic and mechanical torques on the fibers, leading to their in-plane rotation, which is found to have significant effects on the coupled magnetoelastic response of the composite, including the possible development of macroscopic torques on a given finite-size sample of the composite. To eliminate these macroscopic torques, while maintaining the advantageous effects of the fiber rotations, we also investigate the response of a laminated composite consisting of plus/minus orientations of the fibers relative to the layering direction, and subjected to magnetic and mechanical loadings along the layering direction. The results for the actuation tractions, magnetostrictive strain and magnetoelastic moduli demonstrate that the microstructure of these laminated MRE samples can be designed optimally for significantly enhanced magnetoelastic effects. In particular, the actuation tractions and
NASA Astrophysics Data System (ADS)
He, Jin; Lilley, Carmen M.
2009-08-01
Surface stress was incorporated into the finite element absolute nodal coordinate formulation in order to model elastic bending of nanowires in large deformation. The absolute nodal coordinate formulation is a numerical method to model bending structures in large deformation. The generalized Young-Laplace equation was employed to model the surface stress effect on bending nanowires. Effects from surface stress and large deformation on static bending nanowires are presented and discussed. The results calculated with the absolute nodal coordinate formulation incorporated with surface stress show that the surface stress effect makes the bending nanowires behave like softer or stiffer materials depending on the boundary condition. The surface stress effect diminishes as the dimensions of the bending structures increase beyond the nanoscale. The developed algorithm is consistent with the classical absolute nodal coordinate formulation at the macroscale.
NASA Astrophysics Data System (ADS)
Zhang, Fan; Wang, Jianchuan; Liu, Shuhong; Du, Yong
2016-10-01
Sn and Sn-based compounds have been attracting a great interest as promising alternative materials for commercial anodes in lithium ion batteries. In this study, the phase evolution of the Li-Sn system during the lithiated processes and the effect of the elastic-strain energies caused by volume change on the phase transition are investigated by means of first-principles calculations. Our calculated results demonstrate that the distorted Li7Sn3 crystal tends to be formed in order to decrease the elastic-strain energy. In addition, our work indicates that the whole lithiated processes under the elastically constrained condition could be classified into two steps. The first step is the two-phase equilibrium process, in which the thermodynamic driving force is large enough to facilitate the phase transition and the plateau voltage could be established. The second step is considered to be the selective equilibrium, in which the thermodynamic driving force is not enough to facilitate the nucleation of the new equilibrium phase due to the elastically constrained conditions and the plateau voltage unformed. Besides, we find that in the Li0.4Sn matrix the nucleation of the αSn is more preferential than the βSn due to the effects of the elastic-strain energies.
Finite-difference staggered grids in GPUs for anisotropic elastic wave propagation simulation
NASA Astrophysics Data System (ADS)
Rubio, Felix; Hanzich, Mauricio; Farrés, Albert; de la Puente, Josep; María Cela, José
2014-09-01
The 3D elastic wave equations can be used to simulate the physics of waves traveling through the Earth more precisely than acoustic approximations. However, this improvement in quality has a counterpart in the cost of the numerical scheme. A possible strategy to mitigate that expense is using specialized, high-performing architectures such as GPUs. Nevertheless, porting and optimizing a code for such a platform require a deep understanding of both the underlying hardware architecture and the algorithm at hand. Furthermore, for very large problems, multiple GPUs must work concurrently, which adds yet another layer of complexity to the codes. In this work, we have tackled the problem of porting and optimizing a 3D elastic wave propagation engine which supports both standard- and fully-staggered grids to multi-GPU clusters. At the single GPU level, we have proposed and evaluated many optimization strategies and adopted the best performing ones for our final code. At the distributed memory level, a domain decomposition approach has been used which allows for good scalability thanks to using asynchronous communications and I/O.
NASA Astrophysics Data System (ADS)
Nguyen, K. L.; Treyssède, F.; Hazard, C.
2015-05-01
Among the numerous techniques of non-destructive evaluation, elastic guided waves are of particular interest to evaluate defects inside industrial and civil elongated structures owing to their ability to propagate over long distances. However for guiding structures buried in large solid media, waves can be strongly attenuated along the guide axis due to the energy radiation into the surrounding medium, usually considered as unbounded. Hence, searching the less attenuated modes becomes necessary in order to maximize the inspection distance. In the numerical modeling of embedded waveguides, the main difficulty is to account for the unbounded section. This paper presents a numerical approach combining a semi-analytical finite element method and a perfectly matched layer (PML) technique to compute the so-called trapped and leaky modes in three-dimensional embedded elastic waveguides of arbitrary cross-section. Two kinds of PML, namely the Cartesian PML and the radial PML, are considered. In order to understand the various spectral objects obtained by the method, the PML parameters effects upon the eigenvalue spectrum are highlighted through analytical studies and numerical experiments. Then, dispersion curves are computed for test cases taken from the literature in order to validate the approach.
Size dependent vibrations of micro-end mill incorporating strain gradient elasticity theory
NASA Astrophysics Data System (ADS)
Tajalli, S. A.; Movahhedy, M. R.; Akbari, J.
2013-07-01
In this paper, a size-dependent formulation is presented for vibration analysis of micro-end mill tool. The formulation is developed based on the strain gradient elasticity theory in order to enhance the modeling capability of micro-size structures. Due to stubby geometry of micro-tool, the shear deformation and rotary inertia effects are considered in the derivation of equations. Hence, based on the strain gradient Timoshenko beam theory, the extended Hamilton's principle is used to formulate a detailed dynamical model of the rotating micro-tool. The dynamical model includes a set of partial differential equations with gyroscopic coupling produced due to the spindle rotation. The governing equations of motion are reduced and solved by assumed mode model. To this end, an exact dynamic stiffness method is developed and employed to investigate the tool's free vibration characteristics such as structure mode shapes and natural frequencies. Also, the well-known Wittrick-Williams algorithm is utilized to guarantee that none of the natural frequencies are missed during the calculations. The mode shapes obtained from dynamic stiffness formulation can be utilized as base functions in the solution. Also, the proposed approach is applied to investigate the force vibration and chatter instability observed in micro-milling operations.
Carnelli, Davide; Lucchini, Riccardo; Ponzoni, Matteo; Contro, Roberto; Vena, Pasquale
2011-07-01
Anisotropy is one of the most peculiar aspects of cortical bone mechanical behaviour, and the numerical approach can be successfully used to investigate aspects of bone tissue mechanics that analytical methods solve in approximate way or do not cover. In this work, nanoindentation experimental tests and finite element simulations were employed to investigate the elastic-inelastic anisotropic mechanical properties of cortical bone. The model allows for anisotropic elastic and post-yield behaviour of the tissue. A tension-compression mismatch and direction-dependent yield stresses are allowed for. Indentation experiments along the axial and transverse directions were simulated with the purpose to predict the indentation moduli and hardnesses along multiple orientations. Results showed that the experimental transverse-to-axial ratio of indentation moduli, equal to 0.74, is predicted with a ∼3% discrepancy regardless the post-yield material behaviour; whereas, the transverse-to-axial hardness ratio, equal to 0.86, can be correctly simulated (discrepancy ∼6% w.r.t. the experimental results) only employing an anisotropic post-elastic constitutive model. Further, direct comparison between the experimental and simulated indentation tests evidenced a good agreement in the loading branch of the indentation curves and in the peak loads for a transverse-to-axial yield stress ratio comparable to the experimentally obtained transverse-to-axial hardness ratio. In perspective, the present work results strongly support the coupling between indentation experiments and FEM simulations to get a deeper knowledge of bone tissue mechanical behaviour at the microstructural level. The present model could be used to assess the effect of variations of constitutive parameters due to age, injury, and/or disease on bone mechanical performance in the context of indentation testing. PMID:21570077
NASA Technical Reports Server (NTRS)
Buczek, M. B.; Gregory, M. A.; Herakovich, C. T.
1983-01-01
CLFE2D is a two dimensional generalized plane strain finite element code, using a linear, four node, general quadrilateral, isoparametric element. The program is developed to calculate the displacements, strains, stresses, and strain energy densities in a finite width composite laminate. CLFE2D offers any combination of the following load types: nodal displacements, nodal forces, uniform normal strain, or hygrothermal. The program allows the user to input one set of three dimensional orthotropic material properties. The user can then specify the angle of material principal orientation for each element in the mesh. Output includes displacements, stresses, strains and strain densities at points selected by the user. An option is also available to plot the underformed and deformed finite element meshes.
Multi-scale finite element modeling of strain localization in geomaterials with strong discontinuity
NASA Astrophysics Data System (ADS)
Lai, Timothy Yu
2002-01-01
Geomaterials such as soils and rocks undergo strain localization during various loading conditions. Strain localization manifests itself in the form of a shear band, a narrow zone of intense straining. It is now generally recognized that these localized deformations lead to an accelerated softening response and influence the response of structures at or near failure. In order to accurately predict the behavior of geotechnical structures, the effects of strain localization must be included in any model developed. In this thesis, a multi-scale Finite Element (FE) model has been developed that captures the macro- and micro-field deformation patterns present during strain localization. The FE model uses a strong discontinuity approach where a jump in the displacement field is assumed. The onset of strain localization is detected using bifurcation theory that checks when the governing equations lose ellipticity. Two types of bifurcation, continuous and discontinuous are considered. Precise conditions for plane strain loading conditions are reported for each type of bifurcation. Post-localization behavior is governed by the traction relations on the band. Different plasticity models such as Mohr-Coulomb, Drucker-Prager and a Modified Mohr-Coulomb yield were implemented together with cohesion softening and cutoff for the post-localization behavior. The FE model is implemented into a FORTRAN code SPIN2D-LOC using enhanced constant strain triangular (CST) elements. The model is formulated using standard Galerkin finite element method, applicable to problems under undrained conditions and small deformation theory. A band-tracing algorithm is implemented to track the propagation of the shear band. To validate the model, several simulations are performed from simple compression test of soft rock to simulation of a full-scale geosynthetic reinforced soil wall model undergoing strain localization. Results from both standard and enhanced FE method are included for comparison. The
Barabash, R. I.; Agarwal, V.; Koric, S.; Jasiuk, I.; Tischler, J. Z.
2016-01-01
Tmore » he depth-dependent strain partitioning across the interfaces in the growth direction of the NiAl/Cr(Mo) nanocomposite between the Cr and NiAl lamellae was directly measured experimentally and simulated using a finite element method (FEM). Depth-resolved X-ray microdiffraction demonstrated that in the as-grown state both Cr and NiAl lamellae grow along the 111 direction with the formation of as-grown distinct residual ~0.16% compressive strains for Cr lamellae and ~0.05% tensile strains for NiAl lamellae.hree-dimensional simulations were carried out using an implicit FEM. First simulation was designed to study residual strains in the composite due to cooling resulting in formation of crystals. Strains in the growth direction were computed and compared to those obtained from the microdiffraction experiments. Second simulation was conducted to understand the combined strains resulting from cooling and mechanical indentation of the composite. Numerical results in the growth direction of crystal were compared to experimental results confirming the experimentally observed trends.« less
HEMP 3D -- a finite difference program for calculating elastic-plastic flow
Wilkins, M.L.
1993-05-26
The HEMP 3D program can be used to solve problems in solid mechanics involving dynamic plasticity and time dependent material behavior and problems in gas dynamics. The equations of motion, the conservation equations, and the constitutive relations are solved by finite difference methods following the format of the HEMP computer simulation program formulated in two space dimensions and time. Presented here is an update of the 1975 report on the HEMP 3D numerical technique. The present report includes the sliding surface routines programmed by Robert Gulliford.
Transitions in a compressible finite elastic sheet on a fluid substrate
NASA Astrophysics Data System (ADS)
Oshri, Oz; Diamant, Haim
2014-03-01
A thin elastic sheet, supported on a fluid substrate and uniaxially compressed, exhibits two critical transitions: From a flat state to sinusoidal wrinkles and from wrinkles to a localized fold. Previous theoretical studies treated the system in the limits of incompressible and infinite sheets. Both assumptions are relaxed in the current work to obtain details of the transitions and the phase diagram. Deriving an amplitude equation and using a variational approach, we show that the flat-to-wrinkle transition is second-order, whereas the wrinkle-to-fold one is first-order. The pressure-displacement relation is linear above the first transition and becomes parabolic after the second one, in agreement with numerical results. Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel.
Key, S.W.; Krieg, R.D.
1980-01-01
A number of complex issues are addressed which will allow the incorporation of finite strain, inelastic material behavior into the piecewise numerical construction of solutions in solid mechanics. Without recourse to extensive continuum mechanics preliminaries, an elementary time independent plasticity model, an elementary time dependent creep model, and a viscoelastic model are introduced as examples of constitutive equations which are routinely used in engineering calculations. The constitutive equations are all suitable for problems involving large deformations and finite strains. The plasticity and creep models are in rate form and use the symmetric part of the velocity gradient or the stretching to compute the co-rotational time derivative of the Cauchy stress. The viscoelastic model computes the current value of the Cauchy stress from a hereditary integral of a materially invariant form of the stretching history. The current configuration is selected for evaluation of equilibrium as opposed to either the reference configuration or the last established equilibrium configuration. The process of strain incrementation is examined in some depth and the stretching evaluated at the midinterval multiplied by the time step is identified as the appropriate finite strain increment to use with the selected form of the constitutive equations. Discussed is the conversion of rotation rates based on the spin into incremental orthogonal rotations which are then used to update stresses and state variables due to rigid body rotation during the load increment. Comments and references to the literature are directed at numerical integration of the constitutive equations with an emphasis on doing this accurately, if not exactly, for any time step and stretching. This material taken collectively provides an approach to numerical implementation which is marked by its simplicity.
Puricelli, Edela; Fonseca, Jun Sérgio Ono; de Paris, Marcel Fasolo; Sant'Anna, Hervandil
2007-01-01
Background Surgical orthopedic treatment of the mandible depends on the development of techniques resulting in adequate healing processes. In a new technical and conceptual alternative recently introduced by Puricelli, osteotomy is performed in a more distal region, next to the mental foramen. The method results in an increased area of bone contact, resulting in larger sliding rates among bone segments. This work aimed to investigate the mechanical stability of the Puricelli osteotomy design. Methods Laboratory tests complied with an Applied Mechanics protocol, in which results from the Control group (without osteotomy) were compared with those from Test I (Obwegeser-Dal Pont osteotomy) and Test II (Puricelli osteotomy) groups. Mandible edentulous prototypes were scanned using computerized tomography, and digitalized images were used to build voxel-based finite element models. A new code was developed for solving the voxel-based finite elements equations, using a reconditioned conjugate gradients iterative solver. The Magnitude of Displacement and von Mises equivalent stress fields were compared among the three groups. Results In Test Group I, maximum stress was seen in the region of the rigid internal fixation plate, with value greater than those of Test II and Control groups. In Test Group II, maximum stress was in the same region as in Control group, but was lower. The results of this comparative study using the Finite Element Analysis suggest that Puricelli osteotomy presents better mechanical stability than the original Obwegeser-Dal Pont technique. The increased area of the proximal segment and consequent decrease of the size of lever arm applied to the mandible in the modified technique yielded lower stress values, and consequently greater stability of the bone segments. Conclusion This work showed that Puricelli osteotomy of the mandible results in greater mechanical stability when compared to the original technique introduced by Obwegeser-Dal Pont. The
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2005-01-01
A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.
Strain energy release rate determination of stress intensity factors by finite element methods
NASA Technical Reports Server (NTRS)
Walsh, R. M., Jr.; Pipes, R. B.
1985-01-01
The stiffness derivative finite element technique is used to determine the Mode I stress intensity factors for three-crack configurations. The geometries examined include the double edge notch, single edge notch, and the center crack. The results indicate that when the specified guidelines of the Stiffness Derivative Method are used, a high degree of accuracy can be achieved with an optimized, relatively coarse finite element mesh composed of standard, four-node, plane strain, quadrilateral elements. The numerically generated solutions, when compared with analytical ones, yield results within 0.001 percent of each other for the double edge crack, 0.858 percent for the single edge crack, and 2.021 percent for the center crack.
McCarty, K.F. )
1999-09-01
We address whether the elastic strain-energy theory (minimizing the Gibbs energy of a stressed crystal) of McKenzie and co-workers [D. R. McKenzie and M. M. M. Bilek, J. Vac. Sci. Technol. A [bold 16], 2733 (1998)] adequately explains the preferred orientation observed in carbon and BN films. In the formalism, the Gibbs energy of the cubic materials diamond and cubic boron includes the strain that occurs when the phases form, through specific structural transformations, from graphitic precursors. This treatment violates the requirement of thermodynamics that the Gibbs energy be a path-independent, state function. If the cubic phases are treated using the same (path-independent) formalism applied to the graphitic materials, the crystallographic orientation of lowest Gibbs energy is not that observed experimentally. For graphitic (hexagonal) carbon and BN, an elastic strain approach seems inappropriate because the compressive stresses in energetically deposited films are orders of magnitude higher than the elastic limit of the materials. Furthermore, using the known elastic constants of either ordered or disordered graphitic materials, the theory does not predict the orientation observed by experiment. [copyright] [ital 1999 American Vacuum Society.
NASA Astrophysics Data System (ADS)
Pettit, J. R.; Walker, A.; Lowe, M. J. S.
2015-01-01
A common goal when using Finite Element (FE) modelling in time domain wave scattering problems is to minimise model size by only considering a region immediately surrounding a scatterer or feature of interest. The model boundaries must simulate infinite space by minimising the reflection of incident waves. This is a significant and long-standing challenge that has only achieved partial success. Industrial companies wishing to perform such modelling are keen to use established commercial FE packages that offer a thorough history of validation and testing. Unfortunately, this limits the flexibility available to modellers preventing the use of popular research tools such as Perfectly Matched Layers (PML). Unlike PML, Absorbing Layers by Increasing Damping (ALID) have proven successful offering practical implementation into any solver that has representation of material damping. Despite good performance further improvements are desirable. Here, a Stiffness Reduction Method (SRM) has been developed and optimised to operate within a significantly reduced spatial domain. The technique is applied by altering damping and stiffness matrices, inducing decay of incident waves. Variables are expressed as a function of known model constants, easing implementation for generic problems. Analytical and numerical solutions have shown that SRM out performs ALID, with results approaching those of PML.
Parallel computation in a three-dimensional elastic-plastic finite-element analysis
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Bigelow, C. A.; Newman, J. C., Jr.
1992-01-01
A CRAY parallel processing technique called autotasking was implemented in a three-dimensional elasto-plastic finite-element code. The technique was evaluated on two CRAY supercomputers, a CRAY 2 and a CRAY Y-MP. Autotasking was implemented in all major portions of the code, except the matrix equations solver. Compiler directives alone were not able to properly multitask the code; user-inserted directives were required to achieve better performance. It was noted that the connect time, rather than wall-clock time, was more appropriate to determine speedup in multiuser environments. For a typical example problem, a speedup of 2.1 (1.8 when the solution time was included) was achieved in a dedicated environment and 1.7 (1.6 with solution time) in a multiuser environment on a four-processor CRAY 2 supercomputer. The speedup on a three-processor CRAY Y-MP was about 2.4 (2.0 with solution time) in a multiuser environment.
Strain-Based Damage Determination Using Finite Element Analysis for Structural Health Management
NASA Technical Reports Server (NTRS)
Hochhalter, Jacob D.; Krishnamurthy, Thiagaraja; Aguilo, Miguel A.
2016-01-01
A damage determination method is presented that relies on in-service strain sensor measurements. The method employs a gradient-based optimization procedure combined with the finite element method for solution to the forward problem. It is demonstrated that strains, measured at a limited number of sensors, can be used to accurately determine the location, size, and orientation of damage. Numerical examples are presented to demonstrate the general procedure. This work is motivated by the need to provide structural health management systems with a real-time damage characterization. The damage cases investigated herein are characteristic of point-source damage, which can attain critical size during flight. The procedure described can be used to provide prognosis tools with the current damage configuration.
A phase-field model for ductile fracture at finite strains and its experimental verification
NASA Astrophysics Data System (ADS)
Ambati, Marreddy; Kruse, Roland; De Lorenzis, Laura
2016-01-01
In this paper, a phase-field model for ductile fracture previously proposed in the kinematically linear regime is extended to the three-dimensional finite strain setting, and its predictions are qualitatively and quantitatively compared with several experimental results, both from ad-hoc tests carried out by the authors and from the available literature. The proposed model is based on the physical assumption that fracture occurs when a scalar measure of the accumulated plastic strain reaches a critical value, and such assumption is introduced through the dependency of the phase-field degradation function on this scalar measure. The proposed model is able to capture the experimentally observed sequence of elasto-plastic deformation, necking and fracture phenomena in flat specimens; the occurrence of cup-and-cone fracture patterns in axisymmetric specimens; the role played by notches and by their size on the measured displacement at fracture; and the sequence of distinct cracking events observed in more complex specimens.
In vivo bone strain and finite-element modeling of the craniofacial haft in catarrhine primates
Ross, Callum F; Berthaume, Michael A; Dechow, Paul C; Iriarte-Diaz, Jose; Porro, Laura B; Richmond, Brian G; Spencer, Mark; Strait, David
2011-01-01
Hypotheses regarding patterns of stress, strain and deformation in the craniofacial skeleton are central to adaptive explanations for the evolution of primate craniofacial form. The complexity of craniofacial skeletal morphology makes it difficult to evaluate these hypotheses with in vivo bone strain data. In this paper, new in vivo bone strain data from the intraorbital surfaces of the supraorbital torus, postorbital bar and postorbital septum, the anterior surface of the postorbital bar, and the anterior root of the zygoma are combined with published data from the supraorbital region and zygomatic arch to evaluate the validity of a finite-element model (FEM) of a macaque cranium during mastication. The behavior of this model is then used to test hypotheses regarding the overall deformation regime in the craniofacial haft of macaques. This FEM constitutes a hypothesis regarding deformation of the facial skeleton during mastication. A simplified verbal description of the deformation regime in the macaque FEM is as follows. Inferior bending and twisting of the zygomatic arches about a rostrocaudal axis exerts inferolaterally directed tensile forces on the lateral orbital wall, bending the wall and the supraorbital torus in frontal planes and bending and shearing the infraorbital region and anterior zygoma root in frontal planes. Similar deformation regimes also characterize the crania of Homo and Gorilla under in vitro loading conditions and may be shared among extant catarrhines. Relatively high strain magnitudes in the anterior root of the zygoma suggest that the morphology of this region may be important for resisting forces generated during feeding. PMID:21105871
Bone stress and strain modification in diastema closure: 3D analysis using finite element method.
Geramy, Allahyar; Bouserhal, Joseph; Martin, Domingo; Baghaeian, Pedram
2015-09-01
The aim of this study was to analyse the stress and strain distribution in the alveolar bone between two central incisors in the process of diastema closure with a constant force. A 3-dimensional computer modeling based on finite element techniques was used for this purpose. A model of an anterior segment of the mandible containing cortical bone, spongy bone, gingivae, PDL and two central incisors with a bracket in the labial surface of each tooth were designed. The von Mises stress and strain was evaluated in alveolar bone along a path of nodes defined in a cresto-apical direction in the midline between two teeth. It was observed that stress and strain of alveolar bone increased in midline with a constant force to close the diastema regardless of the type of movement in gradual steps of diastema closure, however the stress was higher in the tipping movement than the bodily so it can be suggested that a protocol of force system modification should be introduced to compensate for the stress and strain changes caused by the reduced distance to avoid the unwanted stress alteration during the diastema closure. PMID:26277458
Johnson, P.A. |; Rasolofosaon, P.N.J.
1995-11-01
Nonlinear elastic response in rock is established as a robust and representative characteristic of rock rather than a curiosity. This behavior is illustrated from a variety of experiments conducted over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behavior in rock: (1) Nonlinear response in rock is enormous; (2) the response takes place over a large frequency interval (dc--10{sup 6} Hz at least); (3) the response not only occurs, as is commonly appreciated, at large strains but also at small strains where nonlinear response and the manifestations of this behavior are commonly disregarded. Nonlinear response may manifest itself in a variety of manners, including a nonlinear stress{minus}strain relation (hysteretic/discrete memory), nonlinear dissipation, harmonic generation, and resonant peak shift, all of which are related. The experiments described include: quasistatic stress{minus}strain tests (strains of 10{sup -4}--10{sup -1} at frequencies near dc-1Hz); torsional oscillator experiments (strains of 10{sup {minus}4}--10{sup {minus}7}, frequencies between 0.1 and 100Hz); resonant bar experiments (strains of 10{sup {minus}4}--10{sup {minus}8}, frequencies between 10{sup 3} and 10{sup 4} Hz); and dynamic, propagating wave experiments (strains of 10{sup {minus}6}--10{sup {minus}9}, frequencies between 10{sup 3} and 10{sup 6} Hz). [Work supported by OBES/DOE through the University of California and the Institut Francais du Petrole.
NASA Astrophysics Data System (ADS)
Tůma, K.; Stupkiewicz, S.; Petryk, H.
2016-10-01
A finite-strain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharp-interface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phase-field approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two order-parameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, size-dependent microstructures with diffuse interfaces are calculated for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharp-interface microstructures with interfacial energy effects.
NASA Astrophysics Data System (ADS)
Borisov, Dmitry; Singh, Satish C.; Fuji, Nobuaki
2015-09-01
Seismic full waveform inversion is an objective method to estimate elastic properties of the subsurface and is an important area of research, particularly in seismic exploration community. It is a data-fitting approach, where the difference between observed and synthetic data is minimized iteratively. Due to a very high computational cost, the practical implementation of waveform inversion has so far been restricted to a 2-D geometry with different levels of physics incorporated in it (e.g. elasticity/viscoelasticity) or to a 3-D geometry but using an acoustic approximation. However, the earth is three-dimensional, elastic and heterogeneous and therefore a full 3-D elastic inversion is required in order to obtain more accurate and valuable models of the subsurface. Despite the recent increase in computing power, the application of 3-D elastic full waveform inversion to real-scale problems remains quite challenging on the current computer architecture. Here, we present an efficient method to perform 3-D elastic full waveform inversion for time-lapse seismic data using a finite-difference injection method. In this method, the wavefield is computed in the whole model and is stored on a surface above a finite volume where the model is perturbed and localized inversion is performed. Comparison of the final results using the 3-D finite-difference injection method and conventional 3-D inversion performed within the whole volume shows that our new method provides significant reductions in computational time and memory requirements without any notable loss in accuracy. Our approach shows a big potential for efficient reservoir monitoring in real time-lapse experiments.
Nguyen, Ba Nghiep; Bapanapalli, Satish K.; Kunc, Vlastimil; Phelps, Jay; Tucker III, Charles L.
2009-01-26
This paper proposes a model to predict the elastic-plastic response of injection-molded long-fiber thermoplastics (LFTs). The model accounts for elastic fibers embedded in a thermoplastic resin that exhibits the elastic-plastic behavior obeying the Ramberg-Osgood relation and J-2 deformation theory of plasticity. It also accounts for fiber length and orientation distributions in the composite formed by the injection-molding process. Fiber orientation was predicted using the anisotropic rotary diffusion model recently developed by Phelps and Tucker for LFTs. An incremental procedure using the Eshelby’s equivalent inclusion method and the Mori-Tanaka model is proposed to compute the overall stress increment resulting from an overall strain increment for an aligned fiber composite that contains the same fiber volume fraction and length distribution as the actual composite. The incremental response of the later is then obtained from the solution for the aligned fiber composite that is averaged over all possible fiber orientations using the orientation averaging method. Failure during incremental loading is predicted using the Van Hattum-Bernado model. The elastic-plastic and strength prediction model for LFTs was validated against the experimental stress-strain results obtained for long glass fiber/polypropylene specimens.
Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing
2015-09-30
We report non-destructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 mm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.
Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing
2015-09-30
We report non-destructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 mm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positionsmore » were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.« less
Levine, Lyle E.; Okoro, Chukwudi; Xu, Ruqing
2015-01-01
Nondestructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components. PMID:26594371
NASA Astrophysics Data System (ADS)
Sedighi, Hamid M.
2014-02-01
This paper presents the impact of vibrational amplitude on the dynamic pull-in instability and fundamental frequency of actuated microbeams by introducing the second order frequency-amplitude relationship. The nonlinear governing equation of microbeam predeformed by an electric force including the fringing field effect, based on the strain gradient elasticity theory is considered. The predicted results of the strain gradient elasticity theory are compared with the outcomes that arise from the classical and modified couple stress theory. The influences of basic nondimensional parameters on the pull-in instability as well as the natural frequency are investigated by a powerful asymptotic approach namely the Parameter Expansion Method (PEM). It is demonstrated that two terms in series expansions are sufficient to produce an acceptable solution of the microstructure. The phase portrait of the microstructure shows that by increasing the actuation voltage parameter, the stable center point loses its stability and coalesces with unstable saddle node.
Pettit, J. R.; Lowe, M. J. S.; Walker, A. E.
2015-03-31
Pulse-echo ultrasonic NDE examination of large pressure vessel forgings is a design and construction code requirement in the power generation industry. Such inspections aim to size and characterise potential defects that may have formed during the forging process. Typically these defects have a range of orientations and surface roughnesses which can greatly affect ultrasonic wave scattering behaviour. Ultrasonic modelling techniques can provide insight into defect response and therefore aid in characterisation. However, analytical approaches to solving these scattering problems can become inaccurate, especially when applied to increasingly complex defect geometries. To overcome these limitations a elastic Finite Element (FE) method has been developed to simulate pulse-echo inspections of embedded planar defects. The FE model comprises a significantly reduced spatial domain allowing for a Monte-Carlo based approach to consider multiple realisations of defect orientation and surface roughness. The results confirm that defects aligned perpendicular to the path of beam propagation attenuate ultrasonic signals according to the level of surface roughness. However, for defects orientated away from this plane, surface roughness can increase the magnitude of the scattered component propagating back along the path of the incident beam. This study therefore highlights instances where defect roughness increases the magnitude of ultrasonic scattered signals, as opposed to attenuation which is more often assumed.
NASA Astrophysics Data System (ADS)
Miyashita, Toyokatsu
2006-05-01
A novel acoustic waveguide composed of a line of single defects in a sonic crystal is shown to have desirable properties for acoustic circuits. The absence of a scatterer, i.e., a single defect or a point defect, in artificial crystals such as photonic crystals and phononic crystals leads to some localized resonant modes around the defect. Single defects in a sonic crystal made of acrylic resin cylinders in air are shown in this paper to have resonant modes or defect modes, which are excited successively to form a mode guided along a line of defects. Both a straight waveguide and a sharp bending waveguide composed of lines of single defects are shown equally to have a good transmission with small reflections at the inlet as well as at the outlet within the full band gap of the sonic crystal. Their advantages over conventional line-defect waveguides are clearly shown by their transmission versus frequency characteristics and also by typical examples of their spatial acoustic field distribution. On the basis of these properties, coupled defect-mode waveguides are investigated, and a high mode-coupling ratio is obtained. Defect-mode waveguides in a sonic crystal are expected to be desirable elements for functional acoustic circuits. The results of the elastic finite difference time domain (FDTD) method used as a tool of numerical calculation are also investigated and precisely compared with the experimental band gaps.
Pavlov, D. A.; Bidus, N. V.; Bobrov, A. I.; Vikhrova, O. V.; Volkova, E. I.; Zvonkov, B. N.; Malekhonova, N. V.; Sorokin, D. S.
2015-01-15
The distribution of elastic strains in a system consisting of a quantum-dot layer and a buried GaAs{sub x}P{sub 1−x} layer is studied using geometric phase analysis. A hypothesis is offered concerning the possibility of controlling the process of the formation of InAs quantum dots in a GaAs matrix using a local isovalent phosphorus impurity.
NASA Astrophysics Data System (ADS)
Ring, Uwe; Bernet, Matthias; Tulloch, Andy
2015-04-01
The Sisters Shear Zone (SSZ) on Stewart Island, New Zealand, is a greenschist-facies extensional shear zone active prior to and possibly during the development of the Pacific-Antarctica spreading ridge at ∼76 Ma. We report quantitative kinematic and rotation data as well as apatite fission-track (AFT) ages from the SSZ. Early kinematic indicators associated with the NNE-trending stretching lineation formed under upper greenschist-facies metamorphism and show alternating top-to-the-NNW and top-to-the-SSE senses of shear. During progressive exhumation lowermost greenschist-facies and brittle-ductile kinematic indicators depict a more uniform top-to-the-SSE sense of shear in the topmost SSZ just below the detachment plane. Deformed metagranites in the SSZ allow the reconstruction of deformation and flow parameters. The mean kinematic vorticity number (Wm) ranges from 0.10 to 0.89; smaller numbers prevail in the deeper parts of the shear zone with a higher degree of simple shear deformation in the upper parts of the shear zone (deeper and upper parts relate to present geometry). High finite strain intensity correlates with low Wm and high Wm numbers near the detachment correlate with relatively weak strain intensity. Finite strain shows oblate geometries. Overall, our data indicate vertical and possibly temporal variations in deformation of the SSZ. Most AFT ages cluster around 85-75 Ma. We interpret the AFT ages to reflect the final stages of continental break-up just before and possibly during the initiation of sea-floor spreading between New Zealand and Antarctica.
Hudetz, A G; Monos, E
1981-01-01
Three-dimensional quasi-static mechanical measurements were carried out on cylindrical segments of the dog carotid and iliac arteries for determination of the passive anisotropic elastic properties of the vessel wall. On the basis of passive characteristics of outer diameter vs. intraluminal pressure, and axial extending force vs. intraluminal pressure, picked up at various fixed initial vascular length values, the incremental Young moduli and poisson ratios of the vessel wall were calculated in the 0--33 kPa (0--250 mm Hg) pressure range. The strain energy function of the arteries was approximated by polynomial and exponential models. We found that an exponential energy function with 4-parameters gives more accurate results than the 7- or 12-parameter polynomial functions. According to the results the axial modulus reaches higher values than the tangential and radial moduli at a low tangential stretch level, while at high tangential stretch the tangential modulus is the highest in both carotid and iliac arteries. After elevation of the initial tangential stretch the increase in the tangential modulus is the most pronounced, while the values of radial and axial moduli increased less. A change in the initial axial stretch influences the axial and radial moduli to a similar extent, but has no substantial effect on the value of the tangential modulus. The values of corresponding poisson ratios depend in a similar way on the initial deformation state. The different behaviour of the two Poisson ratios characterizing the mechanical coupling between tangential and axial directions, indicates that the structural coupling between the two main directions is asymmetrical. It is assumed that this property of the passive vascular structure can be explained by the network arrangement of collagen fibres in the vessel wall.
Finite Strain in the Forearc Mantle: Testing the B-type Fabric Anisotropy Hypothesis
NASA Astrophysics Data System (ADS)
Kneller, E. A.; van Keken, P.; Karato, S.; Park, J.
2005-12-01
Seismic observations from many subduction zones show that the seismically fast direction is perpendicular to the direction of convergence. This is opposite of what is expected from models that assume flow is parallel to plate motion and the seismically fast axis of olivine [100] aligns sub-parallel to the shear direction (A-type fabric). Recent deformation experiments on olivine aggregates show that under low-temperature and high-stress conditions, the fast axis of olivine aligns sub-perpendicular to the shear direction (B-type fabric)(Jung and Karato, 2001; Katayama et al., 2004). B-type fabric has potential to explain convergence-perpendicular anisotropy in subduction zones with flow parallel to plate motion. Kneller et al. (2005) used combined data from deformation experiments on olivine aggregates and dynamical models of subduction zones to predict the distribution of B-type fabric in the mantle wedge. This study predicted that the forearc mantle has suitable thermal and stress conditions for B-type fabric and a rapid transition toward the backarc to conditions more suitable for other olivine fabrics. A vertical projection of the volcanic arc into the mantle wedge is predicted to mark the fabric transition between B-type and A-, E-, or C-type fabrics depending on water content. An important aspect not thoroughly investigated by our previous research is finite strain accumulation across the predicted fabric transition. In this study we present finite strain calculation for non-Newtonian subduction zone models with composite water-dependent rheology. This composite rheology includes experimentally based Peierls, dislocation, and diffusion creep. We predict greater than 100 % strain accumulation across 75 km for material traveling into the forearc mantle. This strain accumulation may be sufficient to produce a well developed B-type fabric. Furthermore, material enters the forearc mantle from a low-strain-rate thermal boundary layer at the base of the overriding
NASA Astrophysics Data System (ADS)
Cline, C. J., II; Burnley, P. C.
2013-12-01
In order to extrapolate the rheological behavior of polycrystalline earth materials to conditions and timescales that are unachievable in a laboratory setting, some sort of model is required. Numerical models are particularly appealing for this task but for these models to provide a sound platform for extrapolation they must be based on a complete understanding of all deformation mechanics that are operating in the real material. In a simplified description these mechanics can be thought of as having three components 1) the individual grains, 2) the grain boundaries and 3) the macroscopic aggregate response, which can be thought of as the interaction of the other two components within the polycrystal. Traditionally, the aggregate response is thought to represent the summed or average behavior of all individual grains deforming under the influence of the macroscopic stress tensor but; recent work within our lab using finite element models (FEM) has shown that local stress fields within the aggregate are not representative of the macroscopic stress tensor and can vary in both direction and magnitude. These variations in the stress tensor produce a pattern similar to force chains that are observed in deformation experiments on granular materials; and appear to be a direct consequence of stress percolation which is controlled by the anisotropy of the elastic and plastic strengths of the individual grains. To test this hypothesis we will conduct a suite of deformation experiments utilizing multiple monomineralic polycrystals that have a range of single crystal anisotropies. In order to infer the direction of stress acting on each grain and reconstruct the total modulation of stress direction throughout the sample, we have chosen materials that form microstructures that are sensitive to stress direction, such as deformation twins and kink bands. This experimental technique will allow for a direct comparison between the single crystal anisotropy of a material and the
Donaldson, F E; Pankaj, P; Cooper, D M L; Thomas, C D L; Clement, J G; Simpson, A H R W
2011-06-01
Homogenized elastic properties are often assumed for macro-finite element (FE) models used in orthopaedic biomechanics. The accuracy of material property assignments may have a strong effect on the ability of these models to make accurate predictions. For cortical bone, most macro-scale FE models assume isotropic elastic material behaviour and do not include variation of material properties due to bone micro-architecture. The first aim of the present study was to evaluate the variation of apparent-level (homogenized) orthotropic elastic constants of cortical bone with age and indices of bone micro-architecture. Considerable age-dependent differences in porosity were noted across the cortical thickness in previous research. The second aim of the study was to quantify the resulting differences in elastic constants between the periosteum and endosteum. Specimens were taken from the anterior femoral midshaft of 27 female donors (age 53.4 +/- 23.6 years) and micro-FE (gFE) analysis was used to derive orthotropic elastic constants. The variation of orthotropic elastic constants (Young's moduli, shear moduli, and Poisson's ratios) with various cortical bone micro-architectural indices was investigated. The ratio of canal volume to tissue volume, Ca.V/TV, analogous to porosity, was found to be the strongest predictor (r2(ave) = 0.958) of the elastic constants. Age was less predictive (r2(ave) = 0.385) than Ca.V/TV. Elastic anisotropy increased with increasing Ca.V/TV, leading to lower elastic moduli in the transverse, typically less frequently loaded, directions. Increased Ca.V/TV led to a more substantial reduction in elastic constants at the endosteal aspect than at the periosteal aspect. The results are expected to be most applicable in similar midshaft locations of long bones; specific analysis of other sites would be necessary to evaluate elastic properties elsewhere. It was concluded that Ca.V/TV was the most predictive of cortical bone elastic constants and that
NASA Astrophysics Data System (ADS)
Erler, Norbert; Groß, Michael
2015-05-01
Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.
In situ tooth replica custom implant: a 3-dimensional finite element stress and strain analysis.
Ghuneim, Wael Aly
2013-10-01
This study is a phase of a biomechanical study, a part of a research program concerned with the new concept of in situ tooth replication. The purpose of the study was to evaluate tooth replica under each of two possible circumstances: (1) attachment via periodontal ligament and (2) osseointegration. Replicas were made of Cortoss, a bioactive glass, bone substitute. Three-dimensional finite element analysis was used to assess the stresses and strains resulting from each of 2 types of loads: off-vertical pressure and vertical point force acting on natural mandibular second premolar and corresponding replicas. Natural tooth tolerated 19 MPa pressure or 85 N vertical force, periodontally attached replica tolerated 15 MPa pressure or 80 N force, and osseointegrated replica tolerated 23 MPa pressure or 217 N force.
A thermo-mechanically coupled finite strain model considering inelastic heat generation
NASA Astrophysics Data System (ADS)
Dunić, Vladimir; Busarac, Nenad; Slavković, Vukašin; Rosić, Bojana; Niekamp, Rainer; Matthies, Hermann; Slavković, Radovan; Živković, Miroslav
2016-07-01
The procedure for reuse of finite element method (FEM) programs for heat transfer and structure analysis to solve advanced thermo-mechanical problems is presented as powerful algorithm applicable for coupling of other physical fields (magnetic, fluid flow, etc.). In this case, nonlinear Block-Gauss-Seidel partitioned algorithm strongly couples the heat transfer and structural FEM programs by a component-based software engineering. Component template library provides possibility to exchange the data between the components which solve the corresponding subproblems. The structural component evaluates the dissipative energy induced by inelastic strain. The heat transfer component computes the temperature change due to the dissipation. The convergence is guaranteed by posing the global convergence criterion on the previously locally converged coupled variables. This enables reuse of software and allows the numerical simulation of thermo-sensitive problems.
NASA Technical Reports Server (NTRS)
Allen, Phillip A.; Wells, Douglas N.
2013-01-01
No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.
NASA Astrophysics Data System (ADS)
Lopez-Pamies, Oscar; Goudarzi, Taha; Danas, Kostas
2013-01-01
In Part I, an exact solution was determined for the problem of the overall nonlinear elastic response of Gaussian (or Neo-Hookean) rubber reinforced by a dilute isotropic distribution of rigid particles. Here, this fundamental result is utilized to construct an approximate solution for non-Gaussian rubber reinforced by an isotropic distribution of rigid particles at finite concentration. This is accomplished by means of two different techniques in two successive steps. First, the dilute solution is utilized together with a differential scheme in finite elasticity to generate a solution for Neo-Hookean rubber filled with an isotropic distribution of rigid particles of polydisperse sizes and finite concentration. This non-dilute result is then employed within the context of a new comparison medium method — derived as an extension of Talbot-Willis (1985) variational framework to the non-convex realm of finite elasticity — to generate in turn a corresponding solution for filled non-Gaussian rubber wherein the underlying elastomeric matrix is characterized by any I1-based stored-energy function Ψ(I1) of choice. The solution is fully explicit and remarkably simple. Its key theoretical and practical merits are discussed in detail. Additionally, the constructed analytical solution is confronted to 3D finite-element simulations of the large-deformation response of Neo-Hookean and non-Gaussian rubber reinforced by isotropic distributions of rigid spherical particles with the same size, as well as with different sizes. Good agreement is found among all three sets of results. The implications of this agreement are discussed.
Gao, Jing; Rubin, Jonathan M
2014-09-01
To determine whether ultrasound strain zero-crossing elasticity measurement can be used to discriminate moderate cortical fibrosis or inflammation in renal allografts, we prospectively assessed cortical hardness with quasi-static ultrasound elastography in 38 renal transplant patients who underwent kidney biopsy from January 2013 to June 2013. With the Banff score criteria for renal cortical fibrosis as gold standard, 38 subjects were divided into two groups: group 1 (n = 18) with ≤25% cortical fibrosis and group 2 (n = 20) with >26% cortical fibrosis. We then divided this population again into group 3 (n = 20) with ≤ 25% inflammation and group 4 (n = 18) with >26% inflammation based on the Banff score for renal parenchyma inflammation. To estimate renal cortical hardness in both population divisions, we propose an ultrasound strain relative zero-crossing elasticity measurement (ZC) method. In this technique, the relative return to baseline, that is zero strain, of strain in the renal cortex is compared with that of strain in reference soft tissue (between the abdominal wall and pelvic muscles). Using the ZC point on the reference strain decompression slope as standard, we determined when cortical strain crossed zero during decompression. ZC was negative when cortical strain did not return or returned after the reference, whereas ZC was positive when cortical strain returned ahead of the reference. Fisher's exact test was used to examine the significance of differences in ZC between groups 1 and 2 and between groups 3 and 4. The accuracy of ZC in determining moderate cortical fibrosis and moderate inflammation was examined by receiver operating characteristic analysis. The intra-class correlation coefficient and analysis of variance were used to test inter-rater reliability and reproducibility. ZC had good inter-observer agreement (ICC = 0.912) and reproducibility (p = 0.979). ZCs were negative in 18 of 18 cases in group 1 and positive in 19 of 20 cases in
NASA Astrophysics Data System (ADS)
Treutenaere, S.; Lauro, F.; Bennani, B.; Matsumoto, T.; Mottola, E.
2015-09-01
The use of fabric reinforced polymers in the automotive industry is growing significantly. The high specific stiffness and strength, the ease of shaping as well as the great impact performance of these materials widely encourage their diffusion. The present model increases the predictability of explicit finite element analysis and push the boundaries of the ongoing phenomenological model. Carbon fibre composites made up various preforms were tested by applying different mechanical load up to dynamic loading. This experimental campaign highlighted the physical mechanisms affecting the initial mechanical properties, namely intra- and interlaminar matrix damage, viscoelasticty and fibre failure. The intralaminar behaviour model is based on the explicit formulation of the matrix damage model developed by the ONERA as the given damage formulation correlates with the experimental observation. Coupling with a Maxwell-Wiechert model, the viscoelasticity is included without losing the direct explicit formulation. Additionally, the model is formulated under a total Lagrangian scheme in order to maintain consistency for finite strain. Thus, the material frame-indifference as well as anisotropy are ensured. This allows reorientation of fibres to be taken into account particularly for in-plane shear loading. Moreover, fall within the framework of the total Lagrangian scheme greatly makes the parameter identification easier, as based on the initial configuration. This intralaminar model thus relies upon a physical description of the behaviour of fabric composites and the numerical simulations show a good correlation with the experimental results.
NASA Astrophysics Data System (ADS)
Rout, Matruprasad; Pal, Surjya Kanta; Singh, Shiv Brat
2016-05-01
Studies on the effect of strain path during rolling has been carried out for a long time, but the same has not been done using Finite Element Analysis (FEA). Change in strain path affects the state variables in the rolled plate like stress, strain, temperature etc. In the current work, Finite Element Analysis for cross rolling of AISI 304 austenitic stainless steel has been carried out by rotating the plate by 90° in between the passes. To analyze stress and strain fields in the material for cross rolling, a full 3D model of work-roll and plate has been developed using rigid-viscoplastic finite element method. The stress and strain fields, considering von-Mises yield criteria, are calculated by using updated Lagrangian method. In addition to these, the model also calculates the normal pressure and strain rate distribution in the plate during cross rolling. The nature of the variations of stress and strain fields in the plate, predicted by the model, is in good agreement with the previously published works for unidirectional rolling.
Wang, Huamiao; Clausen, Bjorn; Capolungo, Laurent; Beyerlein, Irene Jane; Wang, Jian; Tome, Carlos N.
2015-07-16
Continuous mechanical tests with strain holds (stress relaxation) and with stress holds (strain relaxation) are performed simultaneously with in-situ neutron measurements to analyze the mechanisms of stress and strain relaxation in Mg AZ31 rolled plate. A dislocation activity based constitutive model, accounting for internal stress statistical distributions, is proposed and implemented into an elastic viscoplastic self-consistent (EVPSC) framework to simultaneously describe both stress and strain relaxation. The model captures the experimental data in terms of macroscopic stress strain curves, evolution of stress and strain during holding, as well as evolution of the internal elastic strains. Model results indicate that the magnitude of the stress relaxed during strain holding is dependent on both, the magnitude of the flow stress and the spread of the resolved shear stress distribution. The magnitude of strain accumulated during stress holding is, on the other hand, dependent on the magnitude of the hardening rate and on the spread of the resolved shear stress distribution. Furthermore, the internal elastic strains are directly correlated with the stress state, and hence the stress relaxation during strain holds has a greater influence on the lattice strains than strain relaxation during stress holds.
Giant elastic tunability in strained BiFeO_{3} near an electrically induced phase transition
Yu, Pu; Vasudevan, Rama K.; Tselev, Alexander; Xue, Fei; Chen, Long -Qing; Maksymovych, Petro; Kalinin, Sergei V.; Balke, Nina; Li, Q.; Cao, Y.; Laanait, N.
2015-01-01
Elastic anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation elastic/piezoresponse spectroscopy, we probed sub-MHz elastic dynamics of a tip bias-induced rhombohedral–tetragonal phase transition of strained (001)-BiFeO_{3} (rhombohedral) ferroelectric thin films from ~10^{3} nm^{3} sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with 2-3 folds enhancement of local piezoresponse. Coupled with phase-field modeling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (e.g., domain walls) on the kinetics of this phase transition, thereby providing fresh insights into the morphotropic phase boundary (MPB) in ferroelectrics. Moreover, the giant electrically tunable elastic stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO_{3} in next-generation frequency-agile electroacoustic devices, based on utilization of the soft modes underlying successive ferroelectric phase transitions.
NASA Astrophysics Data System (ADS)
Yang, Pei; Haibin, Wu
2015-03-01
We study the elastic constants and electronic properties of orthorhombic BiMnO3 under uniaxial strain along the c-axis using the first-principles method. It is found that, beyond the range -0.025 < ɛ < 0.055, the predicted stiffness constants cij cannot demand the Born stability criteria and the compliance constant s44 shows abrupt changes, which accompany phase transition. In addition, the results for magnetism moments and polycrystalline properties are also reported. Additionally, under compressive strain, a band gap transition from the indirect to the direct occurs within -0.019 < ɛ < -0.018. Furthermore, the response of the band gap of orthorhombic BiMnO3 to uniaxial strain is studied.
Band-Gap Modulation of GeCH3 Nanoribbons Under Elastic Strain: A Density Functional Theory Study
NASA Astrophysics Data System (ADS)
Ma, ShengQian; Li, Feng; Jiang, ChunLing
2016-10-01
Using the density functional theory method, we researched the band-gap modulation of GeCH3 nanoribbons under uniaxial elastic strain. The results indicated that the band gap of GeCH3 nanoribbons could be tuned along two directions, namely, stretching or compressing ribbons when ɛ was changed from -10% to 10% in 6-zigzag, 10-zigzag, 13-armchair, and 17-armchair nanoribbons, respectively. The band gap greatly changed with strain. In the case of tension, the amount of change in the band gap was bigger. But in the case of compression, the gradient was steeper. The band gap had a nearly linear relationship when ɛ ranges from 0% to 10%. We also investigated if the band gap is changed with widths. The results showed variation of the band gap did not rely on widths. Therefore, the GeCH3 nanoribbons had the greatest potential application in strain sensors and optical electronics at the nanoscale.
Band-Gap Modulation of GeCH3 Nanoribbons Under Elastic Strain: A Density Functional Theory Study
NASA Astrophysics Data System (ADS)
Ma, ShengQian; Li, Feng; Jiang, ChunLing
2016-06-01
Using the density functional theory method, we researched the band-gap modulation of GeCH3 nanoribbons under uniaxial elastic strain. The results indicated that the band gap of GeCH3 nanoribbons could be tuned along two directions, namely, stretching or compressing ribbons when ɛ was changed from -10% to 10% in 6-zigzag, 10-zigzag, 13-armchair, and 17-armchair nanoribbons, respectively. The band gap greatly changed with strain. In the case of tension, the amount of change in the band gap was bigger. But in the case of compression, the gradient was steeper. The band gap had a nearly linear relationship when ɛ ranges from 0% to 10%. We also investigated if the band gap is changed with widths. The results showed variation of the band gap did not rely on widths. Therefore, the GeCH3 nanoribbons had the greatest potential application in strain sensors and optical electronics at the nanoscale.
Nguyen, Ba N.; Kunc, Vlastimil; Phelps, Jay H; TuckerIII, Charles L.; Bapanapalli, Satish K
2009-01-01
This paper proposes a model to predict the elastic-plastic response of injection-molded long-fiber thermoplastics (LFTs). The model accounts for elastic fibers embedded in a thermoplastic resin that exhibits the elastic-plastic behavior obeying the Ramberg-Osgood relation and J-2 deformation theory of plasticity. It also accounts for fiber length and orientation distributions in the composite formed by the injection-molding process. Fiber orientation was predicted using an anisotropic rotary diffusion model recently developed for LFTs. An incremental procedure using Eshelby's equivalent inclusion method and the Mori-Tanaka assumption is proposed to compute the overall stress increment resulting from an overall strain increment for an aligned-fiber composite that contains the same fiber volume fraction and length distribution as the actual composite. The incremental response of the latter is then obtained from the solution for the aligned-fiber composite by averaging over all fiber orientations. Failure during incremental loading is predicted using the Van Hattum-Bernado model. The model is validated against the experimental stress-strain results obtained for long-glass-fiber/polypropylene specimens.
Kim, Yoon Hyuk; Yao, Zhidong; Kim, Kyungsoo; Park, Won Man
2014-06-01
It may be assumed that the stability is affected when some ligaments are injured or loosened, and this joint instability causes sacroiliac joint pain. Several physical examinations have been used to diagnose sacroiliac pain and to isolate the source of the pain. However, more quantitative and objective information may be necessary to identify unstable or injured ligaments during these tests due to the lack of understanding of the quantitative relationship between the physical tests and the biomechanical parameters that may be related to pains in the sacroiliac joint and the surrounding ligaments. In this study, a three-dimensional finite element model of the sacroiliac joint was developed and the biomechanical conditions for six typical physical tests such as the compression test, distraction test, sacral apex pressure test, thigh thrust test, Patrick's test, and Gaenslen's test were modelled. The sacroiliac joint contact pressure and ligament strain were investigated for each test. The values of contact pressure and the combination of most highly strained ligaments differed markedly among the tests. Therefore, these findings in combination with the physical tests would be helpful to identify the pain source and to understand the pain mechanism. Moreover, the technology provided in this study might be a useful tool to evaluate the physical tests, to improve the present test protocols, or to develop a new physical test protocol.
NASA Astrophysics Data System (ADS)
Ziółkowski, Andrzej
2016-09-01
An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition
NASA Astrophysics Data System (ADS)
Malekan, Mohammad; Barros, Felicio Bruzzi
2016-07-01
Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global-local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global-local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global-local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global-local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global-local enrichments lead to ill-conditioned system matrices and bad convergence rate.
NASA Astrophysics Data System (ADS)
Malekan, Mohammad; Barros, Felicio Bruzzi
2016-11-01
Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global-local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global-local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global-local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global-local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global-local enrichments lead to ill-conditioned system matrices and bad convergence rate.
An experimental method to obtain the elastic strain energy function from torsion-tension tests
NASA Technical Reports Server (NTRS)
Peng, S. T. J.; Landel, R. F.
1976-01-01
It is shown that by employing a torsion-tension test, it is possible to have a complete mapping near the origin of the two principal strain invariants associated with the rate of change of the strain energy function. However, the mathematical representation of the twist moment and normal forces vs strain and the strain energy function are complex. This problem is solved by using a set of solid cylindrical bars with different diameters such that the difference in diameter of two successive bars is small. The stress-strain equations can be grossly oversimplified by considering differences in twist moment and normal force as a function of difference in radius.
Albocher, U.; Barbone, P.E.; Richards, M.S.; Oberai, A.A.; Harari, I.
2014-01-01
We apply the adjoint weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing the displacements and appending a regularization term to the AWE formulation, a dramatic improvement in the reconstruction can be achieved. With these improvements, the advantages of the AWE method as a direct solution approach can be extended to a wider range of problems. PMID:25383085
Barabash, O.M.; Santella, M.; Barabash, R.I.; Ice, G.E.; Tischler, J.
2011-12-14
The indentation-induced elastic-plastic zone in an IN 740 Ni-based superalloy was studied by three-dimensional (3-D) x-ray microdiffraction and electron back scattering diffraction (EBSD). Large lattice reorientations and the formation of geometrically necessary dislocations are observed in the area with a radius of {approx}75 {mu}m. A residual compression zone is found close to the indent edge. An elastic-plastic transition is observed at {approx}20 {mu}m from the indent edge. Depth dependent dislocation densities are determined at different distances from the indent edge.
NASA Technical Reports Server (NTRS)
Deng, Xiaomin; Newman, James C., Jr.
1997-01-01
ZIP2DL is a two-dimensional, elastic-plastic finte element program for stress analysis and crack growth simulations, developed for the NASA Langley Research Center. It has many of the salient features of the ZIP2D program. For example, ZIP2DL contains five material models (linearly elastic, elastic-perfectly plastic, power-law hardening, linear hardening, and multi-linear hardening models), and it can simulate mixed-mode crack growth for prescribed crack growth paths under plane stress, plane strain and mixed state of stress conditions. Further, as an extension of ZIP2D, it also includes a number of new capabilities. The large-deformation kinematics in ZIP2DL will allow it to handle elastic problems with large strains and large rotations, and elastic-plastic problems with small strains and large rotations. Loading conditions in terms of surface traction, concentrated load, and nodal displacement can be applied with a default linear time dependence or they can be programmed according to a user-defined time dependence through a user subroutine. The restart capability of ZIP2DL will make it possible to stop the execution of the program at any time, analyze the results and/or modify execution options and resume and continue the execution of the program. This report includes three sectons: a theoretical manual section, a user manual section, and an example manual secton. In the theoretical secton, the mathematics behind the various aspects of the program are concisely outlined. In the user manual section, a line-by-line explanation of the input data is given. In the example manual secton, three types of examples are presented to demonstrate the accuracy and illustrate the use of this program.
Circum-Slab Mantle Deformation: Insights from Finite Strain and Seismic Anisotropy
NASA Astrophysics Data System (ADS)
Di Leo, J. F.; Li, Z. H.; Ribe, N. M.; Walker, A.; Wookey, J. M.; Kendall, J. M.
2014-12-01
Recent numerical modeling studies of the time-dependent development of texture and seismic anisotropy during subduction have shed light on how the mantle deforms as a slab subducts. It is thus becoming more and more clear that the term "mantle flow" may be too ambiguous in the context of subduction. For instance, it has been suggested that trench-parallel shear wave splitting fast directions (from SKS and source-side S splitting) on the seaward side need not necessarily be the result of trench-parallel movement (i.e., "flow") of mantle material, but are rather due to pure shear deformation in the sub-slab mantle. Here we present results of a numerical modeling study where we have systematically investigated how mantle propagation, finite strain, olivine lattice-preferred orientation (LPO), and SKS splitting vary with slab width in a fully dynamic 3-D subduction model. We find that even in the complex circum-slab flow field, the finite strain ellipsoid (FSE) is a good proxy for LPO. However, it does not necessarily align with the instantaneous mantle flow velocity vector. We identify two distinct domains with different deformation types in the central sub-slab upper mantle: simple shear induced by plate advance dominates at shallow depths and results in trench-normal fast splitting, while pure shear due to slab rollback dominates in the deeper mantle (above 410 km) and produces trench-parallel fast orientations. In our models, the SKS splitting pattern strongly depends on these two competing effects as well as the subduction partition ratio, γ = Xp/Xt, where Xp and Xt are the lengths of plate advance and trench retreat, respectively. If γ < 1 (narrow slabs, < 1000 km), trench-parallel fast directions are produced. In contrast, γ > 1 (wide slabs, > 1000 km), results in trench-normal fast splitting. This may explain the observed dichotomy in natural subduction zones of sub-slab fast splitting patterns (away from slab edges) usually being either trench-parallel or
Brake, M. R. W.
2015-02-17
Impact between metallic surfaces is a phenomenon that is ubiquitous in the design and analysis of mechanical systems. We found that to model this phenomenon, a new formulation for frictional elastic–plastic contact between two surfaces is developed. The formulation is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects. The constitutive model for normal contact is developed as two contiguous loading domains: the elastic regime and a transitionary region in which the plastic response of the materials develops and the elastic response abates. For unloading, the constitutive model is based on an elastic process. Moreover, the normal contact model is assumed to only couple one-way with the frictional/tangential contact model, which results in the normal contact model being independent of the frictional effects. Frictional, tangential contact is modeled using a microslip model that is developed to consider the pressure distribution that develops from the elastic–plastic normal contact. This model is validated through comparisons with experimental results reported in the literature, and is demonstrated to be significantly more accurate than 10 other normal contact models and three other tangential contact models found in the literature.
Brake, M. R. W.
2015-02-17
Impact between metallic surfaces is a phenomenon that is ubiquitous in the design and analysis of mechanical systems. We found that to model this phenomenon, a new formulation for frictional elastic–plastic contact between two surfaces is developed. The formulation is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects. The constitutive model for normal contact is developed as two contiguous loading domains: the elastic regime and a transitionary region in which the plastic response of the materials develops and the elastic response abates. For unloading, the constitutive model ismore » based on an elastic process. Moreover, the normal contact model is assumed to only couple one-way with the frictional/tangential contact model, which results in the normal contact model being independent of the frictional effects. Frictional, tangential contact is modeled using a microslip model that is developed to consider the pressure distribution that develops from the elastic–plastic normal contact. This model is validated through comparisons with experimental results reported in the literature, and is demonstrated to be significantly more accurate than 10 other normal contact models and three other tangential contact models found in the literature.« less
NASA Astrophysics Data System (ADS)
Okudur, O. O.; Vanstreels, K.; De Wolf, I.; Hangen, U.
2016-01-01
Continuous scaling of integrated circuits has led to the introduction of highly porous low dielectric constant (low-k) materials, whose inferior mechanical properties raise concerns regarding the reliability of integrated circuits. Nanoindentation is proven to be a straightforward method to study mechanical properties of films. However, in the case of low-k, the measurement and analysis are complex due to the porous nature of the films and reduced film thicknesses which give rise to substrate effects. A methodology that combines nanoindentation experiments with finite-element simulations is proposed and validated in this study to extract the substrate-free elastic modulus of porous ultra-thin low-k films. Furthermore, it is shown that imperfections of the nanoindentation probe significantly affect the finite-element results. An effective analytical method that captures the actual nanoindenter behavior upon indentation is proposed by taking both tip radius and conical imperfections into account. Using this method combined with finite element modeling, the elastic modulus of sub-100 nm thick low-k films is successfully extracted. Standard indentation tests clearly overestimated the actual modulus for such thin films, which emphasizes the importance of the proposed methodology.
Kelly, D J; Prendergast, P J
2004-01-01
The structure and functionality of tissue-engineered cartilage is determined by the tissue culture conditions and mechanical conditioning during growth. The quality of tissue-engineered cartilage can be evaluated using tests such as the confined compression test. Tissue-engineered cartilage constructs usually consist of an outer layer of cartilage and an inner core of either undeveloped cartilage or degrading scaffold material. A biphasic poro-elastic finite element model was used to demonstrate how such a core influences the reaction force-time curve obtained from a confined compression test. The finite element model predicted that higher volumes of degraded scaffold in the inner core would reduce the aggregate modulus calculated from the confined compression test and raised the estimate of tissue permeability. The predicted aggregate modulus reduced from 0.135 MPa, for a homogenous construct, to 0.068 MPa, for a construct that was only 70% cartilaginous. It was found that biphasic poro-elastic finite modelling should be used in preference to a one-dimensional model that assumed homogeneity in estimating the properties of tissue-engineered cartilage.
Bedolla Pantoja, Marco A; Abbott, Nicholas L
2016-05-25
We report the fabrication of chemically patterned microwells that enable the rapid and facile preparation (by spin coating and patterned dewetting) of thin films of liquid crystals (LCs) that have precise thicknesses (0.7-30 μm), are supported on chemically defined substrates, and have free upper surfaces. We use these microwells to prepare elastically strained nematic LC films supported on silica glass, gold, or polystyrene substrates and thereby characterize the response of the strained LC films to vapors of toluene. We report that low concentrations of toluene vapor (<500 ppm) can partition into the LC to lower the anchoring energy of the LC on these substrates, thus allowing the elastic energy of the strained LC film to drive the LC films through an orientational transition. The central role of the toluene-induced change in surface anchoring energy is supported by additional experiments in which the response of the nematic LC to changes in film thickness and substrate identity are quantified. A simple thermodynamic model captures these trends and yielded estimates of anchoring energies (8-22 μJ/m(2)). Significantly, the orientational transitions observed in these strained LC thin films occur at concentrations of toluene vapor that are almost 1 order of magnitude below those which lead to bulk phase transitions, and they are not triggered by exposure to water vapor. Overall, these results hint at principles for the design of responsive LC-based materials that can be triggered by concentrations of aromatic, volatile organic compounds that are relevant to human health. PMID:27070511
Webster, Duncan; Schulte, Friederike A; Lambers, Floor M; Kuhn, Gisela; Müller, Ralph
2015-03-18
Huiskes et al. hypothesized that mechanical strains sensed by osteocytes residing in trabecular bone dictate the magnitude of load-induced bone formation. More recently, the mechanical environment in bone marrow has also been implicated in bone׳s response to mechanical stimulation. In this study, we hypothesize that trabecular load-induced bone formation can be predicted by mechanical signals derived from an integrative µFE model, incorporating a description of both the bone and marrow phase. Using the mouse tail loading model in combination with in vivo micro-computed tomography (µCT) we tracked load induced changes in the sixth caudal vertebrae of C57BL/6 mice to quantify the amount of newly mineralized and eroded bone volumes. To identify the mechanical signals responsible for adaptation, local morphometric changes were compared to micro-finite element (µFE) models of vertebrae prior to loading. The mechanical parameters calculated were strain energy density (SED) on trabeculae at bone forming and resorbing surfaces, SED in the marrow at the boundary between bone forming and resorbing surfaces, along with SED in the trabecular bone and marrow volumes. The gradients of each parameter were also calculated. Simple regression analysis showed mean SED gradients in the trabecular bone matrix to significantly correlate with newly mineralized and eroded bone volumes R(2)=0.57 and 0.41, respectively, p<0.001). Nevertheless, SED gradients in the marrow were shown to be the best predictor of osteoblastic and osteoclastic activity (R(2)=0.83 and 0.60, respectively, p<0.001). These data suggest that the mechanical environment of the bone marrow plays a significant role in determining osteoblast and osteoclast activity.
NASA Astrophysics Data System (ADS)
Du, Minshu; Wan, Qiong; Wang, Zhongqiang; Cui, Lishan
2016-08-01
The application of elastic strain is a promising approach for tuning bandgap of semiconductors; however, the attainment of a simple method for introducing strain has been a major challenge. Here, martensitic surface relief of FeNiCoTi substrate was utilized to tensilely strain TiO2 nanofilm successfully. The elastic strain effects of photocatalysis were also investigated. It was showed that tensile strain reduced the bandgap of TiO2 nanofilm by 50 meV and contributed to a 33.8% faster photodegradation rate of methyl orange, also the photocurrent of the water oxidation reaction of strained TiO2 was 1.4 times as high as that of unstrained nanofilm.
Efficient implicit integration for finite-strain viscoplasticity with a nested multiplicative split
NASA Astrophysics Data System (ADS)
Shutov, A. V.
2016-07-01
An efficient and reliable stress computation algorithm is presented, which is based on implicit integration of the local evolution equations of multiplicative finite-strain plasticity/viscoplasticity. The algorithm is illustrated by an example involving a combined nonlinear isotropic/kinematic hardening; numerous backstress tensors are employed for a better description of the material behavior. The considered material model exhibits the so-called weak invariance under arbitrary isochoric changes of the reference configuration, and the presented algorithm retains this useful property. Even more: the weak invariance serves as a guide in constructing this algorithm. The constraint of inelastic incompressibility is exactly preserved as well. The proposed method is first-order accurate. Concerning the accuracy of the stress computation, the new algorithm is comparable to the Euler Backward method with a subsequent correction of incompressibility (EBMSC) and the classical exponential method (EM). Regarding the computational efficiency, the new algorithm is superior to the EBMSC and EM. Some accuracy tests are presented using parameters of the aluminum alloy 5754-O and the 42CrMo4 steel. FEM solutions of two boundary value problems using MSC.MARC are presented to show the correctness of the numerical implementation.
Elastic and plastic strain measurement in high temperature environment using laser speckle
NASA Technical Reports Server (NTRS)
Chiang, Fu-Pen
1992-01-01
Two laser speckle methods are described to measure strain in high temperature environment and thermal strain caused by high temperature. Both are non-contact, non-destructive and remote sensing techniques that can be automated. The methods have different but overlapping ranges of application with one being more suitable for large plastic deformation.
NASA Astrophysics Data System (ADS)
Mozafari, E.; Shulumba, N.; Steneteg, P.; Alling, B.; Abrikosov, Igor A.
2016-08-01
We present a theoretical scheme to calculate the elastic constants of magnetic materials in the high-temperature paramagnetic state. Our approach is based on a combination of disordered local moments picture and ab initio molecular dynamics (DLM-MD). Moreover, we investigate a possibility to enhance the efficiency of the simulations of elastic properties using the recently introduced method: symmetry imposed force constant temperature-dependent effective potential (SIFC-TDEP). We have chosen cubic paramagnetic CrN as a model system. This is done due to its technological importance and its demonstrated strong coupling between magnetic and lattice degrees of freedom. We have studied the temperature-dependent single-crystal and polycrystalline elastic constants of paramagentic CrN up to 1200 K. The obtained results at T = 300 K agree well with the experimental values of polycrystalline elastic constants as well as the Poisson ratio at room temperature. We observe that the Young's modulus is strongly dependent on temperature, decreasing by ˜14 % from T = 300 K to 1200 K. In addition we have studied the elastic anisotropy of CrN as a function of temperature and we observe that CrN becomes substantially more isotropic as the temperature increases. We demonstrate that the use of Birch law may lead to substantial errors for calculations of temperature induced changes of elastic moduli. The proposed methodology can be used for accurate predictions of mechanical properties of magnetic materials at temperatures above their magnetic order-disorder phase transition.
Hutula, D.N.; Wiancko, B.E.
1980-03-01
ACCEPT is a three-dimensional finite element computer program for analysis of large-deformation elastic-plastic-creep response of Zircaloy tubes subjected to temperature, surface pressures, and axial force. A twenty-mode, tri-quadratic, isoparametric element is used along with a Zircaloy materials model. A linear time-incremental procedure with residual force correction is used to solve for the time-dependent response. The program features an algorithm which automatically chooses the time step sizes to control the accuracy and numerical stability of the solution. A contact-separation capability allows modeling of interaction of reactor fuel rod cladding with fuel pellets or external supports.
NASA Technical Reports Server (NTRS)
Salpekar, S. A.; Raju, I. S.; Obrien, T. K.
1987-01-01
Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtural crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finite-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.
Strain coupling mechanisms and elastic relaxation associated with spin state transitions in LaCoO3
NASA Astrophysics Data System (ADS)
Zhang, Zhiying; Koppensteiner, Johannes; Schranz, Wilfried; Prabhakaran, Dharmalingam; Carpenter, Michael A.
2011-04-01
Advantage is taken of the wealth of experimental data relating to the evolution with temperature of spin states of Co3 + in LaCoO3 in order to undertake a detailed investigation of the mechanisms by which changes in electronic structure can influence strain, and elastic and anelastic relaxations in perovskites. The macroscopic strain accompanying changes in the spin state in LaCoO3 is predominantly a volume strain arising simply from the change in effective ionic radius of the Co3 + ions. This acts to renormalize the octahedral tilting transition temperature in a manner that is easily understood in terms of coupling between the tilt and spin order parameters. Results from resonant ultrasound spectroscopy at high frequencies (0.1-1.5 MHz) reveal stiffening of the shear modulus which scales qualitatively with a spin order parameter defined in terms of changing Co-O bond lengths. From this finding, in combination with results from dynamic mechanical analysis at low frequencies (0.1-50 Hz) and data from the literature, four distinctive anelastic relaxation mechanisms are identified. The relaxation times of these are displayed on an anelasticity map and are tentatively related to spin-spin relaxation, spin-lattice relaxation, migration of twin walls and migration of magnetic polarons. The effective activation energy for the freezing of twin wall motion below ~ 590 K at low frequencies was found to be 182 ± 21 kJ mol - 1 (1.9 ± 0.2 eV) which is attributed to pinning by pairs of oxygen vacancies, though the local mechanisms appear to have a spread of relaxation times. It seems inevitable that twin walls due to octahedral tilting must have quite different characteristics from the matrix in terms of local spin configurations of Co3 + . A hysteresis in the elastic properties at high temperatures further emphasizes the importance of oxygen content in controlling the properties of LaCoO3.
Le Floc’h, Simon; Cloutier, Guy; Saijo, Yoshifumi; Finet, Gérard; Yazdani, Saami K.; Deleaval, Flavien; Rioufol, Gilles; Pettigrew, Roderic I.; Ohayon, Jacques
2016-01-01
Plaque elasticity (i.e. modulogram) and morphology are good predictors of plaque vulnerability. Recently, our group developed an intravascular ultrasound (IVUS) elasticity reconstruction method which was successfully implemented in vitro using vessel phantoms. In vivo IVUS modulography, however, remains a major challenge as the motion of the heart prevents accurate strain field estimation. We therefore designed a technique to extract accurate strain fields and modulograms from recorded IVUS sequences. We identified a set of four criteria based on tissue overlapping, RF-correlation coefficient between two successive frames, performance of the elasticity reconstruction method to recover the measured radial strain, and reproducibility of the computed modulograms over the cardiac cycle. This 4-CSP was successfully tested on IVUS sequences obtained in twelve patients referred for a directional coronary atherectomy intervention. This study demonstrates the potential of the IVUS modulography technique based on the proposed 4-CSP to detect vulnerable plaques in vivo. PMID:23196202
Umemoto, Takeshi; Ueno, Ei; Matsumura, Takeshi; Yamakawa, Makoto; Bando, Hiroko; Mitake, Tsuyoshi; Shiina, Tsuyoshi
2014-08-01
The aim of this study was to reveal the background to the image variations in strain elastography (strain imaging [SI]) depending on the manner of manipulation (compression magnitude) during elasticity image (EI) acquisition. Thirty patients with 33 breast lesions who had undergone surgery followed by SI assessment in vivo were analyzed. An analytical approach to tissue elasticity based on the stress-elastic modulus (Young's modulus) relationship was adopted. Young's moduli were directly measured ex vivo in surgical specimens ranging from 2.60 kPa (fat) to 16.08 kPa (invasive carcinoma) under the weak-stress condition (<0.2-0.4 kPa, which corresponds to the appropriate "light touch" technique in SI investigation. The contrast (ratio) of lesion to fat in elasticity ex vivo gradually decreased as the stress applied increased (around 1.0 kPa) on the background of significant non-linearity of the breast tissue. Our results indicate that the differences in non-linearity in elasticity between the different tissues within the breast under minimal stress conditions are closely related to the variation in EI quality. The significance of the "pre-load compression" concept in tissue elasticity evaluation is recognized. Non-linearity of elasticity is an essential attribute of living subjects and could provide useful information having a considerable impact on clinical diagnosis in quantitative ultrasound elastography.
Strain concentration factor as a function of strain in a design application
Smith, R.E.
1981-01-01
This paper presents results for a detailed inelastic finite element analysis for a part of the Clinch River Breeder Reactor Control Rod Drive Mechanism. The analysis results indicate that plastic strain concentration factors may in fact be less than corresponding elastic strain concentration factors for nominal strains as low as .2%. This is particularly insightful in that it is presently common practice to approximate inelastic strain concentration factors as the square of the elastic concentration factors. The paper also examines Neuber's relation for predicting strain concentration factors and looks at the variation in the strain concentration factor through the cross-section of the component analyzed.
NASA Astrophysics Data System (ADS)
Liu, P. F.; Yang, Y. H.; Gu, Z. P.; Zheng, J. Y.
2015-12-01
Interaction mechanism between the intralaminar damage and interlaminar delamination of composite laminates is always a challenging issue. It is important to consider the progressive failure and strain softening behaviors simultaneously during the damage modeling and numerical simulation of composites using FEA. This paper performs three-dimensional finite element analysis of the progressive failure and strain localization of composites using FEA. An intralaminar progressive failure model based on the strain components is proposed and the nonlinear cohesive model is used to predict the delamination growth. In particular, the nonlocal integral theory which introduces a length scale into the governing equations is used to regularize the strain localization problems of composite structures. Special finite element codes are developed using ABAQUS to predict the intralaminar and interlaminar damage evolution of composites simultaneously. The carbon fiber/epoxy composite laminates with a central hole demonstrates the developed theoretical models and numerical algorithm by discussing the effects of the mesh sizes and layups patterns. It is shown the strain localization problem can be well solved in the progressive failure analysis of composites when the energy dissipation due to the damage of the fiber, matrix and interface occurs at a relatively wide area.
NASA Astrophysics Data System (ADS)
Frigeri, Sergio; Stefanelli, Ulisse
2012-01-01
We prove the global existence of solutions for a shape-memory alloys constitutive model at finite strains. The model has been presented in Evangelista et al. (Int J Numer Methods Eng 81(6):761-785, 2010) and corresponds to a suitable finite-strain version of the celebrated Souza-Auricchio model for SMAs (Auricchio and Petrini in Int J Numer Methods Eng 55:1255-1284, 2002; Souza et al. in J Mech A Solids 17:789-806, 1998). We reformulate the model in purely variational fashion under the form of a rate-independent process. Existence of suitably weak (energetic) solutions to the model is obtained by passing to the limit within a constructive time-discretization procedure.
Strain-rate Dependence of Elastic Modulus Reveals Silver Nanoparticle Induced Cytotoxicity
Caporizzo, Matthew Alexander; Roco, Charles M.; Ferrer, Maria Carme Coll; Grady, Martha E.; Parrish, Emmabeth; Eckmann, David M.; Composto, Russell John
2015-01-01
Force-displacement measurements are taken at different rates with an atomic force microscope to assess the correlation between cell health and cell viscoelasticity in THP-1 cells that have been treated with a novel drug carrier. A variable indentation-rate viscoelastic analysis, VIVA, is employed to identify the relaxation time of the cells that are known to exhibit a frequency dependent stiffness. The VIVA agrees with a fluorescent viability assay. This indicates that dextran-lysozyme drug carriers are biocompatible and deliver concentrated toxic material (rhodamine or silver nanoparticles) to the cytoplasm of THP-1 cells. By modelling the frequency dependence of the elastic modulus, the VIVA provides three metrics of cytoplasmic viscoelasticity: a low frequency modulus, a high frequency modulus and viscosity. The signature of cytotoxicity by rhodamine or silver exposure is a frequency independent twofold increase in the elastic modulus and cytoplasmic viscosity, while the cytoskeletal relaxation time remains unchanged. This is consistent with the known toxic mechanism of silver nanoparticles, where metabolic stress causes an increase in the rigidity of the cytoplasm. A variable indentation-rate viscoelastic analysis is presented as a straightforward method to promote the self-consistent comparison between cells. This is paramount to the development of early diagnosis and treatment of disease. PMID:26834855
Nakamachi, Eiji; Uchida, Takahiro; Kuramae, Hiroyuki; Morita, Yusuke
2014-08-01
In this study, we developed a multi-scale finite element (FE) analysis code to obtain the stress and strain that occurred in the smooth muscle cell (SMC) at micro-scale, which was seeded in the real fabricated braid fibril artificial blood vessel. This FE code can predict the dynamic response of stress under the blood pressure loading. We try to establish a computer-aided engineering (CAE)-driven scaffold design technique for the blood vessel regeneration. Until now, there occurred the great progresses for the endothelial cell activation and intima layer regeneration in the blood vessel regeneration study. However, there remains the difficulty of the SMC activation and media layer regeneration. Therefore, many researchers are now studying to elucidate the fundamental mechanism of SMC activation and media layer regeneration by using the biomechanical technique. As the numerical tool, we used the dynamic-explicit FE code PAM-CRASH, ESI Ltd. For the material models, the nonlinear viscoelastic constitutive law was adapted for the human blood vessel, SMC and the extra-cellular matrix, and the elastic law for the polyglycolic acid (PGA) fiber. Through macro-FE and micro-FE analyses of fabricated braid fibril tubes by using PGA fiber under the combined conditions of the orientation angle and the pitch of fiber, we searched an appropriate structure for the stress stimulation for SMC functionalization. Objectives of this study are indicated as follows: 1. to analyze the stress and strain of the human blood vessel and SMC, and 2. to calculate stress and strain of the real fabricated braid fibril artificial blood vessel and SMC to search an appropriate PGA fiber structure under combined conditions of PGA fiber numbers, 12 and 24, and the helical orientation angles of fiber, 15, 30, 45, 60, and 75 degrees. Finally, we found a braid fibril tube, which has an angle of 15 degree and 12 PGA fibers, as a most appropriate artificial blood vessel for SMC functionalization.
Development of an elastic cell culture substrate for a novel uniaxial tensile strain bioreactor.
Moles, Matthew D; Scotchford, Colin A; Ritchie, Alastair Campbell
2014-07-01
Bioreactors can be used for mechanical conditioning and to investigate the mechanobiology of cells in vitro. In this study a polyurethane (PU), Chronoflex AL, was evaluated for use as a flexible cell culture substrate in a novel bioreactor capable of imparting cyclic uniaxial tensile strain to cells. PU membranes were plasma etched, across a range of operating parameters, in oxygen. Contact angle analysis and X-ray photoelectron spectroscopy showed increases in wettability and surface oxygen were related to both etching power and duration. Atomic force microscopy demonstrated that surface roughness decreased after etching at 20 W but was increased at higher powers. The etching parameters, 20 W 40 s, produced membranes with high surface oxygen content (21%), a contact angle of 66° ± 7° and reduced topographical features. Etching and protein conditioning membranes facilitated attachment, and growth to confluence within 3 days, of MG-63 osteoblasts. After 2 days with uniaxial strain (1%, 30 cycles/min, 1500 cycles/day), cellular alignment was observed perpendicular to the principal strain axis, and found to increase after 24 h. The results indicate that the membrane supports culture and strain transmission to adhered cells. PMID:23946144
Development of an elastic cell culture substrate for a novel uniaxial tensile strain bioreactor
Moles, Matthew D; Scotchford, Colin A; Ritchie, Alastair Campbell
2014-01-01
Bioreactors can be used for mechanical conditioning and to investigate the mechanobiology of cells in vitro. In this study a polyurethane (PU), Chronoflex AL, was evaluated for use as a flexible cell culture substrate in a novel bioreactor capable of imparting cyclic uniaxial tensile strain to cells. PU membranes were plasma etched, across a range of operating parameters, in oxygen. Contact angle analysis and X-ray photoelectron spectroscopy showed increases in wettability and surface oxygen were related to both etching power and duration. Atomic force microscopy demonstrated that surface roughness decreased after etching at 20 W but was increased at higher powers. The etching parameters, 20 W 40 s, produced membranes with high surface oxygen content (21%), a contact angle of 66° ± 7° and reduced topographical features. Etching and protein conditioning membranes facilitated attachment, and growth to confluence within 3 days, of MG-63 osteoblasts. After 2 days with uniaxial strain (1%, 30 cycles/min, 1500 cycles/day), cellular alignment was observed perpendicular to the principal strain axis, and found to increase after 24 h. The results indicate that the membrane supports culture and strain transmission to adhered cells. © 2013 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 102A: 2356–2364, 2014. PMID:23946144
NASA Technical Reports Server (NTRS)
Salpekar, S. A.; Raju, I. S.; O'Brien, T. K.
1988-01-01
Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtual crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finte-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.
The nonconforming linear strain tetrahedron for a large deformation elasticity problem
NASA Astrophysics Data System (ADS)
Hansbo, Peter; Larsson, Fredrik
2016-08-01
In this paper we investigate the performance of the nonconforming linear strain tetrahedron element introduced by Hansbo (Comput Methods Appl Mech Eng 200(9-12):1311-1316, 2011; J Numer Methods Eng 91(10):1105-1114, 2012). This approximation uses midpoints of edges on tetrahedra in three dimensions with either point continuity or mean continuity along edges of the tetrahedra. Since it contains (rotated) bilinear terms it performs substantially better than the standard constant strain element in bending. It also allows for under-integration in the form of one point Gauss integration of volumetric terms in near incompressible situations. We combine under-integration of the volumetric terms with houglass stabilization for the isochoric terms.
NASA Astrophysics Data System (ADS)
Chakraborty, Bidisha; Heyde, Brecht; Alessandrini, Martino; D'hooge, Jan
2016-04-01
Image registration techniques using free-form deformation models have shown promising results for 3D myocardial strain estimation from ultrasound. However, the use of this technique has mostly been limited to research institutes due to the high computational demand, which is primarily due to the computational load of the regularization term ensuring spatially smooth cardiac strain estimates. Indeed, this term typically requires evaluating derivatives of the transformation field numerically in each voxel of the image during every iteration of the optimization process. In this paper, we replace this time-consuming step with a closed-form solution directly associated with the transformation field resulting in a speed up factor of ~10-60,000, for a typical 3D B-mode image of 2503 and 5003 voxels, depending upon the size and the parametrization of the transformation field. The performance of the numeric and the analytic solutions was contrasted by computing tracking and strain accuracy on two realistic synthetic 3D cardiac ultrasound sequences, mimicking two ischemic motion patterns. Mean and standard deviation of the displacement errors over the cardiac cycle for the numeric and analytic solutions were 0.68+/-0.40 mm and 0.75+/-0.43 mm respectively. Correlations for the radial, longitudinal and circumferential strain components at end-systole were 0.89, 0.83 and 0.95 versus 0.90, 0.88 and 0.92 for the numeric and analytic regularization respectively. The analytic solution matched the performance of the numeric solution as no statistically significant differences (p>0.05) were found when expressed in terms of bias or limits-of-agreement.
Diffraction Profiles of Elasticity Bent Single Crystals with Constant Strain Gradients
Yan,H.; Kalenci, O.; Noyan, I.
2007-01-01
This work presents a set of equations that can be used to predict the dynamical diffraction profile from a non-transparent single crystal with a constant strain gradient examined in Bragg reflection geometry with a spherical incident X-ray beam. In agreement with previous work, the present analysis predicts two peaks: a primary diffraction peak, which would have still been observed in the absence of the strain gradient and which exits the specimen surface at the intersection point of the incident beam with the sample surface, and a secondary (mirage) peak, caused by the deflection of the wavefield within the material, which exits the specimen surface further from this intersection point. The integrated intensity of the mirage peak increases with increasing strain gradient, while its separation from the primary reflection peak decreases. The directions of the rays forming the mirage peak are parallel to those forming the primary diffraction peak. However, their spatial displacement might cause (fictitious) angular shifts in diffractometers equipped with area detectors or slit optics. The analysis results are compared with experimental data from an Si single-crystal strip bent in cantilever configuration, and the implications of the mirage peak for Laue analysis and high-precision diffraction measurements are discussed.
NASA Astrophysics Data System (ADS)
Ankem, Sreeramamurthy; Margolin, Harold
1982-04-01
By use of a NASTRAN18 Computer Program, the Finite Element Method (FEM) has been employed to calculate the effect of particle size, matrix, and volume fraction on the stress-strain relations of α -β titanium alloys. It was found that for a given volume fraction, the calculated stress-strain curve was higher for a finer particle size than for a coarse particle size within the range of the strains considered, and this behavior was seen for all the different volume fraction alloys considered. For a 50:50 vol pct α -β alloy, the stress-strain curve with β, the stronger phase, as the matrix was higher than that with α, the softer phase, as the matrix. The calculated stress-strain curves for four different vol pct α alloys were compared with their corresponding experimental curves, and in general, good agreement was found. Whenever there were discrepancies, they were discussed by comparing the morphology of the mesh used in the calculations with the morphology of the actual materials.
Strain engineering of the elasticity and the Raman shift of nanostructured TiO2
NASA Astrophysics Data System (ADS)
Liu, X. J.; Pan, L. K.; Sun, Z.; Chen, Y. M.; Yang, X. X.; Yang, L. W.; Zhou, Z. F.; Sun, Chang Q.
2011-08-01
Correlation between the elastic modulus (B) and the Raman shift (Δω) of TiO2 and their responses to the variation of crystal size, applied pressure, and measuring temperature have been established as a function depending on the order, length, and energy of a representative bond for the entire specimen. In addition to the derived fundamental information of the atomic cohesive energy, binding energy density, Debye temperature and nonlinear compressibility, theoretical reproduction of the observations clarified that (i) the size effect arises from the under-coordination induced cohesive energy loss and the energy density gain in the surface up to skin depth; (ii) the thermally softened B and Δω results from bond expansion and bond weakening due to vibration; and, (iii) the mechanically stiffened B and Δω results from bond compression and bond strengthening due to mechanical work hardening. With the developed premise, one can predict the changing trends of the concerned properties with derivatives of quantitative information as such from any single measurement alone.
Impact of dislocation cell elastic strain variations on line profiles from deformed copper.
Levine, L. E.; Larson, B. C.; Tischler, J. Z.; Geantil, P.; Kassner, M. E.; Liu, W.; Stoudt, M. R.; NIST; ORNL; Univ. of Southern California
2008-01-01
Energy scanned, sub-micrometer X-ray beams were used to obtain diffraction line profiles from individual dislocation cells in copper single crystals deformed in compression. Sub-micrometer depth resolution was provided by translating a wire through the diffracted beams and using triangulation to determine the depths of the diffracting volumes. Connection to classic volume-averaged results was made by adding the line profiles from 52 spatially resolved dislocation cell measurements. The resulting sub profile is smooth and symmetric, in agreement with early assumptions; the mean strain and full width half maximum are consistent with the average of the parameters extracted from the more exact individual dislocation cell measurements.
Xuan, Chen; Biggins, John
2016-08-01
We deploy linear stability analysis to find the threshold wavelength (λ) and surface tension (γ) of Rayleigh-Plateau type "peristaltic" instabilities in incompressible neo-Hookean solids in a range of cylindrical geometries with radius R_{0}. First we consider a solid cylinder, and recover the well-known, infinite-wavelength instability for γ≥6μR_{0}, where μ is the solid's shear modulus. Second, we consider a volume-conserving (e.g., fluid filled and sealed) cylindrical cavity through an infinite solid, and demonstrate infinite-wavelength instability for γ≥2μR_{0}. Third, we consider a solid cylinder embedded in a different infinite solid, and find a finite-wavelength instability with λ∝R_{0}, at surface tension γ∝μR_{0}, where the constants depend on the two solids' modulus ratio. Finally, we consider an empty cylindrical channel (or filled with expellable fluid) through an infinite solid, and find an instability with finite wavelength, λ≈2R_{0}, for γ≥2.543...μR_{0}. Using finite-strain numerics, we show such a channel jumps at instability to a highly peristaltic state, likely precipitating it's blockage or failure. We argue that finite wavelengths are generic for elastocapillary instabilities, with the simple cylinder's infinite wavelength being the exception rather than the rule. PMID:27627392
Xuan, Chen; Biggins, John
2016-08-01
We deploy linear stability analysis to find the threshold wavelength (λ) and surface tension (γ) of Rayleigh-Plateau type "peristaltic" instabilities in incompressible neo-Hookean solids in a range of cylindrical geometries with radius R_{0}. First we consider a solid cylinder, and recover the well-known, infinite-wavelength instability for γ≥6μR_{0}, where μ is the solid's shear modulus. Second, we consider a volume-conserving (e.g., fluid filled and sealed) cylindrical cavity through an infinite solid, and demonstrate infinite-wavelength instability for γ≥2μR_{0}. Third, we consider a solid cylinder embedded in a different infinite solid, and find a finite-wavelength instability with λ∝R_{0}, at surface tension γ∝μR_{0}, where the constants depend on the two solids' modulus ratio. Finally, we consider an empty cylindrical channel (or filled with expellable fluid) through an infinite solid, and find an instability with finite wavelength, λ≈2R_{0}, for γ≥2.543...μR_{0}. Using finite-strain numerics, we show such a channel jumps at instability to a highly peristaltic state, likely precipitating it's blockage or failure. We argue that finite wavelengths are generic for elastocapillary instabilities, with the simple cylinder's infinite wavelength being the exception rather than the rule.
NASA Astrophysics Data System (ADS)
Xuan, Chen; Biggins, John
2016-08-01
We deploy linear stability analysis to find the threshold wavelength (λ ) and surface tension (γ ) of Rayleigh-Plateau type "peristaltic" instabilities in incompressible neo-Hookean solids in a range of cylindrical geometries with radius R0. First we consider a solid cylinder, and recover the well-known, infinite-wavelength instability for γ ≥6 μ R0 , where μ is the solid's shear modulus. Second, we consider a volume-conserving (e.g., fluid filled and sealed) cylindrical cavity through an infinite solid, and demonstrate infinite-wavelength instability for γ ≥2 μ R0 . Third, we consider a solid cylinder embedded in a different infinite solid, and find a finite-wavelength instability with λ ∝R0 , at surface tension γ ∝μ R0 , where the constants depend on the two solids' modulus ratio. Finally, we consider an empty cylindrical channel (or filled with expellable fluid) through an infinite solid, and find an instability with finite wavelength, λ ≈2 R0 , for γ ≥2.543 ...μ R0 . Using finite-strain numerics, we show such a channel jumps at instability to a highly peristaltic state, likely precipitating it's blockage or failure. We argue that finite wavelengths are generic for elastocapillary instabilities, with the simple cylinder's infinite wavelength being the exception rather than the rule.
Rae, Philip J; Trujillo, Carl; Lovato, Manuel
2009-01-01
The assumption that Young's modulus is strain-rate invariant is tested for 6061-T6 aluminium alloy and 1018 steel over 10 decades of strain-rate. For the same billets of material, 3 quasi-static strain-rates are investigated with foil strain gauges at room temperature. The ultrasonic sound speeds are measured and used to calculate the moduli at approximately 10{sup 4} s{sup -1}. Finally, ID plate impact is used to generate an elastic pre-cursor in the alloys at a strain-rate of approximately 10{sup 6} s{sup -1} from which the longitudinal sound speed may be obtained. It is found that indeed the Young's modulus is strain-rate independent within the experimental accuracy.
Strain Rate Tensor Estimation in Cine Cardiac MRI Based on Elastic Image Registration
NASA Astrophysics Data System (ADS)
Sánchez-Ferrero, Gonzalo Vegas; Vega, Antonio Tristán; Grande, Lucilio Cordero; de La Higuera, Pablo Casaseca; Fernández, Santiago Aja; Fernández, Marcos Martín; López, Carlos Alberola
In this work we propose an alternative method to estimate and visualize the Strain Rate Tensor (SRT) in Magnetic Resonance Images (MRI) when Phase Contrast MRI (PCMRI) and Tagged MRI (TMRI) are not available. This alternative is based on image processing techniques. Concretely, image registration algorithms are used to estimate the movement of the myocardium at each point. Additionally, a consistency checking method is presented to validate the accuracy of the estimates when no golden standard is available. Results prove that the consistency checking method provides an upper bound of the mean squared error of the estimate. Our experiments with real data show that the registration algorithm provides a useful deformation field to estimate the SRT fields. A classification between regional normal and dysfunctional contraction patterns, as compared with experts diagnosis, points out that the parameters extracted from the estimated SRT can represent these patterns. Additionally, a scheme for visualizing and analyzing the local behavior of the SRT field is presented.
Gurson-type elastic-plastic damage model based on strain-rate plastic potential
NASA Astrophysics Data System (ADS)
Balan, Tudor; Cazacu, Oana
2013-12-01
Ductile damage is generally described by stress-space analytical potentials. In this contribution, it is shown that strain rate potentials, which are exact conjugate of the stress-based potentials, can be equally used to describe the dilatational response of porous metals. This framework is particularly appropriate for porous materials with matrix described by complex yield criteria for which a closed-form expression of the stress-based potential is not available. Illustration of the new approach is done for porous metals containing randomly distributed spherical voids in a von Mises elasto-plastic matrix. Furthermore, a general time integration algorithm for simulation of the mechanical response using this new formulation is developed and implemented in Abaqus/Standard. The proposed model and algorithm are validated with respect to the Abaqus built-in GTN model, which is based on a stress potential, through the simulation of a tensile test on a round bar.
NASA Astrophysics Data System (ADS)
Li, Dong-Feng; O'Dowd, Noel P.
2011-12-01
In this work, a three dimensional crystal plasticity-based finite element model is presented to examine the micromechanical behaviour of austenitic stainless steels. The model accounts for realistic polycrystal micromorphology, the kinematics of crystallographic slip, lattice rotation, slip interaction (latent hardening) and geometric distortion at finite deformation. We utilise the model to predict the microscopic lattice strain evolution of austenitic stainless steels during uniaxial tension at ambient temperature with validation through in situ neutron diffraction measurements. Overall, the predicted lattice strains are in very good agreement with those measured in both longitudinal and transverse directions (parallel and perpendicular to the tensile loading axis, respectively). The information provided by the model suggests that the observed nonlinear response in the transverse {200} grain family is associated with a competitive bimodal evolution of strain during inelastic deformation. The results associated with latent hardening effects at the microscale also indicate that in situ neutron diffraction measurements in conjunction with macroscopic uniaxial tensile data may be used to calibrate crystal plasticity models for the prediction of the inelastic material deformation response.
K.R. Arpin; T.F. Trimble
2003-04-01
This testing was undertaken to develop material true stress-true strain curves for elastic-plastic material behavior for use in performing transient analysis. Based on the conclusions of this test, the true stress-true strain curves derived herein are valid for use in elastic-plastic finite element analysis for structures fabricated from these materials. In addition, for the materials tested herein, the ultimate strain values are greater than those values cited as the limits for the elastic-plastic strain acceptance criteria for transient analysis.
NASA Astrophysics Data System (ADS)
Ichimura, Tsuyoshi; Agata, Ryoichiro; Hori, Takane; Hirahara, Kazuro; Hashimoto, Chihiro; Hori, Muneo; Fukahata, Yukitoshi
2016-07-01
As a result of the accumulation of high-resolution observation data, 3-D high-fidelity crustal structure data for large domains are becoming available. However, it has been difficult to use such data to perform elastic/viscoelastic crustal deformation analyses in large domains with quality assurance of the numerical simulation that guarantees convergence of the numerical solution with respect to the discretization size because the costs of analysis are significantly high. This paper proposes a method of constructing a high-fidelity crustal structure finite element (FE) model using high-fidelity crustal structure data and fast FE analysis to reduce the costs of analysis (based on automatic FE model generation for parallel computation, OpenMP/MPI hybrid parallel computation on distributed memory computers, a geometric multigrid, variable preconditioning and multiple precision arithmetic). Using the proposed methods, we construct 10 billion degree-of-freedom high-fidelity crustal structure FE models for the entire Japan, and conduct elastic/viscoelastic crustal deformation analysis using this model with enough high accuracy of the numerical simulation.
NASA Astrophysics Data System (ADS)
Teratani, N.; Sagiya, T.; Nishimura, T.; Yarai, H.; Suito, H.
2014-12-01
Itoigawa-Shizuoka Tectonic Line (ISTL) in central Japan is one of the most active fault systems in Japan. The Japanese government evaluated a M8 class earthquake may occur at the Gofukuji fault in the central ISTL with a possibility of 14% in the next 30 years. So we analyze GPS data around the northern and the central ISTL to monitor tectonic strain accumulation and to propose a fault model for future earthquake in this area. Along the northern and central ISTL, there exist active faults such as the Kamishiro fault (KF), the East Mathumoto Basin fault (EMBF) and the Gofukuji fault (GF). KF and EMBF are east-dipping reverse faults, and GF is a left-lateral strike slip fault. We analyzed GPS data of 34 campaign sites during 2002-2010 and 55 continuous sites during 1998-2013 to obtain 3-dimentional velocities in the ITRF 2008 reference frame. Around GF, the velocity field represents a typical inter-seismic pattern around a strike slip fault. By applying an elastic dislocation model, we estimate a fault slip rate as 5-7 mm/yr with a locking depth of over 5 km. These parameters are consistent with the seismogenic zone depth and the geological slip rate of GF. On the other hand, for KF and EMBF, we model the deformation pattern with faults in an elastic layer overlying a viscoelastic substratum to represent steady contraction. The modeling result shows KF dips at 30-40 degree and its locking depth is only 2 km, implying that the whole fault is creeping. EMBF dips at 40-50 degree with a locking depth of 2 km. The results indicate that there is ongoing stress accumulation around GF, but KF and EMBF accommodates contraction inelastically. GF at the central ISTL is considered to store strain energy more than 1.000 years and a future major earthquake should occur to release shear stress along the central part. The rupture may continue to the south, but more observation and modeling effect is necessary.
NASA Technical Reports Server (NTRS)
Hashemi-Kia, Mostafa; Kilroy, Kevin L.; Parker, G.
1990-01-01
A computational procedure is described which can be used efficiently in identifying modeling errors which may arise from development of a structural finite element model. The procedure, which is referred to as the multi-level strain energy check, is set up in the form of a set of NASTRAN DMAP alters which provide sufficient information about the modeling errors at G-Set, N-Set, and F-Set levels. This technique was applied to two NASTRAN models, namely, the AH-64A and AH-1G models. Two modeling errors were identified for the AH-1G, which were then corrected.
DNAaseI-hypersensitive minichromosomes of SV40 possess an elastic torsional strain in DNA.
Luchnik, A N; Bakayev, V V; Yugai, A A; Zbarsky, I B; Georgiev, G P
1985-01-01
Previously, we have shown that DNA in a small fraction (2-5%) of SV40 minichromosomes was torsionally strained and could be relaxed by treating minichromosomes with topoisomerase I. This fraction was enriched with endogeneous RNA polymerase II (Luchnik et al., 1982, EMBO J., 1, 1353). Here we show that one and the same fraction of SV40 minichromosomes is hypersensitive to DNAase I and is relaxable by topoisomerase I. Moreover, this fraction completely loses its hypersensitivity to DNAase I upon relaxation. The possibility that this fraction of minichromosomes can be represented by naked DNA is ruled out by the results of studying the kinetics of minichromosome digestion by DNAase I in comparison to digestion of pure SV40 DNA and by measuring the buoyant density of SV40 chromatin in equilibrium CsCl gradient. Our data obtained with SV40 minichromosomes may be relevant to the mechanism responsible for DNAase I hypersensitivity in the loops or domains of cellular chromatin. Images PMID:2987817
Varghese, Bino; Short, David; Penmetsa, Ravi; Goswami, Tarun; Hangartner, Thomas
2011-04-29
Finite element (FE) models of long bones constructed from computed-tomography (CT) data are emerging as an invaluable tool in the field of bone biomechanics. However, the performance of such FE models is highly dependent on the accurate capture of geometry and appropriate assignment of material properties. In this study, a combined numerical-experimental study is performed comparing FE-predicted surface strains with strain-gauge measurements. Thirty-six major, cadaveric, long bones (humerus, radius, femur and tibia), which cover a wide range of bone sizes, were tested under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young's modulus for cortex, density-modulus relationship for trabecular bone and Poisson's ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The R(2) values of the measured strains versus load under three-point bending and torsion were 0.96-0.99 and 0.61-0.99, respectively, for all bones in our dataset. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from -6% to 7% under bending and from -37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.
Chao, Jing; Mark, Alison; Fuller, Marina; Barabash, Rozaliya; McIntyre, Stewart; Holt, Richard A.; Klassen, Robert; Liu, W.
2009-01-01
The magnitude and distribution of elastic strain for a nickel alloy 600 (A600) sample that had been subjected to uniaxial tensile stress were measured by micro Laue diffraction (MLD) and neutron diffraction techniques. For a sample that had been dimensionally strained by 1%, both MLD and neutron diffraction data indicated that the global residual elastic strain was on the order of 10{sup -4}, however the micro-diffraction data indicated considerable grain-to-grain variability amongst individual components of the residual strain tensor. A more precise comparison was done by finding those grains in the MLD map that had appropriate
NASA Astrophysics Data System (ADS)
Kroon, M.
2011-11-01
Rubbers and soft biological tissues may undergo large deformations and are also viscoelastic. The formulation of constitutive models for these materials poses special challenges. In several applications, especially in biomechanics, these materials are also relatively thin, implying that in-plane stresses dominate and that plane stress may therefore be assumed. In the present paper, a constitutive model for viscoelastic materials in the finite strain regime and under the assumption of plane stress is proposed. It is assumed that the relaxation behaviour in the direction of plane stress can be treated separately, which makes it possible to formulate evolution laws for the plastic strains on explicit form at the same time as incompressibility is fulfilled. Experimental results from biomechanics (dynamic inflation of dog aorta) and rubber mechanics (biaxial stretching of rubber sheets) were used to assess the proposed model. The assessment clearly indicates that the model is fully able to predict the experimental outcome for these types of material.
Strain-mediated elastic coupling in magnetoelectric nickel/barium-titanate heterostructures
NASA Astrophysics Data System (ADS)
Streubel, Robert; Köhler, Denny; Schäfer, Rudolf; Eng, Lukas M.
2013-02-01
Multiferroic nanomaterials bear the potential for assembling a manifold of novel and smart devices. For room temperature (RT) applications, however, only the BiFeO3 single-phase perovskites are potential candidates to date. Nevertheless, vertical heterostructures separating magnetic and ferroelectric functionality into different layers are now widely proposed to circumvent this lack in materials’ availability. We show here that the second approach is very profitable as illustrated by the strain-mediated coupling between such two layers, i.e., a ferroelectric barium titanate single-crystal (BTO) and a magnetostrictive nickel (Ni) thin film. Applying an electric field across the BTO substrate forces the magnetic easy axis in the Ni film to rotate by 90∘, resulting in a magnetic anisotropy in the range of -1.2 to -33 kJ/m3. We show that local switching proceeds through the nucleation and growth of straight Néel-domain walls at a cost of zigzag walls. The process is fully reversible and continuously tunable as investigated with magnetooptical Kerr microscopy and magnetic force microscopy probing the local in-plane and out-of-plane magnetizations, respectively. Moreover, the degree of anisotropy can be pre-engineered by depositing the Ni film either at RT, above the Curie temperature Tc of BTO, or at an intermediate temperature. Our findings give evidence for using the reported coupling in modern devices, such as magnetoresistive random access memories, spin valves, spin-polarized electron emission, but equally for the bottom-up assembling of magnetizable molecular nanostructures through magnetic domain wall engineering.
NASA Astrophysics Data System (ADS)
Liu, X. J.; Zhou, Z. F.; Yang, L. W.; Li, J. W.; Xie, G. F.; Fu, S. Y.; Sun, C. Q.
2011-04-01
As a group of wonder materials, gold and silver at the nanoscale demonstrate many intriguing properties that cannot be seen from their bulk counterparts. However, consistent insight into the mechanism behind the fascinations and their interdependence given by one integrated model is highly desirable. Based on Goldschmidt-Pauling's rule of bond contraction and its extension to the local bond energy, binding energy density, and atomic cohesive energy, we have developed such a model that is able to reconcile the observed size dependence of the lattice strain, core level shift, elastic modulus, and thermal stability of Au and Ag nanostructures from the perspective of skin-depth bond order loss. Theoretical reproduction of the measured size trends confirms that the undercoordination-induced local bond contraction, bond strength gain, and the associated binding energy density gain, the cohesive energy loss and the tunable fraction of such undercoordinated atoms dictate the observed fascinations, which should shed light on the understanding of the unusual behavior of other nanostructured materials as well.
Brunt, Lucy H; Norton, Joanna L; Bright, Jen A; Rayfield, Emily J; Hammond, Chrissy L
2015-09-18
Abnormal joint morphogenesis is linked to clinical conditions such as Developmental Dysplasia of the Hip (DDH) and to osteoarthritis (OA). Muscle activity is known to be important during the developmental process of joint morphogenesis. However, less is known about how this mechanical stimulus affects the behaviour of joint cells to generate altered morphology. Using zebrafish, in which we can image all joint musculoskeletal tissues at high resolution, we show that removal of muscle activity through anaesthetisation or genetic manipulation causes a change to the shape of the joint between the Meckel's cartilage and Palatoquadrate (the jaw joint), such that the joint develops asymmetrically leading to an overlap of the cartilage elements on the medial side which inhibits normal joint function. We identify the time during which muscle activity is critical to produce a normal joint. Using Finite Element Analysis (FEA), to model the strains exerted by muscle on the skeletal elements, we identify that minimum principal strains are located at the medial region of the joint and interzone during mouth opening. Then, by studying the cells immediately proximal to the joint, we demonstrate that biomechanical strain regulates cell orientation within the developing joint, such that when muscle-induced strain is removed, cells on the medial side of the joint notably change their orientation. Together, these data show that biomechanical forces are required to establish symmetry in the joint during development. PMID:26253758
Brunt, Lucy H.; Norton, Joanna L.; Bright, Jen A.; Rayfield, Emily J.; Hammond, Chrissy L.
2015-01-01
Abnormal joint morphogenesis is linked to clinical conditions such as Developmental Dysplasia of the Hip (DDH) and to osteoarthritis (OA). Muscle activity is known to be important during the developmental process of joint morphogenesis. However, less is known about how this mechanical stimulus affects the behaviour of joint cells to generate altered morphology. Using zebrafish, in which we can image all joint musculoskeletal tissues at high resolution, we show that removal of muscle activity through anaesthetisation or genetic manipulation causes a change to the shape of the joint between the Meckel's cartilage and Palatoquadrate (the jaw joint), such that the joint develops asymmetrically leading to an overlap of the cartilage elements on the medial side which inhibits normal joint function. We identify the time during which muscle activity is critical to produce a normal joint. Using Finite Element Analysis (FEA), to model the strains exerted by muscle on the skeletal elements, we identify that minimum principal strains are located at the medial region of the joint and interzone during mouth opening. Then, by studying the cells immediately proximal to the joint, we demonstrate that biomechanical strain regulates cell orientation within the developing joint, such that when muscle-induced strain is removed, cells on the medial side of the joint notably change their orientation. Together, these data show that biomechanical forces are required to establish symmetry in the joint during development. PMID:26253758
Rayfield, Emily J
2011-01-01
Finite element (FE) analysis is becoming a frequently used tool for exploring the craniofacial biomechanics of extant and extinct vertebrates. Crucial to the application of the FE analysis is the knowledge of how well FE results replicate reality. Here I present a study investigating how accurately FE models can predict experimentally derived strain in the mandible of the ostrich Struthio camelus, when both the model and the jaw are subject to identical conditions in an in-vitro loading environment. Three isolated ostrich mandibles were loaded hydraulically at the beak tip with forces similar to those measured during force transducer pecking experiments. Strains were recorded at four gauge sites at the dorsal and ventral dentary, and medial and lateral surangular. Specimen-specific FE models were created from computed tomography scans of each ostrich and loaded in an identical fashion as in the in-vitro test. The results show that the strain magnitudes, orientation, patterns and maximum : minimum principal strain ratios are predicted very closely at the dentary gauge sites, even though the FE models have isotropic and homogeneous material properties and solid internal geometry. Although the strain magnitudes are predicted at the postdentary sites, the strain orientations and ratios are inaccurate. This mismatch between the dentary and postdentary predictions may be due to the presence of intramandibular sutures or the greater amount of cancellous bone present in the postdentary region of the mandible and requires further study. This study highlights the predictive potential of even simple FE models for studies in extant and extinct vertebrates, but also emphasizes the importance of geometry and sutures. It raises the question of whether different parameters are of lesser or greater importance to FE validation for different taxonomic groups. PMID:20846282
NASA Astrophysics Data System (ADS)
Ooi, B. L.; Gilbert, J. M.; Aziz, A. Rashid A.
2016-08-01
Owing to the increasing demand for harvesting energy from environmental vibration for use in self-powered electronic applications, cantilever-based vibration energy harvesting has attracted considerable interest from various parties and has become one of the most common approaches to converting redundant mechanical energy into electrical energy. As the output voltage produced from a piezoelectric material depends largely on the geometric shape and the size of the beam, there is a need to model and compare the performance of cantilever beams of differing geometries. This paper presents the study of strain distribution in various shapes of cantilever beams, including a convex and concave edge profile elliptical beam that have not yet been discussed in any prior literature. Both analytical and finite-element models are derived and the resultant strain distributions in the beam are computed based on a MATLAB solver and ANSYS finite-element analysis tools. An optimum geometry for a vibration-based energy harvesting system is verified. Finally, experimental results comparing the power density for triangular and rectangular piezoelectric beams are also presented to validate the findings of the study, and the claim, as suggested in the literature, is verified.
NASA Technical Reports Server (NTRS)
Xue, W.-M.; Atluri, S. N.
1985-01-01
In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain 'simplified hybrid-mixed methods' in general, and the so-called 'simplified hybrid-displacement method' in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the 'discrete' BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed at the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.
Nonlinear elastic effects in bismuth whiskers
NASA Astrophysics Data System (ADS)
Powell, B. E.; Skove, M. J.
1983-03-01
Finite deformations have a stress (σ)-strain (ɛ) relation of the form ɛ=s'11σ +δ(s11σ)2, where s'11 is an elastic compliance and δ is a combination of second-order and third-order elastic constants. Tensile tests performed on bismuth whisker crystals oriented in the <111¯> and <11¯0> directions give δ111¯ =7.6±0.5 and δ11¯0 =0±0.3, respectively. Orientations are given in the rhombohedral system in which the angle between axes is approximately 57°.
NASA Astrophysics Data System (ADS)
Lan, Haiqiang; Zhang, Zhongjie
2011-06-01
The finite-difference (FD) method is a powerful tool in seismic wave field modelling for understanding seismic wave propagation in the Earth's interior and interpreting the real seismic data. The accuracy of FD modelling partly depends on the implementation of the free-surface (i.e. traction-free) condition. In the past 40 years, at least six kinds of free-surface boundary condition approximate schemes (such as one-sided, centred finite-difference, composed, new composed, implicit and boundary-modified approximations) have been developed in FD second-order elastodynamic simulation. Herein we simulate seismic wave fields in homogeneous and lateral heterogeneous models using these free-surface boundary condition approximate schemes and evaluate their stability and applicability by comparing with corresponding analytical solutions, and then quantitatively evaluate the accuracies of different approximate schemes from the misfit of the amplitude and phase between the numerical and analytical results. Our results confirm that the composed scheme becomes unstable for the Vs/Vp ratio less than 0.57, and suggest that (1) the one-sided scheme is only accurate to first order and therefore introduces serious errors for the shorter wavelengths, other schemes are all of second-order precision; (2) the new composed, implicit and boundary-modified schemes are stable even when the Vs/Vp ratio is less than 0.2; (3) the implicit and boundary-modified schemes are able to deal with laterally varying (heterogeneous) free surface; (4) in the corresponding stability range, the one-sided scheme shows remarkable errors in both phase and amplitude compared to analytical solution (which means larger errors in travel-time and reflection strength), the other five approximate schemes show better performance in travel-time (phase) than strength (amplitude).
Three-dimensional geometry of kink bands in slates and its relationship with finite strain
NASA Astrophysics Data System (ADS)
Kirschner, D. L.; Teixell, A.
1996-09-01
Contractional, monoclinal kink bands that dip to the south and southwest deform northdipping slaty cleavage in Permian rocks of the Somport area (central Pyrenees). These bands are strongly curved such that the poles (normals) to individual kink bands define E-W-striking great-circle girdles in stereographic nets. The kink bands form an anastomosing network that isolates lozenge-shaped, undeformed domains. Cross-cutting relations between intersecting kink bands indicate that all the kink bands in the Somport slate formed penecontemporaneously during a single deformation event. Total strain accommodated by the kink bands at Somport is small. Bulk shortening has been calculated assuming that slip during kinking was perpendicular to local kink fold axes. Bulk shortening of 3% and less than 1% have been calculated in the subvertical and E-W-striking subhorizontal directions respectively, indicative of constrictonal strain. We propose the unusual geometry of the strongly curved kink bands at Somport is partly the product of non-plane-strain deformation. A model is developed that predicts the formation of up to four sets of kink bands during coaxial, non-plane-strain deformation, while two non-conjugate sets form during non-coaxial, non-plane-strain deformation such as occurred at Somport. This model is a natural extension of models proposed for the geometry and kinematics of brittle faults formed during non-plane-strain deformation. The kink bands at Somport probably formed before the cessation of Pyrenean convergence and were related to a modest gravity-induced spreading in the hinterland of the orogenic belt.
NASA Astrophysics Data System (ADS)
Sun, Yongle; Li, Q. M.; Withers, P. J.
2015-09-01
Realistic simulations are increasingly demanded to clarify the dynamic behaviour of foam materials, because, on one hand, the significant variability (e.g. 20% scatter band) of foam properties and the lack of reliable dynamic test methods for foams bring particular difficulty to accurately evaluate the strain-rate sensitivity in experiments; while on the other hand numerical models based on idealised cell structures (e.g. Kelvin and Voronoi) may not be sufficiently representative to capture the actual structural effect. To overcome these limitations, the strain-rate sensitivity of the compressive and tensile properties of closed-cell aluminium Alporas foam is investigated in this study by means of meso-scale realistic finite element (FE) simulations. The FE modelling method based on X-ray computed tomography (CT) image is introduced first, as well as its applications to foam materials. Then the compression and tension of Alporas foam at a wide variety of applied nominal strain-rates are simulated using FE model constructed from the actual cell geometry obtained from the CT image. The stain-rate sensitivity of compressive strength (collapse stress) and tensile strength (0.2% offset yield point) are evaluated when considering different cell-wall material properties. The numerical results show that the rate dependence of cell-wall material is the main cause of the strain-rate hardening of the compressive and tensile strengths at low and intermediate strain-rates. When the strain-rate is sufficiently high, shock compression is initiated, which significantly enhances the stress at the loading end and has complicated effect on the stress at the supporting end. The plastic tensile wave effect is evident at high strain-rates, but shock tension cannot develop in Alporas foam due to the softening associated with single fracture process zone occurring in tensile response. In all cases the micro inertia of individual cell walls subjected to localised deformation is found to
NASA Astrophysics Data System (ADS)
Li, Hong; Zhang, Wei; Zhang, Zhenguo; Chen, Xiaofei
2015-07-01
A discontinuous grid finite-difference (FD) method with non-uniform time step Runge-Kutta scheme on curvilinear collocated-grid is developed for seismic wave simulation. We introduce two transition zones: a spatial transition zone and a temporal transition zone, to exchange wavefield across the spatial and temporal discontinuous interfaces. A Gaussian filter is applied to suppress artificial numerical noise caused by down-sampling the wavefield from the finer grid to the coarser grid. We adapt the non-uniform time step Runge-Kutta scheme to a discontinuous grid FD method for further increasing the computational efficiency without losing the accuracy of time marching through the whole simulation region. When the topography is included in the modelling, we carry out the discontinuous grid method on a curvilinear collocated-grid to obtain a sufficiently accurate free-surface boundary condition implementation. Numerical tests show that the proposed method can sufficiently accurately simulate the seismic wave propagation on such grids and significantly reduce the computational resources consumption with respect to regular grids.
Pettit, J. R.; Walker, A.; Lowe, M. J. S.
2014-02-18
Defects which posses rough surfaces greatly affect ultrasonic wave scattering behaviour, often reducing the magnitude of reflected signals. Ultrasonic inspections rely upon this response for detecting and sizing flaws. For safety critical components reliable characterisation is crucial. Therefore, providing an accurate means to predict reductions in signal amplitude is essential. An extension of Kirchhoff theory has formed the basis for the UK power industry inspection justifications. However, it is widely recognised that these predictions are pessimistic owing to analytical approximations. A numerical full field modelling approach does not fall victim to such limitations. Here, a Finite Element model is used to aid in setting a non-conservative reporting threshold during the inspection of a large pressure vessel forging that might contain embedded rough defects. The ultrasonic response from multiple rough surfaces defined by the same statistical class is calculated for normal incident compression waves. The approach is validated by comparing coherent scattering with predictions made by Kirchhoff theory. At lower levels of roughness excellent agreement is observed, whilst higher values confirm the pessimism of Kirchhoff theory. Furthermore, the mean amplitude in the specular direction is calculated. This represents the information obtained during an inspection, indicating that reductions due to increasing roughness are significantly less than the coherent component currently being used.
NASA Astrophysics Data System (ADS)
Thizy, C.; Eliot, F.; Ballhause, D.; Olympio, K. R.; Kluge, R.; Shannon, A.; Laduree, G.; Logut, D.; Georges, M. P.
2013-04-01
Thermo-elastic distortions of composite structures have been measured by a holographic camera using a BSO photorefractive crystal as the recording medium. The first test campaign (Phase 1) was performed on CFRP struts with titanium end-fittings glued to the tips of the strut. The samples were placed in a vacuum chamber. The holographic camera was located outside the chamber and configured with two illuminations to measure the relative out-of-plane and in-plane (in one direction) displacements. The second test campaign (Phase 2) was performed on a structure composed of a large Silicon Carbide base plate supported by 3 GFRP struts with glued Titanium end-fittings. Thermo-elastic distortions have been measured with the same holographic camera used in phase 1, but four illuminations, instead of two, have been used to provide the three components of displacement. This technique was specially developed and validated during the phase 2 in CSL laboratory. The system has been designed to measure an object size of typically 250x250 mm2; the measurement range is such that the sum of the largest relative displacements in the three measurement directions is maximum 20 μm. The validation of the four-illuminations technique led to measurement uncertainties of 120 nm for the relative in-plane and out-of-plane displacements, 230 nm for the absolute in-plane displacement and 400 nm for the absolute out-of-plane displacement. For both campaigns, the test results have been compared to the predictions obtained by finite element analyses and the correlation of these results was good.
NASA Astrophysics Data System (ADS)
Tsuzuki, Kentaro; Hasegawa, Hideyuki; Kanai, Hiroshi; Ichiki, Masataka; Tezuka, Fumiaki
2008-05-01
Pathologic changes in arterial walls significantly influence their mechanical properties. We have developed a correlation-based method, the phased tracking method [H. Kanai et al.: IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43 (1996) 791], for measurement of the regional elasticity of the arterial wall. Using this method, elasticity distributions of lipids, blood clots, fibrous tissue, and calcified tissue were measured in vitro by experiments on excised arteries (mean±SD: lipids 89±47 kPa, blood clots 131 ±56 kPa, fibrous tissue 1022±1040 kPa, calcified tissue 2267 ±1228 kPa) [H. Kanai et al.: Circulation 107 (2003) 3018; J. Inagaki et al.: Jpn. J. Appl. Phys. 44 (2005) 4593]. It was found that arterial tissues can be classified into soft tissues (lipids and blood clots) and hard tissues (fibrous tissue and calcified tissue) on the basis of their elasticity. However, there are large overlaps between elasticity distributions of lipids and blood clots and those of fibrous tissue and calcified tissue. Thus, it was difficult to differentiate lipids from blood clots and fibrous tissue from calcified tissue by simply thresholding elasticity value. Therefore, we previously proposed a method by classifying the elasticity distribution in each region of interest (ROI) (not a single pixel) in an elasticity image into lipids, blood clots, fibrous tissue, or calcified tissue based on a likelihood function for each tissue [J. Inagaki et al.: Jpn. J. Appl. Phys. 44 (2006) 4732]. In our previous study, the optimum size of an ROI was determined to be 1,500 µm in the arterial radial direction and 1,500 µm in the arterial longitudinal direction [K. Tsuzuki et al.: Ultrasound Med. Biol. 34 (2008) 573]. In this study, the threshold for the likelihood function used in the tissue classification was set by evaluating the variance in the ultrasonic measurement of radial strain. The recognition rate was improved from 50 to 54% by the proposed thresholding.
Kheirollahi, Hossein; Luo, Yunhua
2015-01-01
Accurate assessment of hip fracture risk is very important to prevent hip fracture and to monitor the effect of a treatment. A subject-specific QCT-based finite element model was constructed to assess hip fracture risk at the critical locations of femur during the single-leg stance and the sideways fall. The aim of this study was to improve the prediction of hip fracture risk by introducing a novel failure criterion to more accurately describe bone failure mechanism. Hip fracture risk index was defined using cross-section strain energy, which is able to integrate information of stresses, strains, and material properties affecting bone failure. It was found that the femoral neck and the intertrochanteric region have higher fracture risk than other parts of the femur, probably owing to the larger content of cancellous bone in these regions. The study results also suggested that women are more prone to hip fracture than men. The findings in this study have a good agreement with those clinical observations reported in the literature. The proposed hip fracture risk index based on strain energy has the potential of more accurate assessment of hip fracture risk. However, experimental validation should be conducted before its clinical applications. PMID:26601105
NASA Astrophysics Data System (ADS)
Das, Sujit; Herklotz, Andreas; Jia Guo, Er; Dörr, Kathrin
2014-04-01
[La0.7Ca0.3MnO3(2.6 nm)/SrTiO3(6.3 nm)]15 superlattices (SLs) have been simultaneously grown by Pulsed Laser Deposition (PLD) on different oxide substrates in an attempt to obtain different residual strain states. The substrates are (100)-oriented SrTiO3 (STO), LaAlO3 (LAO), and piezoelectric 0.72Pb (Mg1.3 Nb2.3)3-0.28PbTiO3 (PMN-PT). The La0.7Ca0.3MnO3 layers show tensile strain of ɛ = 1% on LAO and stronger strain on STO and PMN-PT (ɛ = 1.7%). The magnetization has been measured and is found to be quite different for the three SLs. Reversible biaxial compression of Δɛ=-0.1% using the PMN-PT substrate helps one to estimate which part of the differences in magnetic order among the samples is induced by elastic strain. The influence of elastic strain is found to be substantial, but does not completely account for the different behavior of the samples.
Zou, Chunpeng; Jiao, Yan; Zheng, Chao; Zhao, Yaping; Li, Xingwang
2014-01-01
Background The aim of this study was to investigate the feasibility and value of strain-blood pressure index (SBPI) to assess early changes in elasticity of anterior tibial artery in patients with type 2 diabetes mellitus (T2DM). Material/Methods Eighty-one randomly selected in-patients with T2DM were divided into 2 groups – a vascular complication negative group (n=42) and a vascular complication positive group (n=39). Forty healthy volunteers were enrolled in a control group. Ultrasonographic scans using Xstrain™ technique were conducted for every patient to obtain the maximum circumferential strain (CSmax) of anterior tibial artery; patient blood pressure was also measured for calculating strain-blood pressure index (SBPI=CSmax/[(local pulse pressure)/local diastolic blood pressure] ×100%. Afterwards, SBPIs of various groups were comparatively analyzed. Results Differences in SBPIs among the 3 groups were statistically significant (control group > negative group > positive group, P<0.05). Conclusions SBPI could be used as a new indicator for the evaluation on the anterior tibial arterial elasticity of T2DM patients and it was able to reflect the early elasticity changes in anterior tibial arteries in T2DM patients with atherosclerosis. PMID:25418129
NASA Technical Reports Server (NTRS)
Gayda, J.; Srolovitz, D. J.
1987-01-01
A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, was developed which simulates microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. In this approach, the microstructure is discretized onto a fine lattice. Each element in the lattice is labelled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis was validated by comparing this approach with a closed form, analytical method for stress assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analytical for multiparticle problems were also run and in general the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperature.
Du, Minshu; Cui, Lishan; Cao, Yi; Bard, Allen J
2015-06-17
Both the ligand effect and surface strain can affect the electrocatalytic reactivity. In that matter exists a need to be fundamentally understood; however, there is no effective strategy to isolate the strain effect in electrocatalytic systems. In this research we show how the elastic strain in a platinum nanofilm varies the catalytic activity for the oxygen reduction reaction, a key barrier to the wide applications of fuel cells. NiTi shape memory alloy was selected as the substrate to strain engineer the deposited Pt nanofilm in both compressively and tensilely strained states by taking advantage of the two-way shape memory effect for the first time. We demonstrate that compressive strain weakens the Pt surface adsorption and hence improves the ORR activity, which reflects in a 52% enhancement of the kinetic rate constant and a 27 mV positive shift of the half-wave potential for the compressively strained 5 nm Pt compared to the pristine Pt. Tensile strain has the opposite effect, which is in general agreement with the proposed d-band theory. PMID:25986928
Du, Minshu; Cui, Lishan; Cao, Yi; Bard, Allen J
2015-06-17
Both the ligand effect and surface strain can affect the electrocatalytic reactivity. In that matter exists a need to be fundamentally understood; however, there is no effective strategy to isolate the strain effect in electrocatalytic systems. In this research we show how the elastic strain in a platinum nanofilm varies the catalytic activity for the oxygen reduction reaction, a key barrier to the wide applications of fuel cells. NiTi shape memory alloy was selected as the substrate to strain engineer the deposited Pt nanofilm in both compressively and tensilely strained states by taking advantage of the two-way shape memory effect for the first time. We demonstrate that compressive strain weakens the Pt surface adsorption and hence improves the ORR activity, which reflects in a 52% enhancement of the kinetic rate constant and a 27 mV positive shift of the half-wave potential for the compressively strained 5 nm Pt compared to the pristine Pt. Tensile strain has the opposite effect, which is in general agreement with the proposed d-band theory.
NASA Astrophysics Data System (ADS)
Wakefield, David
Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures. Founded upon their inTENS finite element analysis suite, these activities have broadened to encompass ‘lighter than air' structures such as aerostats, hybrid air-vehicles and stratospheric balloons. Since 2004 Tensys have acted as consultants to the NASA Ultra Long Duration Balloon (ULDB) Program. Early implementations of the super-pressure balloon design chosen for ULDB have shown problems of geometric instability, characterised by improper deployment and the potential for overall geometric instability once deployed. The latter has been reproduced numerically using inTENS, and the former are better understood following a series of large-scale hangar tests simulating launch and ascent. In both cases the solution lies in minimising the film lobing between the tendons. These tendons, which span between base and apex end fittings, cause the characteristic pumpkin shape of the balloons and also provide valuable constraint against excessive film deformation. There is also the requirement to generate a biaxial stress field in order to mobilise in-plane shear stiffness. A consequence of reduced lobing between tendons is the development of higher stresses in the balloon film under pressure. The different thermal characteristics between tendons and film lead to further significant meridional stress under low temperature flight conditions. The non-linear viscoelastic response of the envelope film acts positively to help dissipate excessive stress and local concentrations. However, creep over time may produce lobe geometry variations sufficient to compromise the geometric stability of the balloon. The design of a balloon requires an analysis approach that addresses the questions of stress and stability over the duration of a flight by time stepping analyses using an appropriate material model. This paper summarises the Dynamic Relaxation
Finite strains within recumbent folds of the kishorn Nappe, northwest Scotland
NASA Astrophysics Data System (ADS)
Potts, G. J.
1982-10-01
This study is based on the Torridonian and Cambro-Ordovician rocks of the Kishorn Nappe on the Isle of Skye and the adjacent mainland of Scotland. Grain shape fabric, Skolithos pipe shape analysis and palaeomagnetic techniques have been used to give an indication of the strain distribution and possible mechanisms involved in the generation of the recumbent folds within the Kishorn Nappe. Results indicate that recumbent folding has occurred without internal deformation.
NASA Technical Reports Server (NTRS)
Gayda, J.
1994-01-01
A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, has been developed to simulate microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. Since many of the physical properties of materials are determined by microstructure, it is important to be able to predict and control microstructural development. MCFET uses a microstructural lattice model that can incorporate all relevant driving forces and kinetic considerations. Unlike molecular dynamics, this approach was developed specifically to predict macroscopic behavior, not atomistic behavior. In this approach, the microstructure is discretized into a fine lattice. Each element in the lattice is labeled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis has been validated by comparing this approach with a closed-form, analytical method for stress-assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analyses for multiparticle problems have also been run and, in general, the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperatures. This program is written in FORTRAN for use on a 370 series IBM mainframe. It has been implemented on an IBM 370 running VM/SP and an IBM 3084 running MVS. It requires the IMSL math library and 220K of RAM for execution. The standard distribution medium for this program is a 9-track 1600 BPI magnetic tape in EBCDIC format.
NASA Astrophysics Data System (ADS)
Ali, Nasir; Asghar, Zaheer
2014-09-01
We have investigated the peristaltic motion of a non-Newtonian fluid characterized by the finitely extendable nonlinear elastic-Peterlin (FENE-P) fluid model. A background for the development of the differential constitutive equation of this model has been provided. The flow analysis is carried out both for two-dimensional planar channel and axisymmetric tube. The governing equations have been simplified under the widely used assumptions of long wavelength and low Reynolds number in a frame of reference that moves with constant wave speed. An exact solution is obtained for the stream function and longitudinal pressure gradient with no slip condition. We have portrayed the effects of Deborah number and extensibility parameter on velocity profile, trapping phenomenon, and normal stress. It is observed that normal stress is an increasing function of Deborah number and extensibility parameter. As far as the velocity at the channel (tube) center is concerned, it decreases (increases) by increasing Deborah number (extensibility parameter). The non-Newtonian rheology also affect the size of trapped bolus in a sense that it decreases (increases) by increasing Deborah number (extensibility parameter). Further, it is observed through numerical integration that both Deborah number and extensibility parameter have opposite effects on pressure rise per wavelength and frictional forces at the wall. Moreover, it is shown that the results for the Newtonian model can be deduced as a special case of the FENE-P model
NASA Astrophysics Data System (ADS)
Tullini, Nerio; Tralli, Antonio
2010-01-01
Making use of a mixed variational formulation including the Green function of the soil and assuming as independent fields both the structure displacements and the contact pressure, a finite element (FE) model is derived for the static analysis of a foundation beam resting on elastic half-plane. Timoshenko beam model is adopted to describe structural foundations with low slenderness and to impose displacement compatibility between beam and half-plane without requiring the continuity of the first order derivative of the surface displacements enforced by Euler-Bernoulli beam. Numerical results are obtained by using locking-free Hermite polynomials for the Timoshenko beam and constant reaction over the soil. Foundation beams loaded by many load configurations illustrate accuracy and convergence properties of the proposed formulation. Moreover, the different behaviour of the Euler-Bernoulli and Timoshenko beam models is thoroughly discussed. Rectangular pipe loaded by a force in the upper beam exemplifies the straightforward coupling of the foundation FE with a structure described by usual FEs.
Programmable shape transformation of elastic spherical domes.
Abdullah, Arif M; Braun, Paul V; Hsia, K Jimmy
2016-07-20
We investigate mismatch strain driven programmable shape transformation of spherical domes and report the effects of different geometric and structural characteristics on dome behavior in response to applied mismatch strain. We envision a bilayer dome design where the differential swelling of the inner layer with respect to the passive outer layer in response to changes in dome surroundings (such as the introduction of an organic solvent) introduces mismatch strain within the bilayer system and causes dome shape transformation. Finite element analysis reveals that, in addition to snap-through, spherical domes undergo bifurcation buckling and eventually gradual bending to morph into cylinders with increasing mismatch strain. Besides demonstrating how the snap-through energy barrier depends on the spherical dome shape, our analysis identifies three distinct groups of dome geometries based on their mismatch strain-transformed configuration relationships. Our experiments with polymer-based elastic bilayer domes that exhibit differential swelling in organic solvents qualitatively confirm the finite element predictions. We establish that, in addition to externally applied stimuli (mismatch strain), bilayer spherical dome morphing can be tuned and hence programmed through its geometry and structural characteristics. Incorporation of an elastic instability mechanism such as snap-through within the framework of stimuli-responsive functional devices can improve their response time which is otherwise controlled by diffusion. Hence, our proposed design guidelines can be used to realize deployable, multi-functional, reconfigurable, and therefore, adaptive structures responsive to a diverse set of stimuli across multiple length scales.
Zou, Chunpeng; Jiao, Yan; Li, Xingwang; Zheng, Chao; Chen, Maohua; Hu, Chunhong
2015-01-01
Objective: This study aimed to investigate the correlation between strain and elasticity of the common carotid artery (CCA) by ultrasonography and evaluate its clinical significance in patients with diabetic nephropathy (DN). Methods: A total of 68 DN patients and 54 healthy subjects were randomly recruited from the Ultrasound Department from April 2014 to March 2015. The maximum of circumferential strain (CSmax), maximum of circumferential strain rate (CSRmax), compliance coefficient (CC) and stiffness index (β) of the CCA were determined by ultrasonography in all the patients, and correlation analysis was performed. Results: The CC, CSmax and CSRmax in DN group were significantly lower than in healthy controls (P<0.05), but β was markedly higher than in control group (P<0.05). There was a significantly positive correlation of CSmax and CSRmax with CC and a negative correlation with β in both control group and DN group. Conclusion: There is significant correlation between strain and elastic of the CCA. CSmax and CSRmax may be used to reflect the mechanical characteristics of CCA. PMID:26770367
NASA Astrophysics Data System (ADS)
Britton, Paul; Loughran, Jeff
This paper outlines a computational procedure that has been implemented for the direct measurement of finite material strains from digital images taken of a material surface during plane-strain process experiments. The selection of both hardware and software components of the image processing system is presented, and the numerical procedures developed for measuring the 2D material deformations are described. The algorithms are presented with respect to two-roll milling of sugar cane bagasse, a complex fibro-porous material that undergoes large strains during processing to extract the sucrose-rich liquid. Elaborations are made in regard to numerical developments for other forms of experimentation, algorithm calibrations and measurement improvements. Finite 2D strain results are shown for both confined uniaxial compression and two-roll milling experiments.
A nonlinear elasticity phantom containing spherical inclusions
Pavan, Theo Z.; Madsen, Ernest L.; Frank, Gary R.; Jiang, Jingfeng; Carneiro, Antonio Adilton O.; Hall, Timothy J.
2012-01-01
The strain image contrast of some in vivo breast lesions changes with increasing applied load. This change is attributed to differences in the nonlinear elastic properties of the constituent tissues suggesting some potential to help classify breast diseases by their nonlinear elastic properties. A phantom with inclusions and long-term stability is desired to serve as a test bed for nonlinear elasticity imaging method development, testing, etc. This study reports a phantom designed to investigate nonlinear elastic properties with ultrasound elastographic techniques. The phantom contains four spherical inclusions and was manufactured from a mixture of gelatin, agar and oil. The phantom background and each of the inclusions has distinct Young’s modulus and nonlinear mechanical behavior. This phantom was subjected to large deformations (up to 20%) while scanning with ultrasound, and changes in strain image contrast and contrast-to-noise ratio (CNR) between inclusion and background, as a function of applied deformation, were investigated. The changes in contrast over a large deformation range predicted by the finite element analysis (FEA) were consistent with those experimentally observed. Therefore, the paper reports a procedure for making phantoms with predictable nonlinear behavior, based on independent measurements of the constituent materials, and shows that the resulting strain images (e.g., strain contrast) agrees with that predicted with nonlinear FEA. PMID:22772074
NASA Astrophysics Data System (ADS)
Jain, Rahul; Pal, Surjya Kanta; Singh, Shiv Brat
2016-06-01
Friction Stir Welding (FSW) is a solid state joining process and is handy for welding aluminum alloys. Finite Element Method (FEM) is an important tool to predict state variables of the process but numerical simulation of FSW is highly complex due to non-linear contact interactions between tool and work piece and interdependency of displacement and temperature. In the present work, a three dimensional coupled thermo-mechanical method based on Lagrangian implicit method is proposed to study the thermal history, strain distribution and thermo-mechanical process in butt welding of Aluminum alloy 2024 using DEFORM-3D software. Workpiece is defined as rigid-visco plastic material and sticking condition between tool and work piece is defined. Adaptive re-meshing is used to tackle high mesh distortion. Effect of tool rotational and welding speed on plastic strain is studied and insight is given on asymmetric nature of FSW process. Temperature distribution on the workpiece and tool is predicted and maximum temperature is found in workpiece top surface.
A finite strain nonlinear human mitral valve model with fluid-structure interaction.
Gao, Hao; Ma, Xingshuang; Qi, Nan; Berry, Colin; Griffith, Boyce E; Luo, Xiaoyu
2014-12-01
A computational human mitral valve (MV) model under physiological pressure loading is developed using a hybrid finite element immersed boundary method, which incorporates experimentally-based constitutive laws in a three-dimensional fluid-structure interaction framework. A transversely isotropic material constitutive model is used to characterize the mechanical behaviour of the MV tissue based on recent mechanical tests of healthy human mitral leaflets. Our results show good agreement, in terms of the flow rate and the closing and opening configurations, with measurements from in vivo magnetic resonance images. The stresses in the anterior leaflet are found to be higher than those in the posterior leaflet and are concentrated around the annulus trigons and the belly of the leaflet. The results also show that the chordae play an important role in providing a secondary orifice for the flow when the valve opens. Although there are some discrepancies to be overcome in future work, our simulations show that the developed computational model is promising in mimicking the in vivo MV dynamics and providing important information that are not obtainable by in vivo measurements. PMID:25319496
A finite strain nonlinear human mitral valve model with fluid-structure interaction
Gao, Hao; Ma, Xingshuang; Qi, Nan; Berry, Colin; Griffith, Boyce E; Luo, Xiaoyu
2014-01-01
A computational human mitral valve (MV) model under physiological pressure loading is developed using a hybrid finite element immersed boundary method, which incorporates experimentally-based constitutive laws in a three-dimensional fluid-structure interaction framework. A transversely isotropic material constitutive model is used to characterize the mechanical behaviour of the MV tissue based on recent mechanical tests of healthy human mitral leaflets. Our results show good agreement, in terms of the flow rate and the closing and opening configurations, with measurements from in vivo magnetic resonance images. The stresses in the anterior leaflet are found to be higher than those in the posterior leaflet and are concentrated around the annulus trigons and the belly of the leaflet. The results also show that the chordae play an important role in providing a secondary orifice for the flow when the valve opens. Although there are some discrepancies to be overcome in future work, our simulations show that the developed computational model is promising in mimicking the in vivo MV dynamics and providing important information that are not obtainable by in vivo measurements. © 2014 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd. PMID:25319496
Venkatraman, R. ); Besser, P.R.; Bravman, J.C. ); Brennan, S. )
1994-02-01
Grazing incidence x-ray scattering (GIXS) with a synchrotron source was used to measure elastic strain gradients as a function of temperature in aluminum and aluminum alloy thin films of different thicknesses on silicon. The stresses in the films are induced as a result of the difference in thermal expansion coefficient between film and substrate. Disregarding minor deviations at the surface, it is shown that there are no gross strain gradients in these films in the range of temperatures (between room temperature and 400 [degree]C) considered. Significant x-ray line broadening effects were observed, suggesting an accumulation of dislocations on cooling the films and their annealing out as the films were being reheated. The variation of the dislocation density during thermal cycling compares well in nature with that of the concurrent variation in film stress, indicating that large strain hardening effects contribute towards the film flow stress.
Costanzo, Francesco; Brasseur, James G
2015-03-01
There are strong medical motivations to measure changes in material properties of tubular organs, in vivo and in vitro. The current approach estimates hoop stress from intraluminal pressure using the Laplace law and identifies 'elastic modulus' as the slope of a curve fitted hoop stress plotted against strain data. We show that this procedure is fundamentally flawed because muscle and other soft tissue are closely incompressible, so that the total stress includes a volume-preserving material-dependent hydrostatic response that invalidates the method. Furthermore, we show that the Laplace law incorrectly estimates total stress in biological vessels. However, the great need to estimate elastic modulus leads us to develop an alternative practical method, based on shear stress-strain, i.e. insensitive to nonelastic response from incompressibility, but that uses the same measurement data as the current (incorrect) method. The individual material parameters in the underlying (unknown) constitutive relation combine into an effective shear modulus that is a true measure of elastic response, unaffected by incompressibility and without reference to the Laplace law. Furthermore, our effective shear modulus is determined directly as a function of deformation, rather than as the slope of a fitted curve. We validate our method by comparing effective shear moduli against exact shear moduli for four theoretical materials with different degrees of nonlinearity and numbers of material parameters. To further demonstrate applicability, we reanalyse an in vivo study with our new method and show that it resolves an inconsistent change in modulus with the current method.
Finite Element Simulation of Sheet Metal Forming Using Anisotropic Strain-Rate Potentials
NASA Astrophysics Data System (ADS)
Rabahallah, Meziane; Balan, Tudor; Bouvier, Salima; Bacroix, Brigitte; Teodosiu, Cristian
2007-05-01
In continuum mechanics, plastic anisotropy is described using anisotropic stress potentials or, alternatively, strain-rate potentials. In this work, a stress update algorithm is developed for this later case. The implicit, backward Euler method is adopted. A specific numerical treatment is required to deal with the plasticity criterion, which is not defined explicitly. Also, a sub-stepping procedure is adopted in order to deal with the strong nonlinearity of the yield surfaces when applied to FCC materials. The resulting algorithm is implemented in the static implicit version of the Abaqus FE code. Several recent plastic potentials have been implemented in this framework and their parameters identified for a number of BCC and FCC materials. Numerical simulations of a cup drawing process are performed in order to address the robustness of the implementation and the ability of these potentials to predict e.g. earing for materials with different anisotropy.
Liao, Sheng-Hui; Zhu, Xing-Hao; Xie, Jing; Sohodeb, Vikesh Kumar; Ding, Xi
2016-01-01
The objective of this investigation is to analyze the influence of trabecular microstructure modeling on the biomechanical distribution of the implant-bone interface. Two three-dimensional finite element mandible models, one with trabecular microstructure (a refined model) and one with macrostructure (a simplified model), were built. The values of equivalent stress at the implant-bone interface in the refined model increased compared with those of the simplified model and strain on the contrary. The distributions of stress and strain were more uniform in the refined model of trabecular microstructure, in which stress and strain were mainly concentrated in trabecular bone. It was concluded that simulation of trabecular bone microstructure had a significant effect on the distribution of stress and strain at the implant-bone interface. These results suggest that trabecular structures could disperse stress and strain and serve as load buffers. PMID:27403424
Liao, Sheng-hui; Zhu, Xing-hao; Xie, Jing; Sohodeb, Vikesh Kumar; Ding, Xi
2016-01-01
The objective of this investigation is to analyze the influence of trabecular microstructure modeling on the biomechanical distribution of the implant-bone interface. Two three-dimensional finite element mandible models, one with trabecular microstructure (a refined model) and one with macrostructure (a simplified model), were built. The values of equivalent stress at the implant-bone interface in the refined model increased compared with those of the simplified model and strain on the contrary. The distributions of stress and strain were more uniform in the refined model of trabecular microstructure, in which stress and strain were mainly concentrated in trabecular bone. It was concluded that simulation of trabecular bone microstructure had a significant effect on the distribution of stress and strain at the implant-bone interface. These results suggest that trabecular structures could disperse stress and strain and serve as load buffers. PMID:27403424
An inclusion in one of two joined isotropic elastic half-spaces
NASA Astrophysics Data System (ADS)
Walpole, L. J.
1997-10-01
Two dissimilar, homogeneous and istropic, elastic half-spaces are bonded together over thier infinite plane of contract. An arbitrarily shaped finite part of one of them (an inclusion) tends spontaneously to undergo a unifrom infinitesimal strain, but, as it remains attached to and restrained by the surrounding material, an equilibrated state of stress and strain is established everywhere instead. By adopting a convenient expression for the fundamental field of a point force, we transformed inclusion. For a general shape of the inclussion and for particular spherical and finite cylindrical shapes in detail, we consider the evaluation of the elastic strain energy, especially of the interaction term which depends on the location of the inclusion and both pairs of elastic moduli, and which is of great significance in physical applications.
Albogha, Mhd Hassan; Kitahara, Toru; Todo, Mitsugu; Hyakutake, Hiroto; Takahashi, Ichiro
2016-10-01
Factors responsible for the success or failure of orthodontic mini-implants (OMIs) in clinical settings are unclear. Failure of OMIs was found to be associated with increased maximum principal strain (MaxPN) when assessed using the subject-specific finite element (FE) modeling technique. The purpose of the present study was to identify factors that increase MaxPN and thereby predispose the OMI to failure. Using the FE method, MaxPN was calculated around 28 OMIs placed in orthodontic patients, 6 of which failed during the first 5 months. Sixteen potential risk factors related to patients or to OMI position were measured on computerized tomographic images or calculated in FE models. The impact of these factors on MaxPN was verified using regression analysis. Three factors were found to have significant nonlinear relationships with MaxPN: cortical bone quality, vertical angulation of the OMI, and proximity of the OMI to the tooth in the direction of force. In conclusion, failure of an OMI is a multifactorial problem, and position and angulation of the implant are among the affecting factors. Slight apical inclination and positioning at least 1 mm off the root in the direction of force may significantly decrease failure probability. PMID:26983844
Peng, Qing; De, Suvranu
2014-10-21
Silicane is a fully hydrogenated silicene-a counterpart of graphene-having promising applications in hydrogen storage with capacities larger than 6 wt%. Knowledge of its elastic limit is critical in its applications as well as tailoring its electronic properties by strain. Here we investigate the mechanical response of silicane to various strains using first-principles calculations based on density functional theory. We illustrate that non-linear elastic behavior is prominent in two-dimensional nanomaterials as opposed to bulk materials. The elastic limits defined by ultimate tensile strains are 0.22, 0.28, and 0.25 along armchair, zigzag, and biaxial directions, respectively, an increase of 29%, 33%, and 24% respectively in reference to silicene. The in-plane stiffness and Poisson ratio are reduced by a factor of 16% and 26%, respectively. However, hydrogenation/dehydrogenation has little effect on its ultimate tensile strengths. We obtained high order elastic constants for a rigorous continuum description of the nonlinear elastic response. The limitation of second, third, fourth, and fifth order elastic constants are in the strain range of 0.02, 0.08, and 0.13, and 0.21, respectively. The pressure effect on the second order elastic constants and Poisson's ratio were predicted from the third order elastic constants. Our results could provide a safe guide for promising applications and strain-engineering the functions and properties of silicane monolayers. PMID:25190587
Grassi, Lorenzo; Väänänen, Sami P; Ristinmaa, Matti; Jurvelin, Jukka S; Isaksson, Hanna
2016-03-21
Subject-specific finite element models have been proposed as a tool to improve fracture risk assessment in individuals. A thorough laboratory validation against experimental data is required before introducing such models in clinical practice. Results from digital image correlation can provide full-field strain distribution over the specimen surface during in vitro test, instead of at a few pre-defined locations as with strain gauges. The aim of this study was to validate finite element models of human femora against experimental data from three cadaver femora, both in terms of femoral strength and of the full-field strain distribution collected with digital image correlation. The results showed a high accuracy between predicted and measured principal strains (R(2)=0.93, RMSE=10%, 1600 validated data points per specimen). Femoral strength was predicted using a rate dependent material model with specific strain limit values for yield and failure. This provided an accurate prediction (<2% error) for two out of three specimens. In the third specimen, an accidental change in the boundary conditions occurred during the experiment, which compromised the femoral strength validation. The achieved strain accuracy was comparable to that obtained in state-of-the-art studies which validated their prediction accuracy against 10-16 strain gauge measurements. Fracture force was accurately predicted, with the predicted failure location being very close to the experimental fracture rim. Despite the low sample size and the single loading condition tested, the present combined numerical-experimental method showed that finite element models can predict femoral strength by providing a thorough description of the local bone mechanical response. PMID:26944687
Hanson, David E; Barber, John L; Subramanian, Gopinath
2013-12-14
Molecular networks comprised of crosslinked cis-1,4 polyisoprene, often referred to as "natural rubber," are one of the most common systems for the study of rubber elasticity. Under moderate tensile or compressive strain, network chains begin to assume straighter paths, as local molecular kinks are removed. Isoprene units along the chain backbone are mechanically forced from their equilibrium distributions of 18 possible rotational states into a smaller subset of states, restricted to more linear conformations with the greatest end-to-end distances. There are two consequences to this change: both the configurational entropy and average internal energy decrease. We find that the change in entropy, and resulting change in free energy, gives rise to an elastic force. We derive an expression for a chain extension force constant that we have incorporated in an explicit, three-dimensional meso-scale network simulation code. Using this force model, our simulations predict a macroscopic stress-strain relationship that closely matches published experimental values. We also predict a slight increase in temperature resulting from the change in average internal energy in the affected isoprene units that is consistent with experiments.
Evolution of bulk strain solitons in cylindrical inhomogeneous shells
Shvartz, A. Samsonov, A.; Dreiden, G.; Semenova, I.
2015-10-28
Bulk strain solitary waves in nonlinearly elastic thin-walled cylindrical shells with variable geometrical and physical parameters are studied, and equation for the longitudinal strain component with the variable coefficients is derived. A conservative finite difference scheme is proposed, and the results of numerical simulation of the strain soliton evolution in a shell with the abrupt variations of cross section and physical properties of the material are presented.
Erba, Alessandro
2016-05-18
Symmetry features of the internal-strain tensor of crystals (whose components are mixed second-energy derivatives with respect to atomic displacements and lattice strains) are formally presented, which originate from translational-invariance, atomic equivalences, and atomic invariances. A general computational scheme is devised, and implemented into the public Crystal program, for the quantum-mechanical evaluation of the internal-strain tensor of crystals belonging to any space-group, which takes full-advantage of the exploitation of these symmetry-features. The gain in computing time due to the full symmetry exploitation is documented to be rather significant not just for high-symmetry crystalline systems such as cubic, hexagonal or trigonal, but also for low-symmetry ones such as monoclinic and orthorhombic. The internal-strain tensor is used for the evaluation of the nuclear relaxation term of the fourth-rank elastic and third-rank piezoelectric tensors of crystals, where, apart from a reduction of the computing time, the exploitation of symmetry is documented to remarkably increase the numerical precision of computed coefficients.
Erba, Alessandro
2016-05-18
Symmetry features of the internal-strain tensor of crystals (whose components are mixed second-energy derivatives with respect to atomic displacements and lattice strains) are formally presented, which originate from translational-invariance, atomic equivalences, and atomic invariances. A general computational scheme is devised, and implemented into the public Crystal program, for the quantum-mechanical evaluation of the internal-strain tensor of crystals belonging to any space-group, which takes full-advantage of the exploitation of these symmetry-features. The gain in computing time due to the full symmetry exploitation is documented to be rather significant not just for high-symmetry crystalline systems such as cubic, hexagonal or trigonal, but also for low-symmetry ones such as monoclinic and orthorhombic. The internal-strain tensor is used for the evaluation of the nuclear relaxation term of the fourth-rank elastic and third-rank piezoelectric tensors of crystals, where, apart from a reduction of the computing time, the exploitation of symmetry is documented to remarkably increase the numerical precision of computed coefficients. PMID:27150599
NASA Astrophysics Data System (ADS)
Mukul, Malay; Mitra, Gautam
1998-04-01
The Sheeprock thrust sheet in west-central Utah is an internal thrust sheet in the Provo salient of the Sevier fold-and-thrust belt. We have measured finite strain in quartzites (the dominant lithology), sampled along a square grid within the thrust sheet, using the modified normalized Fry method (McNaught M.A. (1994) Modifying the normalized Fry method for aggregates of non-elliptical grains. Journal of Structural Geology16 493-503). The {X}/{Y} and {X}/{Z} axial ratios from unsampled locations within the sample area were estimated using the spatial statistics approach. The strain ellipsoids exhibit a variable three-dimensional orientation pattern resulting from modification of the initial layer parallel shortening (LPS) strain ellipsoid by fault parallel shear in conjunction with vertical flattening and/or horizontal stretching indicating that the thrust sheet did not undergo plane strain deformation in the transport plane. This suggests that the plane strain assumption used in drawing restorable balanced cross-sections breaks down for internal thrust sheets with more than one penetrative-strain producing deformation event. The {X}/{Z} strain axial ratios decrease away from the thrust towards the middle of the sheet. The {X}/{Y} strain axial ratios from interpolated image diagrams indicate transport-parallel stretching at the front end of the sheet and strike-parallel stretching at the back end of the sheet. The footwall and hanging wall finite strain patterns are similar indicating that most of the strain in the Sheeprock thrust sheet developed early in the deformation history of the thrust sheet before and perhaps during the growth of a large fault propagation fold pair.
Elastic And Plastic Deformations In Butt Welds
NASA Technical Reports Server (NTRS)
Verderaime, V.
1992-01-01
Report presents study of mathematical modeling of stresses and strains, reaching beyond limits of elasticity, in bars and plates. Study oriented toward development of capability to predict stresses and resulting elastic and plastic strains in butt welds.
Correlation of composite material test results with finite element analysis
NASA Astrophysics Data System (ADS)
Guƫu, M.
2016-08-01
In this paper are presented some aspects regarding the method of simulation of composite materials testing with finite element analysis software. There were simulated tensile and shear tests of specimens manufactured from glass fiber reinforced polyester. For specimens manufacturing two types of fabrics were used: unidirectional and bidirectional. Experimentally determined elastic properties of composite material were used as input data. Modeling of composite architecture of the specimens was performed with ANSYS Composite PrepPost software. Finite element analysis stresses and strains on strain gauges bonding area were considered and compared with the real values in a diagram. After results comparison, potential causes of deviations were identified.
Li, Yang; Deng, You-Bin; Bi, Xiao-Jun; Liu, Ya-Ni; Zhang, Jun; Li, Li
2016-07-01
Reduced artery elasticity and reduced myocardial strain were present in patients with bicuspid aortic valve (BAV). Their relation to dilation of proximal aorta is unclear. We aimed to study their relation to dilation of proximal aorta. We studied 57 BAV patients categorized into 2 subgroup according to proximal ascending aortic dimensions (nondilated <35 mm and dilated ≥35 mm). Twenty-nine healthy subjects were recruited as control. Aortic and carotid strain, distensibility and stiffness index were derived. Left ventricular myocardial strain were acquired with speckle-tracking echocardiography. BAV patients with dilation of proximal ascending aorta had lower aortic strain (4.1 ± 4.2 % vs. 7.1 ± 3.5 %) and carotid strain (4.8 ± 1.9 % vs. 10.6 ± 4.2 %), lower aortic distensibility (1.4 ± 1.5 cm(2) dyn(-1) 10(-6) vs. 2.5 ± 1.5 cm(2) dyn(-1) 10(-6)) and carotid distensibility (1.6 ± 0.7 cm(2) dyn(-1) 10(-6) vs. 3.9 ± 2.4 cm(2) dyn(-1) 10(-6)), higher aortic stiffness index (19.7 ± 14.1 vs. 8.3 ± 4.9) and carotid stiffness index (12.2 ± 8.5 vs. 5.0 ± 2.2), and lower global circumferential (-15.9 ± 5.8 % vs. -19.1 ± 4.1 %), radial (19.3 ± 11.6 % vs. 29.8 ± 14.9 %) and longitudinal (-15.7 ± 3.4 % vs. -18.4 ± 3.4 %) compared with those without dilation of proximal ascending aorta. All mean values are different to p < 0.05. Dilation of proximal ascending aorta is associated with more advanced reduction of aortic and carotid elasticity and myocardial strain in BAV patients, supporting the need for detailed and extensive vascular and cardiac surveillance in BAV patients.
NASA Astrophysics Data System (ADS)
Staisch, L.; Styron, R. H.; James, S.; Turner, H. L.; Ashlock, A.; Cavness, C. L.; Collier, X.; Fauria, K.; Feinstein, R.; Murphy, R.; Williams, B.; Mattioli, G. S.; Jansma, P. E.; Cothren, J.
2007-12-01
The Caribbean, North and South American plates are converging at a rate of 2 cm/yr in the central region of the Lesser Antilles arc. Here we report high-precision GPS data in concert with forward modeling of a simplified subduction zone geometry to assess strain accumulation for the Lesser Antilles trench. We are able to constrain both vertical and horizontal surface deformation from campaign and continuous GPS observations from 28 geodetic benchmarks located in Guadeloupe, Dominica and Aves Island. Precise station positions were estimated with GIPSY-OASIS II using an absolute point positioning strategy and final, precise orbits, clocks, earth orientation parameters, and x-files. All position estimates were updated to ITRF05 and a revised Caribbean Euler pole was used to place our observations in a CAR-fixed frame. Surface displacements for each site were estimated over 2-7 years. CAR-fixed velocities are projected onto a 500 kilometer transect from the LA trench to Aves Island and compared to calculated displacements for 88 different subduction models. Finite dislocations within an elastic half-space with variable parameters such as angle of the subducting slab, the downdip extent of the locked zone, and percentage of plate interface locking were investigated. Other parameters, such as trench length and slip remained constant. Using a chi-squared, best-fit statistical criterion, the GPS data constrain the subduction interface to a 75 kilometer downdip extent, a 10° dip angle, and near 50% locking. This implies that the subduction zone offshore Dominica is in an interseismic state, thus accumulating strain and causing small westward and upward displacement of the Lesser Antilles relative to the stable Caribbean interior.
NASA Astrophysics Data System (ADS)
Mosby, Matthew; Matouš, Karel
2015-12-01
Three-dimensional simulations capable of resolving the large range of spatial scales, from the failure-zone thickness up to the size of the representative unit cell, in damage mechanics problems of particle reinforced adhesives are presented. We show that resolving this wide range of scales in complex three-dimensional heterogeneous morphologies is essential in order to apprehend fracture characteristics, such as strength, fracture toughness and shape of the softening profile. Moreover, we show that computations that resolve essential physical length scales capture the particle size-effect in fracture toughness, for example. In the vein of image-based computational materials science, we construct statistically optimal unit cells containing hundreds to thousands of particles. We show that these statistically representative unit cells are capable of capturing the first- and second-order probability functions of a given data-source with better accuracy than traditional inclusion packing techniques. In order to accomplish these large computations, we use a parallel multiscale cohesive formulation and extend it to finite strains including damage mechanics. The high-performance parallel computational framework is executed on up to 1024 processing cores. A mesh convergence and a representative unit cell study are performed. Quantifying the complex damage patterns in simulations consisting of tens of millions of computational cells and millions of highly nonlinear equations requires data-mining the parallel simulations, and we propose two damage metrics to quantify the damage patterns. A detailed study of volume fraction and filler size on the macroscopic traction-separation response of heterogeneous adhesives is presented.
Elastic-plastic analysis of the SS-3 tensile specimen
Majumdar, S.
1998-09-01
Tensile tests of most irradiated specimens of vanadium alloys are conducted using the miniature SS-3 specimen which is not ASTM approved. Detailed elastic-plastic finite element analysis of the specimen was conducted to show that, as long as the ultimate to yield strength ratio is less than or equal to 1.25 (which is satisfied by many irradiated materials), the stress-plastic strain curve obtained by using such a specimen is representative of the true material behavior.
A simplified method for elastic-plastic-creep structural analysis
NASA Technical Reports Server (NTRS)
Kaufman, A.
1985-01-01
A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.
A simplified method for elastic-plastic-creep structural analysis
NASA Technical Reports Server (NTRS)
Kaufman, A.
1984-01-01
A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.
NASA Astrophysics Data System (ADS)
McKnight, Geoff; Doty, Robert; Herrera, Guillermo; Henry, Chris
2007-04-01
Morphing structures have the potential to significantly improve vehicle performance over existing fixed component designs. In this paper, we examine new composite material design approaches to provide combined high stiffness and large reversible deformation. These composites employ shape memory polymers (SMP) matrices combined with segmented metallic reinforcement to create materials with variable stiffness properties and reversible accommodation of relatively large strains. By adjusting the temperature of the sample, the storage modulus can be varied up to 200x. We demonstrate the segmented composite concept in prototype materials made using thermoplastic polyurethane SMP reinforced with interlocking segmented steel platelets. Measured storage moduli varied from 5-12 GPa, below SMP T g, and 0.1-0.5 GPa above SMP T g. The samples demonstrated more than 95% recovery from induced axial strains of 5% at 80°C. Viscoelastic effects are dominant in this regime and we investigate the rate dependence of strain recovery.
NASA Technical Reports Server (NTRS)
Houseman, G.; England, P.
1986-01-01
The present investigation has the objective to perform numerical experiments on a rheologically simple continuum model for the continental lithosphere. It is attempted to obtain a better understanding of the dynamics of continental deformation. Calculations are presented of crustal thickness distributions, stress, strain, strain rate fields, latitudinal displacements, and finite rotations, taking into account as basis a model for continental collision which treats the litoshphere as a thin viscous layer subject to indenting boundary conditions. The results of this paper support the conclusions of England and McKenzie (1982) regarding the role of gravity in governing the deformation of a thin viscous layer subject to indenting boundary conditions. The results of the experiments are compared with observations of topography, stress and strain rate fields, and palaeomagnetic latitudinal displacements in Asia.
NASA Astrophysics Data System (ADS)
Baqersad, Javad
Health monitoring of rotating structures such as wind turbines and helicopter rotors is generally performed using conventional sensors that provide a limited set of data at discrete locations near or on the hub. These sensors usually provide no data on the blades or interior locations where failures may occur. Within this work, an unique expansion algorithm was extended and combined with finite element (FE) modeling and an optical measurement technique to identify the dynamic strain in rotating structures. The merit of the approach is shown by using the approach to predict the dynamic strain on a small non-rotating and rotating wind turbine. A three-bladed wind turbine having 2.3-meter long blades was placed in a semi-built-in boundary condition using a hub, a machining chuck, and a steel block. A finite element model of the three wind turbine blades assembled to the hub was created and used to extract resonant frequencies and mode shapes. The FE model was validated and updated using experimental modal tests. For the non-rotating optical test, the turbine was excited using a sinusoidal excitation, a pluck test, arbitrary impacts on three blades, and random force excitations with a mechanical shaker. The response of the structure to the excitations was measured using three-dimensional point tracking. A pair of high-speed cameras was used to measure the displacement of optical targets on the structure when the blades were vibrating. The measured displacements at discrete locations were expanded and applied to the finite element model of the structure to extract the full-field dynamic strain. The results of the work show an excellent correlation between the strain predicted using the proposed approach and the strain measured with strain-gages for all of the three loading conditions. Similar to the non-rotating case, optical measurements were also preformed on a rotating wind turbine. The point tracking technique measured both rigid body displacement and flexible
NASA Astrophysics Data System (ADS)
Li, Li; Wei, P. J.
2015-03-01
The propagation behaviour of Love wave in an initially stressed functionally graded magnetic-electric-elastic half-space carrying a homogeneous layer is investigated. The material parameters in the substrate are assumed to vary exponentially along the thickness direction only. The velocity equations of Love wave are derived on the electrically or magnetically open circuit and short circuit boundary conditions, based on the equations of motion of the graded magnetic-electric-elastic mate- rial with the initial stresses and the free traction boundary conditions of surface and the continuous boundary conditions of interface. The dispersive curves are obtained numerically and the influences of the initial stresses and the material gradient index on the dispersive curves are dis- cussed. The investigation provides a basis for the development of new functionally graded magneto-electro-elastic surface wave devices.
Béland, Laurent Karim; Machado-Charry, Eduardo; Pochet, Pascal; Mousseau, Normand
2014-10-06
Here we investigate Ge mixing at the Si(001) surface and characterize the 2 N Si(001) reconstruction by means of hybrid quantum and molecular mechanics calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to correctly take into account long range deformation induced by reconstructed and defective surfaces. We focus in particular on the dimer vacancy line (DVL) and its interaction with Ge adatoms. We first show that calculated formation energies for these defects are highly dependent on the choice of chemical potential and that the latter must be chosen carefully. Characterizing the effect of the DVL on the deformation field,more » we also find that the DVL favors Ge segregation in the fourth layer close to the DVL. Using the activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex diffusion path permits the substitution of the Ge atom in the fourth layer, with barriers compatible with mixing observed at intermediate temperature. We also show that the use of QM/MM results in much more signi cant corrections at the saddle points (up to 0.5 eV) that at minima, demonstrating its importance for describing kinetics correctly.« less
Béland, Laurent Karim; Machado-Charry, Eduardo; Pochet, Pascal; Mousseau, Normand
2014-10-06
Here we investigate Ge mixing at the Si(001) surface and characterize the 2 N Si(001) reconstruction by means of hybrid quantum and molecular mechanics calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to correctly take into account long range deformation induced by reconstructed and defective surfaces. We focus in particular on the dimer vacancy line (DVL) and its interaction with Ge adatoms. We first show that calculated formation energies for these defects are highly dependent on the choice of chemical potential and that the latter must be chosen carefully. Characterizing the effect of the DVL on the deformation field, we also find that the DVL favors Ge segregation in the fourth layer close to the DVL. Using the activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex diffusion path permits the substitution of the Ge atom in the fourth layer, with barriers compatible with mixing observed at intermediate temperature. We also show that the use of QM/MM results in much more signi cant corrections at the saddle points (up to 0.5 eV) that at minima, demonstrating its importance for describing kinetics correctly.
NASA Astrophysics Data System (ADS)
Béland, Laurent Karim; Machado-Charry, Eduardo; Pochet, Pascal; Mousseau, Normand
2014-10-01
We investigate Ge mixing at the Si(001) surface and characterize the 2×N Si(001) reconstruction by means of hybrid quantum and molecular mechanics calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to correctly take into account long-range deformation induced by reconstructed and defective surfaces. We focus in particular on the dimer vacancy line (DVL) and its interaction with Ge adatoms. We first show that calculated formation energies for these defects are highly dependent on the choice of chemical potential and that the latter must be chosen carefully. Characterizing the effect of the DVL on the deformation field, we also find that the DVL favors Ge segregation in the fourth layer close to the DVL. Using the activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex diffusion path permits the substitution of the Ge atom in the fourth layer, with barriers compatible with mixing observed at intermediate temperature. We also show that the use of QM/MM results in much more significant corrections at the saddle points (up to 0.5 eV) that at minima, demonstrating its importance for describing kinetics correctly.
Bhatia, Varun A; Edwards, W Brent; Troy, Karen L
2014-08-22
Bone strains resulting from physical activity are thought to be a primary driver of bone adaptation, but cannot be directly noninvasively measured. Because bone adapts nonuniformly, physical activity may make an important independent structural contribution to bone strength that is independent of bone mass and density. Our objective was to create and validate methods for subject-specific finite element (FE) model generation that would accurately predict the surface strains experienced by the distal radius during an in vivo loading task, and to apply these methods to a group of 23 women aged 23-35 to examine variations in strain, bone mass and density, and physical activity. Four cadaveric specimens were experimentally tested and specimen-specific FE models were developed to accurately predict periosteal surface strains (root mean square error=16.3%). In the living subjects, when 300 N load was simulated, mean strains were significantly inversely correlated with BMC (r=-0.893), BMD (r=-0.892) and physical activity level (r=-0.470). Although the group of subjects was relatively homogenous, BMD varied by two-fold (range: 0.19-0.40 g/cm(3)) and mean energy-equivalent strain varied by almost six-fold (range: 226.79-1328.41 με) with a simulated 300 N load. In summary, we have validated methods for estimating surface strains in the distal radius that occur while leaning onto the palm of the hand. In our subjects, strain varied widely across individuals, and was inversely related to bone parameters that can be measured using clinical CT, and inversely related to physical activity history. PMID:24882740
Sui, Tan; Lunt, Alexander J G; Baimpas, Nikolaos; Sandholzer, Michael A; Hu, Jianan; Dolbnya, Igor P; Landini, Gabriel; Korsunsky, Alexander M
2014-01-01
Human enamel is a typical hierarchical mineralized tissue with a two-level composite structure. To date, few studies have focused on how the mechanical behaviour of this tissue is affected by both the rod orientation at the microscale and the preferred orientation of mineral crystallites at the nanoscale. In this study, wide-angle X-ray scattering was used to determine the internal lattice strain response of human enamel samples (with differing rod directions) as a function of in situ uniaxial compressive loading. Quantitative stress distribution evaluation in the birefringent mounting epoxy was performed in parallel using photoelastic techniques. The resulting experimental data was analysed using an advanced multiscale Eshelby inclusion model that takes into account the two-level hierarchical structure of human enamel, and reflects the differing rod directions and orientation distributions of hydroxyapatite crystals. The achieved satisfactory agreement between the model and the experimental data, in terms of the values of multidirectional strain components under the action of differently orientated loads, suggests that the multiscale approach captures reasonably successfully the structure-property relationship between the hierarchical architecture of human enamel and its response to the applied forces. This novel and systematic approach can be used to improve the interpretation of the mechanical properties of enamel, as well as of the textured hierarchical biomaterials in general.
NASA Astrophysics Data System (ADS)
Avazmohammadi, Reza; Ponte Castañeda, Pedro
2014-04-01
This paper presents a homogenization-based constitutive model for the mechanical behaviour of particle-reinforced elastomers with random microstructures subjected to finite deformations. The model is based on a recently improved version of the tangent second-order (TSO) method (Avazmohammadi and Ponte Castañeda, J. Elasticity 112 (2013) p.139-183) for two-phase, hyperelastic composites and is able to directly account for the shape, orientation, and concentration of the particles. After a brief summary of the TSO homogenization method, we describe its application to composites consisting of an incompressible rubber reinforced by aligned, spheroidal, rigid particles, undergoing generally non-aligned, three-dimensional loadings. While the results are valid for finite particle concentrations, in the dilute limit they can be viewed as providing a generalization of Eshelby's results in linear elasticity. In particular, we provide analytical estimates for the overall response and microstructure evolution of the particle-reinforced composites with generalized neo-Hookean matrix phases under non-aligned loadings. For the special case of aligned pure shear and axisymmetric shear loadings, we give closed-form expressions for the effective stored-energy function of the composites with neo-Hookean matrix behaviour. Moreover, we investigate the possible development of "macroscopic" (shear band-type) instabilities in the homogenized behaviour of the composite at sufficiently large deformations. These instabilities whose wavelengths are much larger than the typical size of the microstructure are detected by making use of the loss of strong ellipticity condition for the effective stored-energy function of the composites. The analytical results presented in this paper will be complemented in Part II (Avazmohammadi and Ponte Castaneda, Phil. Mag. (2014)) of this work by specific applications for several representative microstructures and loading configurations.
Structure and elastic properties of boron suboxide at 240 GPa
NASA Astrophysics Data System (ADS)
Lu, Y. P.; He, D. W.
2009-04-01
Structure and elastic properties of boron suboxide at high pressure have been investigated using generalized gradient approximation within the plane-wave pseudopotential density functional theory. The elastic constants are calculated using the finite strain method. The pressure dependences of lattice parameters, elastic constants, aggregate elastic moduli, and sound velocities of boron suboxide are predicted. It is found that the most stable structure of hcp boron suboxide at zero pressure corresponds to the ratio c /a of about 2.274 and the equilibrium lattice parameters a0 and c0 are about 5.331 and 12.124 Å, respectively. The high-pressure elastic constants indicate that boron suboxide is mechanically stable up to 368 GPa. The pressure dependence of the calculated normalized volume and the aggregate elastic moduli agree well with the recent experimental results. The sound velocities along different directions for the structure of boron suboxide are obtained. It shows that the velocities of the shear wave decrease as pressure increases but those of all the longitudinal waves increase with pressure. Moreover, the azimuthal anisotropy of the compression and shear aggregate wave velocities for different pressures are predicted. They change behavior with increasing pressure around 87 GPa because of an electronic topological transition. A refined analysis has been made to reveal the high pressure elastic anisotropy in boron suboxide.
Elastic Face, An Anatomy-Based Biometrics Beyond Visible Cue
Tsap, L V; Zhang, Y; Kundu, S J; Goldgof, D B; Sarkar, S
2004-03-29
This paper describes a face recognition method that is designed based on the consideration of anatomical and biomechanical characteristics of facial tissues. Elastic strain pattern inferred from face expression can reveal an individual's biometric signature associated with the underlying anatomical structure, and thus has the potential for face recognition. A method based on the continuum mechanics in finite element formulation is employed to compute the strain pattern. Experiments show very promising results. The proposed method is quite different from other face recognition methods and both its advantages and limitations, as well as future research for improvement are discussed.
Mechanistic Constitutive Models for Rubber Elasticity and Viscoelasticity
Puso, M
2003-01-21
Physically based models which describe the finite strain behavior of vulcanized rubber are developed. Constitutive laws for elasticity and viscoelasticity are derived by integrating over orientation space the forces due to each individual polymer chain. A novel scheme is presented which effectively approximates these integrals in terms of strain and strain invariants. In addition, the details involving the implementation of such models into a quasi-static large strain finite element formulation are provided. In order to account for the finite extensibility of a molecular chain, Langevin statistics is used to model the chain response. The classical statistical model of rubber assumes that polymer chains interact only at the chemical crosslinks. It is shown that such model when fitted for uniaxial tension data cannot fit compression or equibiaxial data. A model which incorporates the entanglement interactions of surrounding chains, in addition to the finite extensibility of the chains, is shown to give better predictions than the classical model. The technique used for approximating the orientation space integral was applied to both the classical and entanglement models. A viscoelasticity model based on the force equilibration process as described by Doi and Edwards is developed. An assumed form for the transient force in the chain is postulated. The resulting stress tensor is composed of an elastic and a viscoelastic portion with the elastic stress given by the proposed entanglement model. In order to improve the simulation of experimental data, it was found necessary to include the effect of unattached or dangling polymer chains in the viscoelasticity model. The viscoelastic effect of such chains is the manifestation of a disengagement process. This disengagement model for unattached polymer chains motivated an empirical model which was very successful in simulating the experimental results considered.
Indentation-derived elastic modulus of multilayer thin films: Effect of unloading induced plasticity
Jamison, Ryan Dale; Shen, Yu -Lin
2015-08-13
Nanoindentation is useful for evaluating the mechanical properties, such as elastic modulus, of multilayer thin film materials. A fundamental assumption in the derivation of the elastic modulus from nanoindentation is that the unloading process is purely elastic. In this work, the validity of elastic assumption as it applies to multilayer thin films is studied using the finite element method. The elastic modulus and hardness from the model system are compared to experimental results to show validity of the model. Plastic strain is shown to increase in the multilayer system during the unloading process. Additionally, the indentation-derived modulus of a monolayer material shows no dependence on unloading plasticity while the modulus of the multilayer system is dependent on unloading-induced plasticity. Lastly, the cyclic behavior of the multilayer thin film is studied in relation to the influence of unloading-induced plasticity. Furthermore, it is found that several cycles are required to minimize unloading-induced plasticity.
Vladimirov, I. N.; Tini, V.; Kiliclar, Y.; Reese, S.
2011-05-04
In this paper, we discuss the application of a newly developed coupled material model of finite anisotropic multiplicative plasticity and continuum damage to the numerical prediction of the forming limit diagram at fracture (FLDF). The model incorporates Hill-type plastic anisotropy, nonlinear Armstrong-Frederick kinematic hardening and nonlinear isotropic hardening. The numerical examples examine the simulation of forming limit diagrams at fracture by means of the so-called Nakajima stretching test. Comparisons with experimental data for aluminium sheets show a good agreement with the finite element results.
Yamaguchi, Takashi; Fukuda, Takashi Kakeshita, Tomoyuki; Harjo, Stefanus; Nakamoto, Tatsushi
2014-06-09
An Fe{sub 3}Pt alloy with degree of order 0.75 exhibits a second-order-like martensitic transformation from a cubic structure to a tetragonal one at about 90 K; its tetragonality c/a changes nearly continuously from 1 to 0.945 on cooling from 90 K to 14 K. We have investigated the change in lattice parameters in a single crystal of the Fe{sub 3}Pt alloy at 93 K under compressive stresses, σ, applied in the [001] direction by neutron diffraction. The tetragonality c/a has decreased continuously from 1 to 0.907 with an increase in |σ| up to |σ| = 280 MPa; the corresponding lattice strain in the [001] direction, due to the continuous structure change, increases from 0% to 6.1%. When the stress of 300 MPa is reached, c/a has changed abruptly from 0.907 to 0.789 due to a first-order martensitic transformation.
Ahmadzadeh, Hossein; Freedman, Benjamin R; Connizzo, Brianne K; Soslowsky, Louis J; Shenoy, Vivek B
2015-08-01
As tendons are loaded, they reduce in volume and exude fluid to the surrounding medium. Experimental studies have shown that tendon stretching results in a Poisson's ratio greater than 0.5, with a maximum value at small strains followed by a nonlinear decay. Here we present a computational model that attributes this macroscopic observation to the microscopic mechanism of the load transfer between fibrils under stretch. We develop a finite element model based on the mechanical role of the interfibrillar-linking elements, such as thin fibrils that bridge the aligned fibrils or macromolecules such as glycosaminoglycans (GAGs) in the interfibrillar sliding and verify it with a theoretical shear-lag model. We showed the existence of a previously unappreciated structure-function mechanism whereby the Poisson's ratio in tendon is affected by the strain applied and interfibrillar-linker properties, and together these features predict tendon volume shrinkage under tensile loading. During loading, the interfibrillar-linkers pulled fibrils toward each other and squeezed the matrix, leading to the Poisson's ratio larger than 0.5 and fluid expulsion. In addition, the rotation of the interfibrillar-linkers with respect to the fibrils at large strains caused a reduction in the volume shrinkage and eventual nonlinear decay in Poisson's ratio at large strains. Our model also predicts a fluid flow that has a radial pattern toward the surrounding medium, with the larger fluid velocities in proportion to the interfibrillar sliding. PMID:25934322
NASA Astrophysics Data System (ADS)
Tahouneh, Vahid; Naei, Mohammad Hasan
2016-03-01
The main purpose of this paper is to investigate the effect of bidirectional continuously graded nanocomposite materials on free vibration of thick shell panels rested on elastic foundations. The elastic foundation is considered as a Pasternak model after adding a shear layer to the Winkler model. The panels reinforced by randomly oriented straight single-walled carbon nanotubes are considered. The volume fractions of SWCNTs are assumed to be graded not only in the radial direction, but also in axial direction of the curved panel. This study presents a 2-D six-parameter power-law distribution for CNTs volume fraction of 2-D continuously graded nanocomposite that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. The benefit of using generalized power-law distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. The material properties are determined in terms of local volume fractions and material properties by Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient numerical tool is used to discretize governing equations and to implement boundary conditions. The fast rate of convergence of the method is shown and results are compared against existing results in literature. Some new results for natural frequencies of the shell are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded nanocomposite volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded nanocomposite materials.
NASA Astrophysics Data System (ADS)
Jamalpoor, A.; Ahmadi-Savadkoohi, A.; Hosseini-Hashemi, Sh
2016-10-01
This paper deals with the theoretical analysis of free vibration and biaxial buckling of magneto-electro-elastic (MEE) microplate resting on Kelvin-Voigt visco-Pasternak foundation and subjected to initial external electric and magnetic potentials, using modified strain gradient theory (MSGT). Kirchhoff plate model and Hamilton’s principle are employed to extract the governing equations of motion. Governing equations were analytically solved to obtain clear closed-form expression for complex natural frequencies and buckling loads using Navier’s approach. Numerical results are presented to reveal variations of natural frequency and buckling load ratio of MEE microplate against different amounts of the length scale parameter, initial external electric and magnetic potentials, aspect ratio, damping and transverse and shear stiffness parameters of the visco-Pasternak foundation, length to thickness ratio, microplate thickness and higher modes. Numerical results of this study illustrate that by increasing thickness-to-material length scale parameter ratio, both natural frequency and buckling load ratio predicted by MSGT and modified couple stress theory are reduced because the non-dimensional length scale parameter tends to decrease the stiffness of structures and make them more flexible. In addition, results show that initial external electric and initial external magnetic potentials have no considerable influence on the buckling load ratio and frequency of MEE microplate as the microplate thickness increases.
Hallquist, J.O.
1983-02-01
This report provides a user's manual for NIKE2D and a brief description of the implicit algorithm. Sample applications are presented including a simulation of the necking of a uniaxial tension specimen, a static analysis of an O-ring seal, and a cylindrical bar impacting a rigid wall. NIKE2D is a fully vectorized, implicit, finite-deformation, large-strain, finite-element code for analyzing the response of two-dimensional axisymmetric and plane-strain solids. A variety of loading conditions can be handled including traction boundary conditions, displacement boundary conditions, concentrated nodal point laods, body force loads due to base accelerations, and body-force loads due to spinning. Slide-lines with interface friction are available. Elastic, orthotropic-elastic-plastic, thermo-elastic-plactic, soil and crushable foam, linear viscoelastic, thermo-orthotropic elastic, and elastic-creep materials models are implemented. Nearly incompressible behavior that arises in plasticity problems and elasticity problems with Poisson's ratio approaching 0.5 is accounted for in the element formulation to preclude mesh lock-ups and associated anomalous stress states. Four-node isoparametric elements are used for the spatial discretization, and profile (bandwidth) minimization is optional.
Hofmann, Felix; Song, Xu; Abbey, Brian; Jun, Tea-Sung; Korsunsky, Alexander M
2012-05-01
An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load-bearing components in high-performance safety-critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'-type mechanisms. It is strongly dependent on the anisotropic single-crystal elastic-plastic behaviour, local morphology and microstructure, and grain-to-grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro-scale is key. The diffraction of highly penetrating synchrotron X-rays is well suited to this purpose and micro-beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5-25 keV, limiting penetration into the material, so that only thin samples or near-surface regions can be studied. In this paper the development of high-energy transmission Laue (HETL) micro-beam X-ray diffraction is described, extending the micro-beam Laue technique to significantly higher photon energies (50-150 keV). It allows the probing of thicker sample sections, with the potential for grain-level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large-grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is
NASA Astrophysics Data System (ADS)
Hasegawa, Kei; Geller, Robert J.; Hirabayashi, Nobuyasu
2016-06-01
We present a theoretical analysis of the error of synthetic seismograms computed by higher-order finite-element methods (ho-FEMs). We show the existence of a previously unrecognized type of error due to degenerate coupling between waves with the same frequency but different wavenumbers. These results are confirmed by simple numerical experiments using the spectral element method as an example of ho-FEMs. Errors of the type found by this study may occur generally in applications of ho-FEMs.
Shinya, Akikazu; Ballo, Ahmed M; Lassila, Lippo V J; Shinya, Akiyoshi; Närhi, Timo O; Vallittu, Pekka K
2011-03-01
This study analyzed stress and strain mediated by 2 different implant materials, titanium (Ti) and experimental fiber-reinforced composite (FRC), on the implant and on the bone tissue surrounding the implant. Three-dimensional finite element models constructed from a mandibular bone and an implant were subjected to a load of 50 N in vertical and horizontal directions. Postprocessing files allowed the calculation of stress and strain within the implant materials and stresses at the bone-to-implant interface (stress path). Maximum stress concentrations were located around the implant on the rim of the cortical bone in both implant materials; Ti and overall stresses decreased toward the Ti implant apex. In the FRC implant, a stress value of 0.6 to 2.0 MPa was detected not only on the screw threads but also on the implant surface between the threads. Clear differences were observed in the strain distribution between the materials. Based on the results, the vertical load stress range of the FRC implant was close to the stress level for optimal bone growth. Furthermore, the stress at the bone around the FRC implant was more evenly distributed than that with Ti implant.
Three-dimensional elastic analysis of a composite double cantilever beam specimen
NASA Technical Reports Server (NTRS)
Raju, I. S.; Shivakumar, K. N.; Crews, J. H., Jr.
1988-01-01
Attention is given to the stresses and the strain energy release rate along the delamination front in the present three-dimensional elastic analysis of a 24-ply, cocured double-cantilever beam specimen by means of 20-noded parabolic-isoparametric finite elements. At the free surface, the strain energy release rate was found to be substantially smaller than the plane strain value; this is suggested to be due to the free-surface effect that exists where the delamination meets the surface edge.
Finite element model for brittle fracture and fragmentation
Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin; Samulyak, Roman; Lu, Cao
2016-06-01
A new computational model for brittle fracture and fragmentation has been developed based on finite element analysis of non-linear elasticity equations. The proposed model propagates the cracks by splitting the mesh nodes alongside the most over-strained edges based on the principal direction of strain tensor. To prevent elements from overlapping and folding under large deformations, robust geometrical constraints using the method of Lagrange multipliers have been incorporated. In conclusion, the model has been applied to 2D simulations of the formation and propagation of cracks in brittle materials, and the fracture and fragmentation of stretched and compressed materials.
NASA Technical Reports Server (NTRS)
Hofmann, R.
1980-01-01
The STEALTH code system, which solves large strain, nonlinear continuum mechanics problems, was rigorously structured in both overall design and programming standards. The design is based on the theoretical elements of analysis while the programming standards attempt to establish a parallelism between physical theory, programming structure, and documentation. These features have made it easy to maintain, modify, and transport the codes. It has also guaranteed users a high level of quality control and quality assurance.
NASA Astrophysics Data System (ADS)
Zhang, J. L.; Liu, X.; Yuan, Y.; Mang, H. A.
2015-01-01
A multiscale model of fiber-reinforced fine concrete is developed, with special emphasis on the interfacial transition zone (ITZ). It does not only allow the prediction of the modulus of elasticity but also permits the determination of the strain and stress field. The model is based on the mathematical homogenization method and implemented in the frame of the finite element method. A comparison of model predictions with experimental results taken from the literature validates the model's effectiveness for prediction of the elasticity modulus. The effect of the thickness and of the elasticity modulus of the ITZ on the elasticity modulus of the homogenized material as well as the influence of the strength of the ITZ on the elastic limit of the homogenized material, are investigated numerically. Furthermore, a sensitivity analysis is carried out to evaluate the influence of fine-scale factors on the elasticity modulus of ultra-high performance concrete.
ERIC Educational Resources Information Center
Girill, T. R.
1972-01-01
The Boyle-Mariotte gas law was formulated in terms of pneumatic springs," subsumed by Hooke under his own stress-strain relation, and generally regarded as a law of elasticity. The subsequent development of Boyle's principle and elasticity provide thought-provoking test cases for Kuhn's notations of paradigm and puzzle solving in physics.…
NASA Astrophysics Data System (ADS)
Yu, Betty; Kang, Soo-Young; Akthakul, Ariya; Ramadurai, Nithin; Pilkenton, Morgan; Patel, Alpesh; Nashat, Amir; Anderson, Daniel G.; Sakamoto, Fernanda H.; Gilchrest, Barbara A.; Anderson, R. Rox; Langer, Robert
2016-08-01
We report the synthesis and application of an elastic, wearable crosslinked polymer layer (XPL) that mimics the properties of normal, youthful skin. XPL is made of a tunable polysiloxane-based material that can be engineered with specific elasticity, contractility, adhesion, tensile strength and occlusivity. XPL can be topically applied, rapidly curing at the skin interface without the need for heat- or light-mediated activation. In a pilot human study, we examined the performance of a prototype XPL that has a tensile modulus matching normal skin responses at low strain (<40%), and that withstands elongations exceeding 250%, elastically recoiling with minimal strain-energy loss on repeated deformation. The application of XPL to the herniated lower eyelid fat pads of 12 subjects resulted in an average 2-grade decrease in herniation appearance in a 5-point severity scale. The XPL platform may offer advanced solutions to compromised skin barrier function, pharmaceutical delivery and wound dressings.
Yu, Betty; Kang, Soo-Young; Akthakul, Ariya; Ramadurai, Nithin; Pilkenton, Morgan; Patel, Alpesh; Nashat, Amir; Anderson, Daniel G; Sakamoto, Fernanda H; Gilchrest, Barbara A; Anderson, R Rox; Langer, Robert
2016-08-01
We report the synthesis and application of an elastic, wearable crosslinked polymer layer (XPL) that mimics the properties of normal, youthful skin. XPL is made of a tunable polysiloxane-based material that can be engineered with specific elasticity, contractility, adhesion, tensile strength and occlusivity. XPL can be topically applied, rapidly curing at the skin interface without the need for heat- or light-mediated activation. In a pilot human study, we examined the performance of a prototype XPL that has a tensile modulus matching normal skin responses at low strain (<40%), and that withstands elongations exceeding 250%, elastically recoiling with minimal strain-energy loss on repeated deformation. The application of XPL to the herniated lower eyelid fat pads of 12 subjects resulted in an average 2-grade decrease in herniation appearance in a 5-point severity scale. The XPL platform may offer advanced solutions to compromised skin barrier function, pharmaceutical delivery and wound dressings. PMID:27159017
A theoretical study of the elastic and thermal properties of ScRu compound under pressure
NASA Astrophysics Data System (ADS)
Huang, Shuo; Li, Rui-Zi; Qi, San-Tao; Chen, Bao; Shen, Jiang
2014-06-01
The elastic and thermal properties of ScRu under pressure are studied using a first-principles pseudopotential method within the generalized gradient approximation. The calculated lattice parameter and formation enthalpy are in good agreement with the previous experimental and theoretical results. From the static finite strain technique, we obtained three independent elastic constants (C 11, C 12 and C 44) and various secondary elasticity parameters such as shear modulus, Young’s modulus and elastic anisotropy, as functions of pressure. This study also provided the pressure and temperature variations of the bulk modulus, Debye temperature, thermal expansion coefficient and heat capacity in wide pressure (0-60 GPa) and temperature (0-1800 K) ranges.
Analysis of local strain in aluminum interconnects by convergent beam electron diffraction
NASA Astrophysics Data System (ADS)
Krämer, Stephan; Mayer, Joachim
1999-11-01
Energy filtered convergent beam electron diffraction (CBED) was used to investigate localized strain in aluminum interconnects. An analysis of the higher order Laue zone (HOLZ) line positions in CBED patterns makes it possible to measure the lattice strain with high accuracy (˜104) and high spatial resolution (10 to 100 nm). The strain development in a single grain was measured during thermal cycling between -170 °C and +100 °C. The grain showed reversible, elastic behavior over the whole temperature range building up large strains at low temperatures. By comparing with finite element simulations, a detailed understanding of the tri-axial strain state could be achieved.
Schrock, P; Lüpke, M; Seifert, H; Staszyk, C
2013-12-01
This study investigated the hypothetical contribution of biomechanical loading to the onset of equine odontoclastic tooth resorption and hypercementosis (EOTRH) and to elucidate the physiological age-related positional changes of the equine incisors. Based on high resolution micro-computed tomography (μCT) datasets, 3-dimensional models of entire incisor arcades and the canine teeth were constructed representing a young and an old incisor dentition. Special attention was paid to constructing an anatomically correct model of the periodontal ligament (PDL). Using previously determined Young's moduli for the equine incisor PDL, finite element (FE) analysis was performed. Resulting strains, stresses and strain energy densities (SEDs), as well as the resulting regions of tension and compression within the PDL and the surrounding bone were investigated during occlusion. The results showed a distinct distribution pattern of high stresses and corresponding SEDs in the PDL and bone. Due to the tooth movement, peaks of SEDs were obtained in the PDL as well as in the bone on the labial and palatal/lingual sides of the alveolar crest. At the root, highest SEDs were detected in the PDL on the palatal/lingual side slightly occlusal of the root tip. This distribution pattern of high SEDs within the PDL coincides with the position of initial resorptive lesions in EOTRH affected teeth. The position of high SEDs in the bone can explain the typical age-related alteration of shape and angulation of equine incisors.
Nonlinear Visco-Elastic Response of Composites via Micro-Mechanical Models
NASA Technical Reports Server (NTRS)
Gates, Thomas S.; Sridharan, Srinivasan
2005-01-01
Micro-mechanical models for a study of nonlinear visco-elastic response of composite laminae are developed and their performance compared. A single integral constitutive law proposed by Schapery and subsequently generalized to multi-axial states of stress is utilized in the study for the matrix material. This is used in conjunction with a computationally facile scheme in which hereditary strains are computed using a recursive relation suggested by Henriksen. Composite response is studied using two competing micro-models, viz. a simplified Square Cell Model (SSCM) and a Finite Element based self-consistent Cylindrical Model (FECM). The algorithm is developed assuming that the material response computations are carried out in a module attached to a general purpose finite element program used for composite structural analysis. It is shown that the SSCM as used in investigations of material nonlinearity can involve significant errors in the prediction of transverse Young's modulus and shear modulus. The errors in the elastic strains thus predicted are of the same order of magnitude as the creep strains accruing due to visco-elasticity. The FECM on the other hand does appear to perform better both in the prediction of elastic constants and the study of creep response.
Serra-Hsu, Frederick; Cheng, Jiqi; Lynch, Ted
2016-01-01
Ultrasound has been widely used to nondestructively evaluate various materials, including biological tissues. Quantitative ultrasound has been used to assess bone quality and fracture risk. A pulsed phase-locked loop (PPLL) method has been proven for very sensitive tracking of ultrasound time-of-flight (TOF) changes. The objective of this work was to determine if the PPLL TOF tracking is sensitive to bone deformation changes during loading. The ability to noninvasively detect bone deformations has many implications, including assessment of bone strength and more accurate osteoporosis diagnostics and fracture risk prediction using a measure of bone mechanical quality. Fresh sheep femur cortical bone shell samples were instrumented with three 3-element rosette strain gauges and then tested under mechanical compression with eight loading levels using an MTS machine. Samples were divided into two groups based on internal marrow cavity content: with original marrow, or replaced with water. During compressive loading ultrasound waves were measured through acoustic transmission across the mid-diaphysis of bone. Finite element analysis (FEA) was used to describe ultrasound propagation path length changes under loading based on μCT-determined bone geometry. The results indicated that PPLL output correlates well to measured axial strain, with R2 values of 0.70 ± 0.27 and 0.62 ± 0.29 for the marrow and water groups, respectively. The PPLL output correlates better with the ultrasound path length changes extracted from FEA. For the two validated FEA tests, correlation was improved to R2 = 0.993 and R2 = 0.879 through cortical path, from 0.815 and 0.794 via marrow path, respectively. This study shows that PPLL readings are sensitive to displacement changes during external bone loading, which may have potential to noninvasively assess bone strain and tissue mechanical properties. PMID:21765205
NASA Astrophysics Data System (ADS)
Cowgill, E.; Gold, R. D.; Arrowsmith, R.; Friedrich, A. M.
2015-12-01
In elastic rebound theory, hazard increases as interseismic strain rebuilds after rupture. This model is challenged by the temporal variation in the pacing of major earthquakes that is both predicted by mechanical models and suggested by some long paleoseismic records (e.g., 1-3). However, the extent of such behavior remains unclear due to a lack of long (5-25 ky) records of fault slip. Using Monte Carlo analysis of 11 offset landforms, we determined a 16-ky record of fault slip for the active, left-lateral Altyn Tagh fault, which bounds the NW margin of the Tibetan Plateau. This history reveals a pulse of accelerated slip between 6.4 and 6.0 ka, during which the fault slipped 9 +14/-2 m at a rate of 23 +35/-5 mm/y, or ~3x the 16 ky average of 8.1 +1.2/-0.9mm/y. These two modes of earthquake behavior suggest temporal variation in the rates of stress storage and release. The simplest explanation for the pulse is a cluster of 2-8 Mw > 7.5 earthquakes. Such supercyclicity has been reported for the Sunda (4) and Cascadia (3) megathrusts, but contrasts with steady slip along the strike-slip Alpine fault (5), for example. A second possibility is that the pulse reflects a single, unusually large rupture. However, this Black Swan event is unlikely: empirical scaling relationships require a Mw 8.2 rupture of the entire 1200-km-long ATF to produce 7 m of average slip. Likewise, Coulomb stress change from rupture on the adjacent North Altyn fault is of modest magnitude and overlap with the ATF. Poor temporal correlation between precipitation and the slip pulse argues against climatically modulated changes in surface loading (lakes/ice) or pore-fluid pressure. "Paleoslip" studies such as this sacrifice the single-event resolution of paleoseismology in exchange for long records that quantify both the timing and magnitude of fault slip averaged over multiple ruptures, and are essential for documenting temporal variations in fault slip as we begin to use calibrated physical
Elastic-plastic models for multi-site damage
NASA Technical Reports Server (NTRS)
Actis, Ricardo L.; Szabo, Barna A.
1994-01-01
This paper presents recent developments in advanced analysis methods for the computation of stress site damage. The method of solution is based on the p-version of the finite element method. Its implementation was designed to permit extraction of linear stress intensity factors using a superconvergent extraction method (known as the contour integral method) and evaluation of the J-integral following an elastic-plastic analysis. Coarse meshes are adequate for obtaining accurate results supported by p-convergence data. The elastic-plastic analysis is based on the deformation theory of plasticity and the von Mises yield criterion. The model problem consists of an aluminum plate with six equally spaced holes and a crack emanating from each hole. The cracks are of different sizes. The panel is subjected to a remote tensile load. Experimental results are available for the panel. The plasticity analysis provided the same limit load as the experimentally determined load. The results of elastic-plastic analysis were compared with the results of linear elastic analysis in an effort to evaluate how plastic zone sizes influence the crack growth rates. The onset of net-section yielding was determined also. The results show that crack growth rate is accelerated by the presence of adjacent damage, and the critical crack size is shorter when the effects of plasticity are taken into consideration. This work also addresses the effects of alternative stress-strain laws: The elastic-ideally-plastic material model is compared against the Ramberg-Osgood model.
On the Assumed Natural Strain method to alleviate locking in solid-shell NURBS-based finite elements
NASA Astrophysics Data System (ADS)
Caseiro, J. F.; Valente, R. A. F.; Reali, A.; Kiendl, J.; Auricchio, F.; Alves de Sousa, R. J.
2014-06-01
In isogeometric analysis (IGA), the functions used to describe the CAD geometry (such as NURBS) are also employed, in an isoparametric fashion, for the approximation of the unknown fields, leading to an exact geometry representation. Since the introduction of IGA, it has been shown that the high regularity properties of the employed functions lead in many cases to superior accuracy per degree of freedom with respect to standard FEM. However, as in Lagrangian elements, NURBS-based formulations can be negatively affected by the appearance of non-physical phenomena that "lock" the solution when constrained problems are considered. In order to alleviate such locking behaviors, the Assumed Natural Strain (ANS) method proposed for Lagrangian formulations is extended to NURBS-based elements in the present work, within the context of solid-shell formulations. The performance of the proposed methodology is assessed by means of a set of numerical examples. The results allow to conclude that the employment of the ANS method to quadratic NURBS-based elements successfully alleviates non-physical phenomena such as shear and membrane locking, significantly improving the element performance.
Podczeck, Fridrun; Newton, J Michael; Fromme, Paul
2015-11-10
The aim of this work was to ascertain the influence of the position of the breaking line of bevel-edged tablets in a three-point bending test. Two different brands of commercially available, flat-round, bevel-edged tablets with a single central breaking line were studied. Breaking line positions tested, relative to the upper loading roll, were 0°, 22.5°, 45°, 67.5° and 90°. The breaking line faced either up- or downwards during the test. The practical results were compared with FEM results simulating similar test configurations. Tablets failed mainly across the failure plane, resulting in two tablet halves. An exception to this was found for tablets where the breaking line faced down and was positioned at an angle of 22.5° relative to the loading plane. Here the crack followed the breaking line in the centre of the tablets and only diverged towards the loading plane position at the edges of the tablets. The breaking line facing upwards resulted in a significantly higher tensile strength of the tablets compared to it facing downwards. However, with one exception, the orientation of the breaking line relative to the loading plane appeared not to affect the tensile strength values. A fully elastic FEM model indicated that both the position of the breaking line relative to the loading plane and as to whether the breaking line faced up- or downwards during the bending test would result in considerably different failure loads during practical experiments. The results also suggested that regardless of the breaking line position, when it is facing down crack propagation should start at the outer edges propagating towards the midpoint of the discs until failure occurs. Failure should hence always result in equal tablet halves, whereby the failure plane should coincide with the loading plane. Neither predictions fully reflected the practical behaviour of the tablets. Using a brittle cracking FEM model significantly larger tensile stresses for tablets with the breaking
A finite element model of ferroelectric/ferroelastic polycrystals
HWANG,STEPHEN C.; MCMEEKING,ROBERT M.
2000-02-17
A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, but different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, strain versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate (PLZT) are modeled well below the Curie temperature.
Wang, R.-V.; McIntyre, Paul C.; Baniecki, John D.; Nomura, Kenji; Shioga, Takeshi; Kurihara, Kazuaki; Ishii, Masatoshi
2005-11-07
We demonstrate that large and simultaneous improvements in permittivity, tunability, and leakage current density of (Ba,Sr)TiO{sub 3} (BST)-based thin-film capacitors can be achieved by yttrium doping. We have found that, for a low deposition temperature (520 deg. C) sputtering process, Y-doped BST capacitors exhibit tenfold lower leakage current density (<10{sup -9} A/cm{sup 2} at 100 KV/cm) and 70% higher permittivity than nominally undoped BST-based capacitors. Furthermore, this work suggests an intriguing correlation between dopant concentration-dependent elastic strain in the films and their enhanced dielectric properties.
NASA Astrophysics Data System (ADS)
Hüter, Claas; Friák, Martin; Weikamp, Marc; Neugebauer, Jörg; Goldenfeld, Nigel; Svendsen, Bob; Spatschek, Robert
2016-06-01
We investigate nonlinear elastic deformations in the phase field crystal model and derived amplitude equation formulations. Two sources of nonlinearity are found, one of them is based on geometric nonlinearity expressed through a finite strain tensor. This strain tensor is based on the inverse right Cauchy-Green deformation tensor and correctly describes the strain dependence of the stiffness for anisotropic and isotropic behavior. In isotropic one- and two-dimensional situations, the elastic energy can be expressed equivalently through the left deformation tensor. The predicted isotropic low-temperature nonlinear elastic effects are directly related to the Birch-Murnaghan equation of state with bulk modulus derivative K'=4 for bcc. A two-dimensional generalization suggests K2D '=5 . These predictions are in agreement with ab initio results for large strain bulk deformations of various bcc elements and graphene. Physical nonlinearity arises if the strain dependence of the density wave amplitudes is taken into account and leads to elastic weakening. For anisotropic deformation, the magnitudes of the amplitudes depend on their relative orientation to the applied strain.
Sewell, T. D.; Bedrov, D.; Menikoff, Ralph; Smith, G. D.
2001-01-01
Atomistic molecular dynamics simulations have been used to calculate isothermal elastic properties for {beta}-, {alpha}-, and {delta}-HMX. The complete elastic tensor for each polymorph was determined at room temperature and pressure via analysis of microscopic strain fluctuations using formalism due to Rahman and Parrinello [J. Chem. Phys. 76,2662 (1982)]. Additionally, the isothermal compression curve was computed for {beta}-HMX for 0 {le} p {le} 10.6 GPa; the bulk modulus K and its pressure derivative K{prime} were obtained from two fitting forms employed previously in experimental studies of the {beta}-HMX equation of state. Overall, the results indicate good agreement between the bulk modulus predicted from the measured and calculated compression curves. The bulk modulus determined directly from the elastic tensor of {beta}-HMX is in significant disagreement with the compression curve-based results. The explanation for this discrepancy is an area of current research.
Zacharias, Mario; Paul, Indranil; Garst, Markus
2015-07-10
We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Because of long-range shear forces of the solid, at such transitions the phonon velocities vanish, if at all, only along certain crystallographic directions, and, consequently, the critical phonon fluctuations are suppressed to a lower dimensional manifold and governed by a Gaussian fixed point. In the case of symmetry-breaking elastic transitions, a characteristic critical phonon thermodynamics arises that is found, e.g., to violate Debye's T(3) law for the specific heat. We point out that quantum critical elasticity is triggered whenever a critical soft mode couples linearly to the strain tensor. In particular, this is relevant for the electronic Ising-nematic quantum phase transition in a tetragonal crystal as discussed in the context of certain cuprates, ruthenates, and iron-based superconductors. PMID:26207483
NASA Technical Reports Server (NTRS)
Wu, R. W.; Witmer, E. A.
1972-01-01
A user-oriented FORTRAN 4 computer program, called JET 3, is presented. The JET 3 program, which employs the spatial finite-element and timewise finite-difference method, can be used to predict the large two-dimensional elastic-plastic transient Kirchhoff-type deformations of a complete or partial structural ring, with various support conditions and restraints, subjected to a variety of initial velocity distributions and externally-applied transient forcing functions. The geometric shapes of the structural ring can be circular or arbitrarily curved and with variable thickness. Strain-hardening and strain-rate effects of the material are taken into account.
Higher-order elastic constants and megabar pressure effects of bcc tungsten: Ab initio calculations
NASA Astrophysics Data System (ADS)
Vekilov, Yu. Kh.; Krasilnikov, O. M.; Lugovskoy, A. V.; Lozovik, Yu. E.
2016-09-01
The general method for the calculation of n th (n ≥2 ) order elastic constants of the loaded crystal is given in the framework of the nonlinear elasticity theory. For the crystals of cubic symmetry under hydrostatic compression, the two schemes of calculation of the elastic constants of second, third, and fourth order from energy-finite strain relations and stress-finite strain relations are implemented. Both techniques are applied for the calculation of elastic constants of orders from second to fourth to the bcc phase of tungsten at a 0-600 GPa pressure range. The energy and stress at the various pressures and deformations are obtained ab initio in the framework of projector augmented wave+generalized gradient approximation (PAW+GGA) method, as implemented in Vienna Ab initio Simulation Package (VASP) code. Using the obtained results, we found the pressure dependence of Grüneisen parameters for long-wave acoustic modes in this interval. The Lamé constants of second and third order were estimated for polycrystalline tungsten. The proposed method is applicable for crystals with arbitrary symmetry.
Elastic-plastic analysis of AS4/PEEK composite laminate using a one-parameter plasticity model
NASA Technical Reports Server (NTRS)
Sun, C. T.; Yoon, K. J.
1992-01-01
A one-parameter plasticity model was shown to adequately describe the plastic deformation of AS4/PEEK (APC-2) unidirectional thermoplastic composite. This model was verified further for unidirectional and laminated composite panels with and without a hole. The elastic-plastic stress-strain relations of coupon specimens were measured and compared with those predicted by the finite element analysis using the one-parameter plasticity model. The results show that the one-parameter plasticity model is suitable for the analysis of elastic-plastic deformation of AS4/PEEK composite laminates.
Turner, Todd J.; Shade, Paul A; Bernier, Joel V.; Li, Shiu Fai; Schuren, Jay C.; Lind, Jonathan F.; Lienert, Ulrich; Kenesei, Peter; Suter, Robert; Blank, Basil; Almer, Jonathan
2016-01-01
We present both near-field HEDM data that maps out the grain morphology and intragranular crystallographic orientations and far-field HEDM data that provides the grain centroid, grain average crystallographic orientation, and grain average elastic strain tensor for each grain. Finally, we provide a finite element mesh that can be utilized to simulate deformation in the volume of this Ti-7Al specimen.
Kuryliuk, V. V. Korotchenkov, O. A.
2013-08-15
Within the elastic continuum model, with the use of the finite-element method, the stress-strain state of silicon-germanium heterostructures with semispherical germanium islands grown on an oxidized silicon surface is calculated. It is shown that as the density of islands is increased to limiting values, in the SiGe structure with open quantum dots the value and spatial distribution of the elastic-strain fields significantly change. The results of theoretical calculation allow the heterostructure portions with the maximum variation in the stress-strain state to be determined. The position of such a portions can be controlled by changing the density of islands.
A Method for Connecting Dissimilar Finite Element Meshes in Three Dimensions
Dohrmann, C.R.; Heinstein, M.W.; Key, S.W.
1998-11-12
A method is presented for connecting dissimilar finite element meshes in three dimensions. The method combines the concept of master and slave surfaces with the uniform strain approach for surface, corrections finite elements- By modifyhg the are made to element formulations boundaries of elements on the slave such that first-order patch tests are passed. The method can be used to connect meshes which use different element types. In addition, master and slave surfaces can be designated independently of relative mesh resolutions. Example problems in three-dimensional linear elasticity are presented.
NASA Astrophysics Data System (ADS)
Akhras, G.; Cheung, M. S.; Li, W.
1994-08-01
In the present study, a finite strip method for the elastic analysis of anisotropic laminated composite plates is developed according to higher-order shear deformation theory. This theory accounts for the parabolic distribution of the transverse shear strains through the thickness of the plate and for zero transverse shear stresses on the plate surfaces. In comparison with the finite strip method based on first-order shear deformation theory, the present method gives improved results while using approximately the same number of degrees of freedom. It also eliminates the need for shear correction factors in calculating the transverse shear stiffness.
Elasticity of Wadsleyite at 12 GPa1073K
W Liu; J Kung; B Li; N Nishiyama; Y Wang
2011-12-31
Elasticity of (Mg{sub 0.87}Fe{sub 0.13}){sub 2}SiO{sub 4} wadsleyite has been measured at simultaneous high pressure and high temperature to 12 GPa and 1073 K using ultrasonic interferometry in conjunction with synchrotron X-radiation. The elastic moduli and their pressure and temperature derivatives are precisely determined using pressure-standard-free third-order and fourth-order finite strain equations. Combined with previous thermoelastic data on olivine, the density, velocity and acoustic impedance contrasts between {alpha}- and {beta}-(Mg{sub 0.9}Fe{sub 0.1}){sub 2}SiO{sub 4} at 410-km depth are calculated along a 1673 K adiabatic geotherm. Both the third- and fourth-order finite strain equation fitting results give estimation of {approx}33-58% olivine content in the upper mantle to account for a seismic discontinuity of {approx}5% velocity jumps, and 8.5% (P wave) and 11.1% (S wave) impedance jumps at 410 km depth.
Comparison of two methods for describing the strain profiles in quantum dots
Pryor, C.; Kim, J.; Wang, L.W.; Williamson, A.J.; Zunger, A.
1998-03-01
The electronic structure of interfaces between lattice-mismatched semiconductors is sensitive to the strain. We compare two approaches for calculating such inhomogeneous strain{emdash}continuum elasticity [(CE), treated as a finite difference problem] and atomistic elasticity. While for {ital small} strain the two methods must agree, for the large strains that exist between lattice-mismatched III-V semiconductors (e.g., 7{percent} for InAs/GaAs outside the linearity regime of CE) there are discrepancies. We compare the strain profile obtained by both approaches (including the approximation of the correct C{sub 2} symmetry by the C{sub 4} symmetry in the CE method) when applied to C{sub 2}-symmetric InAs pyramidal dots capped by GaAs. {copyright} {ital 1998 American Institute of Physics.}
A model for compression-weakening materials and the elastic fields due to contractile cells
NASA Astrophysics Data System (ADS)
Rosakis, Phoebus; Notbohm, Jacob; Ravichandran, Guruswami
2015-12-01
We construct a homogeneous, nonlinear elastic constitutive law that models aspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers in such networks buckle when in compression. We model this as a loss of stiffness in compression in the stress-strain relations of the homogeneous constitutive model. Problems that model a contracting biological cell in a finite matrix are solved. It is found that matrix displacements and stresses induced by cell contraction decay slower (with distance from the cell) in a compression weakening material than linear elasticity would predict. This points toward a mechanism for long-range cell mechanosensing. In contrast, an expanding cell would induce displacements that decay faster than in a linear elastic matrix.
Elastic properties of solids at high pressure
NASA Astrophysics Data System (ADS)
Vekilov, Yu Kh; Krasilnikov, O. M.; Lugovskoy, A. V.
2015-11-01
This review examines the elastic response of solids under load. The definitions of isothermal and adiabatic elastic constants of ( n≥2) for a loaded crystal are given. For the case of hydrostatic pressure, two techniques are proposed for calculating the second-, third-, and fourth-order elastic constants from the energy-strain and stress-strain relations. As an example, using the proposed approach within the framework of the density functional theory, the second- to fourth-order elastic constants of bcc tungsten are calculated for the pressure range of 0-600 GPa.
Feng, Guo-Hua; Huang, Wei-Lun
2014-12-01
This paper presents a smart tuning-fork-shaped ionic polymer metal composite (IPMC) clamping actuator for biomedical applications. The two fingers of the actuator, which perform the clamping motion, can be electrically controlled through a unique electrode design on the IPMC material. The generated displacement or strain of the fingers can be sensed using an integrated soft strain-gage sensor. The IPMC actuator and associated soft strain gage were fabricated using a micromachining technique. A 13.5×4×2 mm(3) actuator was shaped from Nafion solution and a selectively grown metal electrode formed the active region. The strain gage consisted of patterned copper foil and polyethylene as a substrate. The relationship between the strain gage voltage output and the displacement at the front end of the actuator's fingers was characterized. The equivalent Young's modulus, 13.65 MPa, of the soft-strain-gage-integrated IPMC finger was analyzed. The produced clamping force exhibited a linear increasing rate of 1.07 mN/s, based on a dc driving voltage of 7 V. Using the developed actuator to clamp soft matter and simultaneously acquire its Young's modulus was achieved. This demonstrated the feasibility of the palpation function and the potential use of the actuator in minimally invasive surgery.
Feng, Guo-Hua; Huang, Wei-Lun
2014-12-01
This paper presents a smart tuning-fork-shaped ionic polymer metal composite (IPMC) clamping actuator for biomedical applications. The two fingers of the actuator, which perform the clamping motion, can be electrically controlled through a unique electrode design on the IPMC material. The generated displacement or strain of the fingers can be sensed using an integrated soft strain-gage sensor. The IPMC actuator and associated soft strain gage were fabricated using a micromachining technique. A 13.5×4×2 mm(3) actuator was shaped from Nafion solution and a selectively grown metal electrode formed the active region. The strain gage consisted of patterned copper foil and polyethylene as a substrate. The relationship between the strain gage voltage output and the displacement at the front end of the actuator's fingers was characterized. The equivalent Young's modulus, 13.65 MPa, of the soft-strain-gage-integrated IPMC finger was analyzed. The produced clamping force exhibited a linear increasing rate of 1.07 mN/s, based on a dc driving voltage of 7 V. Using the developed actuator to clamp soft matter and simultaneously acquire its Young's modulus was achieved. This demonstrated the feasibility of the palpation function and the potential use of the actuator in minimally invasive surgery. PMID:25491826
Thermal fluctuations and rubber elasticity.
Xing, Xiangjun; Goldbart, Paul M; Radzihovsky, Leo
2007-02-16
The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation. PMID:17359034
Thermal Fluctuations and Rubber Elasticity
NASA Astrophysics Data System (ADS)
Xing, Xiangjun; Goldbart, Paul M.; Radzihovsky, Leo
2007-02-01
The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation.
Quasi-Static Viscoelastic Finite Element Model of an Aircraft Tire
NASA Technical Reports Server (NTRS)
Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.
1999-01-01
An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.
Finite-element analysis of crack growth under monotonic and cyclic loading
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr.
1977-01-01
An elastic-plastic (incremental) finite-element analysis, in conjunction with a crack-growth criterion, was used to study crack-growth behavior under monotonic and cyclic loading. The crack-growth criterion was based on crack-tip strain. Whenever the crack-tip strain equals or exceeds a critical strain value, the crack grows. The effects of element-mesh size, critical strain, strain hardening, and specimen type (tension or bending) on crack growth under monotonic loading were investigated. Crack growth under cyclic loading (constant amplitude and simple variable amplitude) were also studied. A combined hardening theory, which incorporates features of both isotropic and kinematic hardening under cyclic loading, was also developed for smooth yield surfaces and was used in the analysis.
NASA Astrophysics Data System (ADS)
Salami, N.; Shokri, A. A.; Elahi, S. M.
2016-03-01
Electronic and magnetic properties of a molybdenum disulfide (MoS2) monolayer with some intrinsic and extrinsic vacancies are investigated using ab initio method in the presence of planar strain distributions. The calculations are carried out within the density functional theory (DFT) as implemented in SIESTA package. By using fully relaxed structures and applying a full spin-polarized description to the system, we concentrate on created magnetic moment due to the vacancies under different planar strains. The results show that the extrinsic MoS6 vacancy induces a net magnetic moment of 6.00 μB per supercell. Also, it is found that the pure MoS2 monolayer for the most cases does not show any magnetic properties under the planar strain. While the net magnetic moment of MoS2 monolayer with the vacancies enhances as the planar tensile strain is applied. The tunable magnetic moment of MoS2 monolayer may be utilized for the development of spintronic and flexible electronic nano-devices.
A survey of mixed finite element methods
NASA Technical Reports Server (NTRS)
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
NASA Astrophysics Data System (ADS)
Brand, M.; Rubin, M. B.
2013-02-01
The objective of this paper is to develop constitutive equations of a Cosserat point element (CPE) for the numerical solution of transient large planar motions of elastic-plastic and elastic-viscoplastic beams with rigid cross-sections. Specifically, attention is limited to response of a material with constant yield strength. A yield function is proposed which couples the inelastic responses of tension and shear. Another yield function is proposed for bending which depends on a hardening variable that models motion of the elastic-plastic boundary in the beam's cross-section. Evolution equations are proposed for elastic strains and the hardening variable and an overstress-type formulation is used for elastic-viscoplastic response. In contrast, with standard finite element approaches the CPE model needs no integration through the element region. Also, an implicit scheme is developed to integrate the evolution equations without iteration. Examples of transient large motions of beams, which are impulsively loaded, indicate that the CPE produces reasonably accurate response relative results in the literature and full three-dimensional calculations using ABAQUS.
A method for calculating strain energy release rate based on beam theory
NASA Technical Reports Server (NTRS)
Sun, C. T.; Pandey, R. K.
1993-01-01
The Timoshenko beam theory was used to model cracked beams and to calculate the total strain energy release rate. The root rotation of the beam segments at the crack tip were estimated based on an approximate 2D elasticity solution. By including the strain energy released due to the root rotations of the beams during crack extension, the strain energy release rate obtained using beam theory agrees very well with the 2D finite element solution. Numerical examples were given for various beam geometries and loading conditions. Comparisons with existing beam models were also given.
Improved method for calculating strain energy release rate based on beam theory
NASA Technical Reports Server (NTRS)
Sun, C. T.; Pandey, R. K.
1994-01-01
The Timoshenko beam theory was used to model cracked beams and to calculate the total strain-energy release rate. The root rotations of the beam segments at the crack tip were estimated based on an approximate two-dimensional elasticity solution. By including the strain energy released due to the root rotations of the beams during crack extension, the strain-energy release rate obtained using beam theory agrees very well with the two-dimensional finite element solution. Numerical examples were given for various beam geometries and loading conditions. Comparisons with existing beam models were also given.
Time-dependent strains and stresses in a pumpkin balloon
NASA Technical Reports Server (NTRS)
Gerngross, T.; Xu, Y.; Pellegrino, S.
2006-01-01
This paper presents a study of pumpkin-shaped superpressure balloons, consisting of gores made from a thin polymeric film attached to high stiffness, meridional tendons. This type of design is being used for the NASA ULDB balloons. The gore film shows considerable time-dependent stress relaxation, whereas the behaviour of the tendons is essentially time-independent. Upon inflation and pressurization, the "instantaneous", i.e. linear-elastic strain and stress distribution in the film show significantly higher values in the meridional direction. However, over time, and due to the biaxial visco-elastic stress relaxation of the the material, the hoop strains increase and the meridional stresses decrease, whereas the remaining strain and stress components remain substantially unchanged. These results are important for a correct assessment of the structural integrity of a pumpkin balloon in a long-duration mission, both in terms of the material performance and the overall stability of the shape of the balloon. An experimental investigation of the time dependence of the biaxial strain distribution in the film of a 4 m diameter, 48 gore pumpkin balloon is presented. The inflated shape of selected gores has been measured using photogrammetry and the time variation in strain components at some particular points of these gores has been measured under constant pressure and temperature. The results show good correlation with a numerical study, using the ABAQUS finite-element package, that includes a widely used model of the visco-elastic response of the gore material:
Nematic fluctuations and semisoft elasticity in liquid-crystal elastomers.
Petelin, Andrej; Čopič, Martin
2013-06-01
We give a detailed theory of nematic fluctuations in liquid-crystal elastomers (LCEs) and calculate relaxation rates as obtained by dynamic light scattering (DLS). In ideal LCEs, a nematic state is formed by a spontaneous orientational symmetry breaking of an isotropic state, manifesting itself in an existence of a coupled director-shear soft mode (Goldstone mode). The relaxation rate of the soft mode (a pure bend and a pure splay mode) goes to zero in a long-wavelength limit. In a real, nonideal sample with a locked-in anisotropy, on the other hand, the relaxation rates of these modes become finite. Nonideal elastomers are characterized by a plateau in the stress-strain curve, and the soft mode can be detected only upon stretching to the point of elastic instability at which the director starts to rotate. We use the semisoft model of Gaussian elasticity to derive relaxation rates as a function of deformation for different scattering geometries. We show that the bend-mode relaxation rate goes to zero at the threshold strain, so it is the soft mode. The splay mode, on the other hand, is not soft because the relaxation rate is finite at the threshold strain. We provide experimental evidence and compare DLS measurements of splay and bend modes of two side-chain LCE samples differing in crosslinking densities. Results of both samples are in complete agreement with the predictions of the semisoft model, which indicates that director relaxation properties are not influenced much by the crosslinking conditions.
Elastic modulus of viral nanotubes
NASA Astrophysics Data System (ADS)
Zhao, Yue; Ge, Zhibin; Fang, Jiyu
2008-09-01
We report an experimental and theoretical study of the radial elasticity of tobacco mosaic virus (TMV) nanotubes. An atomic force microscope tip is used to apply small radial indentations to deform TMV nanotubes. The initial elastic response of TMV nanotubes can be described by finite-element analysis in 5nm indentation depths and Hertz theory in 1.5nm indentation depths. The derived radial Young’s modulus of TMV nanotubes is 0.92±0.15GPa from finite-element analysis and 1.0±0.2GPa from the Hertz model, which are comparable with the reported axial Young’s modulus of 1.1GPa [Falvo , Biophys. J. 72, 1396 (1997)].
Significance of Strain in Formulation in Theory of Solid Mechanics
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.
2003-01-01
The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.
Varga, Peter; Hesse, Bernhard; Langer, Max; Schrof, Susanne; Männicke, Nils; Suhonen, Heikki; Pacureanu, Alexandra; Pahr, Dieter; Peyrin, Françoise; Raum, Kay
2015-04-01
Osteocytes are hypothesized to regulate bone remodeling guided by both biological and mechanical stimuli. Morphology of the lacunar-canalicular network of osteocytes has been hypothesized to be strongly related to the level of mechanical loading and to various bone diseases. Finite element modeling could help to better understand the mechanosensation process by predicting the physiological strain environment. The aims of this study were to (i) quantify the lacunar-canalicular morphology in the cortex of the human femur; (ii) predict the in situ local deformations around and in osteocytes by means of case-specific finite element models; and (iii) investigate the potential relationship between morphology and deformations. Human femoral cortical bone samples were imaged using synchrotron X-ray phase nano-tomography with 50 nm voxel size. Rectangular volumes of interest were selected to contain single osteocyte lacunae and the surrounding matrix. Lacunar-canalicular morphology was quantified and the cell geometry was artificially reconstructed based on a priori assumptions. Finite element models of the volumes of interest were generated, containing the extracellular matrix, osteocyte and peri-cellular matrix, and subjected to uniaxial compression. The morphological analysis revealed that canalicular number was dictated by lacunar size, that the spacing of canaliculi fell within a narrow range, suggesting that these pores are well distributed throughout the bone matrix and indicated the trend that lacunae at the outer osteon boundary were less elongated than others. No apparent relationship was found between the morphological parameters and the predicted strains. The globally applied strain was amplified locally by factors up to 10 and up to 70 in the extracellular matrix and the in cells, respectively. Cell deformations were localized mainly at the body-dendrite junctions, with magnitudes reaching the in vitro stimulatory threshold reported for osteocytes.
Finite elements using absolute nodal coordinates for large-deformation flexible multibody dynamics
NASA Astrophysics Data System (ADS)
Dmitrochenko, Oleg
2008-06-01
A family of structural finite elements using a modern absolute nodal coordinate formulation (ANCF) is discussed in the paper with many applicationsE This approach has been initiated in 1996 by A. Shabana. It introduces large displacements of 2D/3D finite elements relative to the global reference frame without using any local frame. The elements employ finite slopes as nodal variables and can be considered as generalizations of ordinary finite elements that use infinitesimal slopes. In contrast to other large deformation formulations, the equations of motion contain constant mass matrices and generalized gravity forces as well as zero centrifugal and Coriolis inertia forces. The only nonlinear term is a vector of elastic forces. This approach allows applying known abstractions of real elastic bodies: Euler-Bernoulli beams, Timoshenko beams and more general models as well as Kirchhoff and Mindlin plate theories. Shabana et al. proposed a sub-family of thick beam and plate finite elements with large deformations and employ the 3D theory of continuum mechanics. Despite the universality of such approach it has to use extra degrees of freedom when simulating thin beams and plates, which case is most important. In our research, we propose another sub-family of thin beams as well as rectangular and triangle plates. We use Kirchhoff plate theory with nonlinear strain-displacement relationships to obtain elastic forces. A number of static and dynamic simulation examples of problems with 2D/3D very elastic beams and plate underwent large displacements and/or deformations will be shown in the presentation.
Mechanism of lens capsular rupture following blunt trauma: a finite element study.
Liu, Xiaoyu; Wang, Lizhen; Du, Chengfei; Li, Deyu; Fan, Yubo
2015-01-01
Blunt impact on the eye could results in lens capsular rupture that allows foreign substances to enter into the lens and leads to cataract formation. This paper aimed to investigate the mechanism of lens capsular rupture using finite element (FE) method. A FE model of the human eye was developed to simulate dynamic response of the lens capsule to a BB (a standard 4.5-mm-diameter pellet) impact. Sensitivity studies were conducted to evaluate the effect of the parameters on capsular rupture, including the impact velocity, the elastic modulus of the lens, the thickness and the elastic modulus of the lens capsule. The results indicated that the lens was subjected to anterior compression and posterior intension when the eye was stricken by a BB pellet. The strain on the posterior capsule (0.392) was almost twice as much as that on the anterior capsule (0.207) at an impact velocity of 20 m/s. The strain on the capsule was proportional to the impact velocity, while the capsular strain showed no significant change when the lens modulus elastic varied with age. The findings confirmed that blunt traumatic capsular rupture is the result of shockwave propagation throughout the eye. The posterior capsule is subjected to greater tension in blunt trauma, which is the main cause that ruptures are more commonly found on the posterior capsule than the anterior capsule. Also, thinner thickness and lower elastic modulus would contribute to the posterior capsular rupture.
Automatic finite element generators
NASA Technical Reports Server (NTRS)
Wang, P. S.
1984-01-01
The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.
Inelastic Strain Analysis of Solder Joint in NASA Fatigue Specimen
NASA Technical Reports Server (NTRS)
Dasgupta, Abhijit; Oyan, Chen
1991-01-01
The solder fatigue specimen designed by NASA-GSFC/UNISYS is analyzed in order to obtain the inelastic strain history during two different representative temperature cycles specified by UNISYS. In previous reports (dated July 25, 1990, and November 15, 1990), results were presented of the elastic-plastic and creep analysis for delta T = 31 C cycle, respectively. Subsequent results obtained during the current phase, from viscoplastic finite element analysis of the solder fatigue specimen for delta T = 113 C cycle are summarized. Some common information is repeated for self-completeness. Large-deformation continuum formulations in conjunction with a standard linear solid model is utilized for modeling the solder constitutive creep-plasticity behavior. Relevant material properties are obtained from the literature. Strain amplitudes, mean strains, and residual strains (as well as stresses) accumulated due to a representative complete temperature cycle are obtained as a result of this analysis. The partitioning between elastic strains, time-independent inelastic (plastic) strains, and time-dependent inelastic (creep) strains is also explicitly obtained for two representative cycles. Detailed plots are presented for two representative temperature cycles. This information forms an important input for fatigue damage models, when predicting the fatigue life of solder joints under thermal cycling
An experimental/analytical comparison of strains in encapsulated assemblies
Guess, T.R.; Burchett, S.N.
1991-11-01
A combined experimental and analytical study of strains developed in encapsulated assemblies during casting, curing and thermal excursions is described. The experimental setup, designed to measure in situ strains, consisted of thin, closed-end, Kovar tubes that were instrumented with strain gages and thermocouples before being over-cast with a polymeric encapsulant. Four bisphenol A (three diethanolamine cured and one anhydride cured) epoxy-based materials and one urethane elastomeric material were studied. After cure of the encapsulant, tube strains were measured over the temperature range of {minus}55{degrees}C to 90{degrees}C. The thermal excursion experiments were then numerically modeled using finite element analyses and the computed strains were compared to the experimental strains. The predicted strains were over estimated (conservative) when a linear, elastic, temperature-dependent material model was assumed for the encapsulant and the stress free temperature T{sub i} was assumed to correspond to the cure temperature {Tc} of the encapsulant. Very good agreement was obtained with linear elastic calculations provided that the stress free temperature corresponded to the onset of the glassy-to-rubbery transition range of the encapsulant. Finally, excellent agreement was obtained in one of the materials (828/DEA) when a viscoelastic material model was utilized and a stress free temperature corresponding to the cure temperature was assumed. 13 refs., 20 figs., 3 tabs.
Validation experiments on finite element models of an ostrich (Struthio camelus) cranium
Bright, Jen A.; Rayfield, Emily J.
2015-01-01
The first finite element (FE) validation of a complete avian cranium was performed on an extant palaeognath, the ostrich (Struthio camelus). Ex-vivo strains were collected from the cranial bone and rhamphotheca. These experimental strains were then compared to convergence tested, specimen-specific finite element (FE) models. The FE models contained segmented cortical and trabecular bone, sutures and the keratinous rhamphotheca as identified from micro-CT scan data. Each of these individual materials was assigned isotropic material properties either from the literature or from nanoindentation, and the FE models compared to the ex-vivo results. The FE models generally replicate the location of peak strains and reflect the correct mode of deformation in the rostral region. The models are too stiff in regions of experimentally recorded high strain and too elastic in regions of low experimentally recorded low strain. The mode of deformation in the low strain neurocranial region is not replicated by the FE models, and although the models replicate strain orientations to within 10° in some regions, in most regions the correlation is not strong. Cranial sutures, as has previously been found in other taxa, are important for modifying both strain magnitude and strain patterns across the entire skull, but especially between opposing the sutural junctions. Experimentally, we find that the strains on the surface of the rhamphotheca are much lower than those found on nearby bone. The FE models produce much higher principal strains despite similar strain ratios across the entirety of the rhamphotheca. This study emphasises the importance of attempting to validate FE models, modelling sutures and rhamphothecae in birds, and shows that whilst location of peak strain and patterns of deformation can be modelled, replicating experimental data in digital models of avian crania remains problematic. PMID:26500813
NASA Astrophysics Data System (ADS)
Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.
2013-03-01
A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.
Asare-Asher, Samuel; Connor, Jason N; Sedev, Rossen
2015-07-01
Liquid marbles are liquid droplets covered densely with small particles. They exhibit hydrophobic properties even on hydrophilic surfaces and this behaviour is closely related to the Cassie wetting state and the phenomenon of superhydrophobicity. Typical liquid marbles are of millimetre size but their properties are analogous to smaller capsules and droplets of Pickering emulsions. We study water marbles covered with an uneven multilayer of polyethylene particles. Their elastic properties were assessed under quasi-static conditions. The liquid marbles are highly elastic and can sustain a reversible deformation of up to 30%. The spring constant is of the same order of magnitude as that for bare water droplets. Therefore the elasticity of the liquid marble is provided mainly by the liquid menisci between the particles. Upon further compression, the spring constant increases up to the point of breakage. This increase may be due to capillary attraction acting across the emerging cracks in the particle coating. The stress-strain curve for liquid marbles is similar to that obtained with liquid-filled microcapsules. A mechanical scaling description proposed for capsules is qualitatively applicable for liquid marbles. The exact mechanical role of the multilayer particle network remains elusive.
Schichtel, N; Korte, C; Hesse, D; Janek, J
2009-05-01
Ionic transport in solids parallel to grain or phase boundaries is usually strongly enhanced compared to the bulk. Transport perpendicular to an interface (across an interface) is often much slower. Therefore in modern micro- and nanoscaled devices, a severe influence on the ionic/atomic transport properties can be expected due to the high density of interfaces.Transport processes in boundaries of ionic materials are still not understood on an atomic scale. In most of the studies on ionic materials the interfacial transport properties are explained by the influence of space charge regions. Here we discuss the influence of interfacial strain at semicoherent or coherent heterophase boundaries on ionic transport along these interfaces in ionic materials. A qualitative model is introduced for (untilted and untwisted) hetero phase boundaries. For experimental verification, the interfacial oxygen ionic conductivity of different multilayer systems consisting of cubic ZrO(2) stabilised by aliovalent dopands (YSZ, CSZ) and an insulating oxide is investigated as a function of structural mismatch. Recent results on extremely fast ionic conduction in YSZ/SrTiO(3) thin film systems ("colossal ionic concuctivity at interfaces") is discussed from the viewpoint of strain effects.
Strain mapping analysis of textile composites
NASA Astrophysics Data System (ADS)
Ivanov, Dmitry; Ivanov, Sergey; Lomov, Stepan; Verpoest, Ignaas
2009-03-01
The focus of the work is meso-scale analysis (scale level of the fabric unit cell) of textile composite deformation and failure. The surface strain measurement is used for: (1) experimental investigation, which includes study of strain distribution at various stages of deformation, plasticity detection, damage initiation; (2) numerical validation of the correspondent finite element (FE) models. Two examples are considered: carbon-epoxy triaxial-braided and glass polypropylene-woven composite. The surface strain measurement (by digital image correlation technique) accompanies the tensile tests, aiming at: (1) elastic anisotropic constants characterisation, (2) study of non-linear material behaviour (for the thermoplastic composite), (3) control of homogeneity of the macro-strain distribution, and (4) analysis of damage initiation in brittle composites. Validation of meso-FE models by strain measurements encounters difficulties arising from (1) resolution of the strain measurements, (2) irregularities of the initial structure such as random layer nesting, ply interaction, and deviation of yarns from their theoretical position, which affects the measured strain fields. The paper discusses these difficulties and demonstrates a qualitative agreement with the FE analysis of idealised composite configurations.
NASA Astrophysics Data System (ADS)
Shahzamanian, M. M.; Sahari, B. B.; Bayat, M.; Mustapha, F.; Ismarrubie, Z. N.
2013-01-01
In this paper, finite element contact analysis of a functionally graded (FG) brake disk in contact with a pad, subjected to rotation, contact pressure, and frictional heat, is presented. The material properties vary through the thickness according to a power-law characterized by a grading index, n. The contact surfaces are full-ceramic with full-metal free surface. The effects of n on the displacement, contact status, strain and stress are investigated. From the analysis, thermo-elastic and contact results are extremely dependent on n. Hence, n is an important criteria for the design of FG brake disks for automotive and aircraft applications.
Universal Elasticity and Fluctuations of Nematic Gels
NASA Astrophysics Data System (ADS)
Xing, Xiangjun; Radzihovsky, Leo
2003-04-01
We study elasticity of spontaneously orientationally ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infrared fixed point. Namely, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible, and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local heterogeneities down to dlc<3.
Kupczik, K; Dobson, C A; Fagan, M J; Crompton, R H; Oxnard, C E; O’Higgins, P
2007-01-01
Crucial to the interpretation of the results of any finite element analysis of a skeletal system is a test of the validity of the results and an assessment of the sensitivity of the model parameters. We have therefore developed finite element models of two crania of Macaca fascicularis and investigated their sensitivity to variations in bone material properties, the zygomatico-temporal suture and the loading regimen applied to the zygomatic arch. Maximum principal strains were validated against data derived from ex vivo strain gauge experiments using non-physiological loads applied to the macaque zygomatic arch. Elastic properties of the zygomatic arch bone and the zygomatico-temporal suture obtained by nanoindentation resulted in a high degree of congruence between experimental and simulated strains. The findings also indicated that the presence of a zygomatico-temporal suture in the model produced strains more similar to experimental values than a completely separated or fused arch. Strains were distinctly higher when the load was applied through the modelled superficial masseter compared with loading an array of nodes on the arch. This study demonstrates the importance of the accurate selection of the material properties involved in predicting strains in a finite element model. Furthermore, our findings strongly highlight the influence of the presence of craniofacial sutures on strains experienced in the face. This has implications when investigating craniofacial growth and masticatory function but should generally be taken into account in functional analyses of the craniofacial system of both extant and extinct species. PMID:17229282
Indentation-derived elastic modulus of multilayer thin films: Effect of unloading induced plasticity
Jamison, Ryan Dale; Shen, Yu -Lin
2015-08-13
Nanoindentation is useful for evaluating the mechanical properties, such as elastic modulus, of multilayer thin film materials. A fundamental assumption in the derivation of the elastic modulus from nanoindentation is that the unloading process is purely elastic. In this work, the validity of elastic assumption as it applies to multilayer thin films is studied using the finite element method. The elastic modulus and hardness from the model system are compared to experimental results to show validity of the model. Plastic strain is shown to increase in the multilayer system during the unloading process. Additionally, the indentation-derived modulus of a monolayermore » material shows no dependence on unloading plasticity while the modulus of the multilayer system is dependent on unloading-induced plasticity. Lastly, the cyclic behavior of the multilayer thin film is studied in relation to the influence of unloading-induced plasticity. Furthermore, it is found that several cycles are required to minimize unloading-induced plasticity.« less
Fracture imaging with converted elastic waves
Nihei, K.T.; Nakagawa, S.; Myer, L.R.
2001-05-29
This paper examines the seismic signatures of discrete, finite-length fractures, and outlines an approach for elastic, prestack reverse-time imaging of discrete fractures. The results of this study highlight the importance of incorporating fracture-generated P-S converted waves into the imaging method, and presents an alternate imaging condition that can be used in elastic reverse-time imaging when a direct wave is recorded (e.g., for crosswell and VSP acquisition geometries).
General dynamical equations of motion for elastic body systems
NASA Astrophysics Data System (ADS)
Weng, Shui-Lin; Greenwood, Donald T.
1992-12-01
A modeling technique capable of determining the time response of a single body (rigid or flexible) that is, in general, undergoing large elastic deformations, coupled with large, nonsteady translational and rotational motions, is presented. The derivations of the governing equations of motion are based on Lagrange's form of d'Alembert's principle. The general dynamical equations of motion are expressed in terms of stress and strain tensors, kinematic variables, the velocity and angular velocity coefficients, and generalized forces. The formulation of these equations is discussed in detail. Numerical simulations that involve finite elastic deformations coupled with large, nonsteady rotational motions are presented for a beam attached to a rotating base. Effects such as centrifugal stiffening and softening, membrane strain effect, and vibrations induced by Coriolis forces are accommodated. The effects of rotary inertia as well as shear deformation are also included in the equations of motion. Although discussions here are restricted to a single body, the formulation allows the capability of a general dynamical formalism for handling multibody (rigid or flexible) dynamics.
Cavitation, Elasticity and Fracture in Strong Hydrogels
NASA Astrophysics Data System (ADS)
Cui, Jun; Madkour, Ahmad; Tew, Gregory; Crosby, Alfred
2010-03-01
The interplay between the molecular network and material microstructure of a polymer-based hydrogel is critical for determining both the low strain elastic properties and fracture toughness. We present a novel complex hydrogel network developed by introducing polydimethylsiloxane (PDMS) into a polyethylene glycol (PEG)-based network. Using a combination of conventional characterization techniques, as well as the recently developed technique of cavitation rheology, we investigate the balance of elasticity and fracture in these complex networks. The polymer network maintains elasticity, with negligible hysteresis, at large strains over a wide range of swelling ratios. These properties are investigated across a continuum of length scales ranging from microns to centimeters by taking advantage of cavitation rheology, which uses the onset of an elastic instability to quantify local network mechanics. We compare our results with established scaling theories to describe both the elastic and fracture properties as a function of polymer volume fraction.
Elasticity limits structural superlubricity in large contacts
NASA Astrophysics Data System (ADS)
Sharp, Tristan A.; Pastewka, Lars; Robbins, Mark O.
2016-03-01
Geometrically imposed force cancellations lead to ultralow friction between rigid incommensurate crystalline asperities. Elastic deformations may avert this cancellation but are difficult to treat analytically in finite and three-dimensional systems. We use atomic-scale simulations to show that elasticity affects the friction only after the contact radius a exceeds a characteristic length set by the core width of interfacial dislocations bcore. As a increases past bcore, the frictional stress for both incommensurate and commensurate surfaces decreases to a constant value. This plateau corresponds to a Peierls stress that drops exponentially with increasing bcore but remains finite.
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr.; Warren, Jerry E.; Elliott, Kenny B.; Song, Kyongchan; Raju, Ivatury S.
2012-01-01
Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.
NASA Astrophysics Data System (ADS)
Favache, Audrey; Ryelandt, Sophie; Melchior, Maxime; Zeb, Gul; Carbonnelle, Pierre; Raskin, Jean-Pierre; Pardoen, Thomas
2016-01-01
Accurate measurement of the mechanical properties of ultra-thin films with thicknesses typically below 100 nm is a challenging issue with an interest in many fields involving coating technologies, microelectronics, and MEMS. A bilayer curvature based method is developed for the simultaneous determination of the elastic mismatch strain and Young's modulus of ultra-thin films. The idea is to deposit the film or coating on very thin cantilevers in order to amplify the curvature compared to a traditional "Stoney" wafer curvature test, hence the terminology "micro-Stoney." The data reduction is based on the comparison of the curvatures obtained for different supporting layer thicknesses. The elastic mismatch strain and Young's modulus are obtained from curvature measurements of cantilevers before and after the film deposition. The data reduction scheme relies on both analytical and finite element calculations, depending on the magnitude of the curvature. The experimental validation has been performed on ultra-thin low pressure chemical vapor deposited silicon nitride films with thickness ranging between 54 and 133 nm deposited on silicon cantilevers. The technique is sensitive to the cantilever geometry, in particular, to the thickness ratio and width/thickness ratio. Therefore, the precision in the determination of the latter quantities determines the accuracy on the extracted elastic mismatch strain and elastic modulus. The method can be potentially applied to films as thin as a few nanometers.
Favache, Audrey; Ryelandt, Sophie; Melchior, Maxime; Zeb, Gul; Carbonnelle, Pierre; Raskin, Jean-Pierre; Pardoen, Thomas
2016-01-01
Accurate measurement of the mechanical properties of ultra-thin films with thicknesses typically below 100 nm is a challenging issue with an interest in many fields involving coating technologies, microelectronics, and MEMS. A bilayer curvature based method is developed for the simultaneous determination of the elastic mismatch strain and Young's modulus of ultra-thin films. The idea is to deposit the film or coating on very thin cantilevers in order to amplify the curvature compared to a traditional "Stoney" wafer curvature test, hence the terminology "micro-Stoney." The data reduction is based on the comparison of the curvatures obtained for different supporting layer thicknesses. The elastic mismatch strain and Young's modulus are obtained from curvature measurements of cantilevers before and after the film deposition. The data reduction scheme relies on both analytical and finite element calculations, depending on the magnitude of the curvature. The experimental validation has been performed on ultra-thin low pressure chemical vapor deposited silicon nitride films with thickness ranging between 54 and 133 nm deposited on silicon cantilevers. The technique is sensitive to the cantilever geometry, in particular, to the thickness ratio and width/thickness ratio. Therefore, the precision in the determination of the latter quantities determines the accuracy on the extracted elastic mismatch strain and elastic modulus. The method can be potentially applied to films as thin as a few nanometers. PMID:26827345
MHOST: An efficient finite element program for inelastic analysis of solids and structures
NASA Technical Reports Server (NTRS)
Nakazawa, S.
1988-01-01
An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.
NASA Astrophysics Data System (ADS)
Gopinath, Thamilselvan; Raja, Samikannu; Ikeda, Tadashige
2011-03-01
The use of surface bonded (MFC) and embedded (SAFC) piezoelectric composite actuators is examined through a numerical study. Modelling schemes are therefore developed by applying the isoparametric finite element approach to idealize normal strain to electric field and shear strain to electric field relations. A four noded coupled finite element is developed to compute the electro-mechanical responses of the active plate. A linear quadratic regulator is employed to perform the active vibration control studies. The system matrices of the smart plate structure are obtained and used in the state-space control model. Two elastic modes are considered, namely bending and torsion of the active plate. The emphasis is given to evaluate the performance of two different kinds of flexible piezoelectric actuators in vibration control application.
The high strain compression of micro- and nano-sized random irregular honeycombs
NASA Astrophysics Data System (ADS)
You, J. F.; Zhang, H. C.; Zhu, H. X.; Kennedy, D.
2016-09-01
This paper investigates the effects of cell wall thickness, initial stress/strain, and cell regularity on the high strain compressive responses of micro- and nano-sized low density random irregular honeycombs. The strain gradient effects at the micrometer scale, and the surface elasticity and initial stress effects at the nanometer scale are incorporated into the dominant deformation mechanisms in finite element simulations. It is found that the dimensionless compressive stress strain relation strongly depends on the thickness of the cell walls at the micron scale, and at the nano-meter scale, this relation is not only size-dependent, but are also tunable and controllable over a large range. It is also found that under high strain compression, the Poisson’s ratios of micro- and nano-sized low density random irregular honeycombs strongly depend on the cell regularity, but are almost independent of the cell wall thickness and the amplitudes of the initial stress or strain.
Croft, M.; Shukla, V.; Akdogan, E. K.; Sadangi, R.; Ignatov, A.; Balarinni, L.; Tsakalakos, T.; Jisrawi, N.; Zhong, Z.; Horvath, K.
2009-05-01
Elastic and plastic strain evolution under four-point bending has been studied by synchrotron energy dispersive x-ray diffraction. Measured strain profiles across the specimen thickness showed an increasing linear elastic strain gradient under increasing four-point bending load up to approx2 kN. The bulk elastic modulus of Ti-6Al-4V was determined as 118 GPa. The onset of plastic deformation was found to set in at a total in-plane strain of approx0.008, both under tension and compression. Plastic deformation under bending is initiated in the vicinity of the surface and at a stress of 1100 MPa, and propagates inward, while a finite core region remains elastically deformed up to 3.67 kN loading. The onset of the plastic regime and the plastic regime itself has been verified by monitoring the line broadening of the (100) peak of alpha-Ti. The effective compression/tension stress-strain curve has been obtained from the scaling collapse of strain profile data taken at seven external load levels. A similar multiple load scaling collapse of the plastic strain variation has also been obtained. The level of precision in strain measurement reported herein was evaluated and found to be 1.5x10{sup -5} or better.
On the response of rubbers at high strain rates.
Niemczura, Johnathan Greenberg
2010-02-01
In this report, we examine the propagation of tensile waves of finite deformation in rubbers through experiments and analysis. Attention is focused on the propagation of one-dimensional dispersive and shock waves in strips of latex and nitrile rubber. Tensile wave propagation experiments were conducted at high strain-rates by holding one end fixed and displacing the other end at a constant velocity. A high-speed video camera was used to monitor the motion and to determine the evolution of strain and particle velocity in the rubber strips. Analysis of the response through the theory of finite waves and quantitative matching between the experimental observations and analytical predictions was used to determine an appropriate instantaneous elastic response for the rubbers. This analysis also yields the tensile shock adiabat for rubber. Dispersive waves as well as shock waves are also observed in free-retraction experiments; these are used to quantify hysteretic effects in rubber.
NASA Astrophysics Data System (ADS)
Renaud, Guillaume; Talmant, Maryline; Marrelec, Guillaume
2016-10-01
The nonlinear elasticity of solids at the microstrain level has been recently studied by applying dynamic acousto-elastic testing. It is the analog of conventional quasi-static acousto-elastic experiments but the strain-dependence (or stress-dependence) of ultrasonic wave-speed is measured with an applied strain ranging from 10-7 to 10-5 and produced by a stationary elastic wave. In conventional quasi-static acousto-elastic experiments, the strain is applied in a quasi-static manner; it exceeds 10-4 and can reach 10-2. In this work, we apply dynamic acousto-elastic testing to measure the third-order elastic constants of two isotropic materials: polymethyl methacrylate and dry Berea sandstone. The peak amplitude of the dynamic applied strain is 8 × 10-6. The method is shown to be particularly suitable for materials exhibiting large elastic nonlinearity like sandstones, since the measurement is performed in the domain of validity of the third-order hyperelastic model. In contrast, conventional quasi-static acousto-elastic experiments in such materials are often performed outside the domain of validity of the third-order hyperelastic model and the stress-dependence of the ultrasonic wave-speed must be extrapolated at zero stress, leading to approximate values of the third-order elastic constants. The uncertainty of the evaluation of the third-order elastic constants is assessed by repeating multiple times the measurements and with Monte-Carlo simulations. The obtained values of the Murnaghan third-order elastic constants are l = -73 GPa ± 9%, m = -34 GPa ± 9%, and n = -61 GPa ± 10% for polymethyl methacrylate, and l = -17 000 GPa ± 20%, m = -11 000 GPa ± 10%, and n = -30 000 GPa ± 20% for dry Berea sandstone.
Elastic properties of spherically anisotropic piezoelectric composites
NASA Astrophysics Data System (ADS)
Wei, En-Bo; Gu, Guo-Qing; Poon, Ying-Ming
2010-09-01
Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.
Energy dissipation associated with crack extension in an elastic-plastic material
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Crews, J. H., Jr.
1987-01-01
Crack extension in elastic-plastic material involves energy dissipation through the creation of new crack surfaces and additional yielding around the crack front. An analytical procedure, using a two-dimensional elastic-plastic finite element method, was developed to calculate the energy dissipation components during a quasi-static crack extension. The fracture of an isotropic compact specimen was numerically simulated using the critical crack-tip-opening-displacement (CTOD) growth criterion. Two specimen sizes were analyzed for three values of critical CTOD. Results from the analyses showed that the total energy dissipation rate consisted of three components: the crack separation energy rate, the plastic energy dissipation rate, and the residual strain energy rate. All three energy dissipation components and the total energy dissipation rate initially increased with crack extension and finally reached constant values.
Energy dissipation associated with crack extension in an elastic-plastic material
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Crews, J. H., Jr.
1987-01-01
Crack extension in elastic-plastic material involves energy dissipation through the creation of new crack surfaces and additional yielding around the crack front. An analytical procedure, using a two-dimensional elastic-plastic finite element method, was developed to calculate the energy dissipation components during a quasi-static crack extension. The fracture of an isotropic compact specimen was numerically simulated using the critical crack-tip-opening-displacement (CTOD) growth criterion. Two specimen sizes were analyzed for three values of critical CTOD. Results from the analysis showed that the total energy dissipation rate consisted of three components: the crack separation energy rate, the plastic energy dissipation rate, and the residual strain energy rate. All three energy dissipation components and the total energy dissipation rate initially increased with crack extension and finally reached constant values.
Estimation of Nonlinear Elasticity Parameter of Tissues by Ultrasound
NASA Astrophysics Data System (ADS)
Nitta, Naotaka; Shiina, Tsuyoshi
2002-05-01
In this paper, a new parameter that quantifies the intensity of tissue nonlinear elasticity is introduced as the nonlinear elasticity parameter. This parameter is defined based on the empirical information that the nonlinear elastic behavior of soft tissues exhibits an exponential character. To visualize the quantitative nonlinear elasticity parameter, an ultrasonic imaging procedure involving the three-dimensional finite element method (3-D FEM) is presented. Experimental investigations that visualize the nonlinear elasticity parameter distribution of a chicken gizzard and a pig kidney embedded in a gelatin-based phantom were performed. The values extracted by ultrasound and 3-D FEM were compared with those measured by the direct mechanical compression test. Experimental results revealed that the nonlinear elasticity parameter values extracted by ultrasound and 3-D FEM exhibited good agreement with those measured by the mechanical compression test, and that the intensity of tissue nonlinear elasticity could be visualized quantitatively by the defined nonlinear elasticity parameter.
NASA Astrophysics Data System (ADS)
Vattré, A.; Denoual, C.
2016-07-01
A thermodynamically consistent framework for combining nonlinear elastoplasticity and multivariant phase-field theory is formulated at large strains. In accordance with the Clausius-Duhem inequality, the Helmholtz free energy and time-dependent constitutive relations give rise to displacive driving forces for pressure-induced martensitic phase transitions in materials. Inelastic forces are obtained by using a representation of the energy landscape that involves the concept of reaction pathways with respect to the point group symmetry operations of crystal lattices. On the other hand, additional elastic forces are derived for the most general case of large strains and rotations, as well as nonlinear, anisotropic, and different elastic pressure-dependent properties of phases. The phase-field formalism coupled with finite elastoplastic deformations is implemented into a three-dimensional Lagrangian finite element approach and is applied to analyze the iron body-centered cubic (α-Fe) into hexagonal close-packed (ɛ-Fe) phase transitions under high hydrostatic compression. The simulations exhibit the major role played by the plastic deformation in the morphological and microstructure evolution processes. Due to the strong long-range elastic interactions between variants without plasticity, a forward α → ɛ transition is energetically unfavorable and remains incomplete. However, plastic dissipation releases considerably the stored strain energy, leading to the α ↔ ɛ ↔α‧ (forward and reverse) polymorphic phase transformations with an unexpected selection of variants.
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Pai, Shantaram S.; Hopkins, Dale A.
2007-01-01
The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity is referred to as the completed Beltrami-Michell formulation (CBMF), and it is the integrated force method (IFM) in structures. The dual integrated force method (IFMD) with displacement as the primary unknown has been formulated. IFM and IFMD produce identical responses. The variational derivation of the CBMF yielded the new boundary compatibility conditions. The CBMF can be used to solve stress, displacement, and mixed boundary value problems. The IFM in structures produced high-fidelity response even with a modest finite element model. The IFM has influenced structural design considerably. A fully utilized design method for strength and stiffness limitation has been developed. The singularity condition in optimization has been identified. The CBMF and IFM tensorial approaches are robust formulations because of simultaneous emphasis on the equilibrium equation and the compatibility condition.
Effects of physical exercise on the elasticity and elastic components of the rat aorta.
Matsuda, M; Nosaka, T; Sato, M; Ohshima, N
1993-01-01
To evaluate the effects of exercise on aortic wall elasticity and elastic components, young male rats underwent various exercise regimes for 16 weeks. In the exercised rats, the aortic incremental elastic modulus decreased significantly when under physiological strain. The aortic content of elastin increased significantly and the calcium content of elastin decreased significantly in the exercised group. The accumulated data from the exercised and sedentary groups revealed that the elastin calcium content was related positively to the incremental elastic modulus. We concluded that physical exercise from an early age decreases the calcium deposit in aortic wall elastin and that this effect probably produced in the exercised rats a distensible aorta.
Stored energy function and compressibility of compressible rubberlike materials under large strain
NASA Technical Reports Server (NTRS)
Peng, S. T. J.; Landel, R. F.
1975-01-01
By using new invariants in the theory of finite elasticity an expression is obtained for the stored energy function of slightly compressible materials in which the effects of the distortional change (change of shape) and of the volume change are clearly separated. The volume-related terms are expressed as a function of the third invariant, the classical compressibility, and an induced anisotropy of the effective compressibility which is due to the large deformations. After evaluating the terms, using data on pressure, volume, uniaxial strain, and fractional volume change vs strain data on natural rubber from the literature, it is shown that the volume change contribution to the total stress observed in a simple tensile experiment can be clearly separated from the distortional contribution, even at finite strains.
NASA Technical Reports Server (NTRS)
Burns, S. W.; Mathison, S.; Herakovich, C. T.
1986-01-01
ANISAP is a 3-D finite element FORTRAN 77 computer code for linear elastic, small strain, analysis of laminated composites with arbitrary geometry including free edges and holes. Individual layers may be isotropic or transversely isotropic in material principal coordinates; individual layers may be rotated off-axis about a global z-axis. The laminate may be a hybrid. Three different isoparametric elements, variable order of gaussian integration, calculation of stresses at element boundaries, and loading by either nodal displacement of forces are included in the program capability. Post processing capability includes failure analysis using the tensor polynominal failure criterion.
Contact stresses in meshing spur gear teeth: Use of an incremental finite element procedure
NASA Technical Reports Server (NTRS)
Hsieh, Chih-Ming; Huston, Ronald L.; Oswald, Fred B.
1992-01-01
Contact stresses in meshing spur gear teeth are examined. The analysis is based upon an incremental finite element procedure that simultaneously determines the stresses in the contact region between the meshing teeth. The teeth themselves are modeled by two dimensional plain strain elements. Friction effects are included, with the friction forces assumed to obey Coulomb's law. The analysis assumes that the displacements are small and that the tooth materials are linearly elastic. The analysis procedure is validated by comparing its results with those for the classical two contacting semicylinders obtained from the Hertz method. Agreement is excellent.
Aggregation-structure-elasticity relationship of gels
NASA Astrophysics Data System (ADS)
Ma, Hang-Shing
Aerogel is a mesoporous, low-density material which is desirable for applications like thermal insulation and low-k interlayer dielectric. However, its lack of mechanical integrity hinders its development. Experiments have shown that aerogels exhibit a scaling relationship E ∝ rho m between modulus E and density rho, with the exponent m usually between 3 and 4. The objective of the dissertation is to use computer modeling to understand how the random aggregation process accounts for the fractal structure and the compliant nature of aerogels. Model gels were created by the diffusion-limited cluster-cluster aggregation (DLCA), which simulates random aggregation leading to the sol-gel transition. Then each resulting structure was modeled as an elastic beam network and numerically compressed using the finite element method (FEM). Analyses showed that the DLCA gels reproduced the scaling relationship after trimming the non-contributive dangling branches from the mechanically efficient looped networks. The dangling bond deflection (DEF) model was therefore developed to model the random rotational movement of the dangling branches and the subsequent loop structure formation. Model gels with extensive loops and negligible dangling branches were simulated by combining the DLCA and DEF models. Representation of the aerogel networks by the DLCADEF models was validated for the resemblance of the fractal geometry and elastic behavior. The lack of mechanical integrity in aerogels is a natural consequence of the random aggregation and the resulting fractal structure. Fractal clusters are created in the early stage of aggregation, each of which is characterized by a dense core and sparse perimeter. These clusters grow in size until they percolate at the gel point by knitting together at the perimeters. The gel structure possesses a "blob-and-link" architecture, with the blobs representing the rigid cores of the fractal clusters, and the links corresponding to the tenuous chains
2016-01-01
Purpose This study investigated the effects of bone density and crestal cortical bone thickness at the implant-placement site on micromotion (relative displacement between the implant and bone) and the peri-implant bone strain distribution under immediate-loading conditions. Methods A three-dimensional finite element model of the posterior mandible with an implant was constructed. Various bone parameters were simulated, including low or high cancellous bone density, low or high crestal cortical bone density, and crestal cortical bone thicknesses ranging from 0.5 to 2.5 mm. Delayed- and immediate-loading conditions were simulated. A buccolingual oblique load of 200 N was applied to the top of the abutment. Results The maximum extent of micromotion was approximately 100 μm in the low-density cancellous bone models, whereas it was under 30 μm in the high-density cancellous bone models. Crestal cortical bone thickness significantly affected the maximum micromotion in the low-density cancellous bone models. The minimum principal strain in the peri-implant cortical bone was affected by the density of the crestal cortical bone and cancellous bone to the same degree for both delayed and immediate loading. In the low-density cancellous bone models under immediate loading, the minimum principal strain in the peri-implant cortical bone decreased with an increase in crestal cortical bone thickness. Conclusions Cancellous bone density may be a critical factor for avoiding excessive micromotion in immediately loaded implants. Crestal cortical bone thickness significantly affected the maximum extent of micromotion and peri-implant bone strain in simulations of low-density cancellous bone under immediate loading. PMID:27382504
Elasticity and Broken Symmetry in Nematic Elastomers
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Ranjan; Lubensky, T. C.; Xing, Xiangjun; Radzihovsky, Leo
2002-03-01
In nematic elastomers, the coupling between the internal liquid crystalline degrees of freedom and elastic strains lead to novel thermodynamic and mechanical behavior. Their remarkable properties make them candidates for a number of applications including artificial muscles and actuators. Other than their technological importance, their behavior highlights a major theme of physics: the interplay between broken symmetries and long-wavelength elasticity and hydrodynamics. In this talk my primary focus will be to show how the elastic "softness" and the pronounced nonlinear stress-strain relations in these materials arise as a consequence of broken rotational symmetry. We will reproduce these properties using simple models in a way that highlights this interplay between broken rotational symmetry and elasticity.
Computational Simulation of the High Strain Rate Tensile Response of Polymer Matrix Composites
NASA Technical Reports Server (NTRS)
Goldberg, Robert K.
2002-01-01
A research program is underway to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Under these types of loading conditions, the material response can be highly strain rate dependent and nonlinear. State variable constitutive equations based on a viscoplasticity approach have been developed to model the deformation of the polymer matrix. The constitutive equations are then combined with a mechanics of materials based micromechanics model which utilizes fiber substructuring to predict the effective mechanical and thermal response of the composite. To verify the analytical model, tensile stress-strain curves are predicted for a representative composite over strain rates ranging from around 1 x 10(exp -5)/sec to approximately 400/sec. The analytical predictions compare favorably to experimentally obtained values both qualitatively and quantitatively. Effective elastic and thermal constants are predicted for another composite, and compared to finite element results.
Finite element analysis on the fracture of rubber toughened polymer blends
Wu, Y.; Mai, Y.W.; Wu, J.
1997-12-31
The effect of rubber particle volume fraction on the constitutive relation and fracture toughness of polymer blends was studied using elastic-plastic Finite Element Analysis (FEA). The effect of rubber particle cavitation on the stress-strain state at a crack tip was also investigated. Stress analysis reveals that because of the high rubber bulk modulus, the hydrostatic stress inside the rubber particle is close to that in the adjacent matrix material element. As a result, the rubber particle imposes a severe plastic constraint to the surrounding matrix and limits its plastic strain. Rubber particle cavitation can effectively release the constraint and enable large scale plastic strain to occur. Different failure criteria were used to determine the optimum rubber particle volume fraction for the polymer blends studied in this paper.