Large Strain

A micromechanics framework for the development of continuum-level constitutive models for the large-strain deformation of porous hyperelastic materials is presented. A kinematically admissible deformation field is assumed which enables the derivation of a strain energy density function for the porous material. The strain energy density function depends on the properties of the incompressible hyperelastic matrix material, the initial level of porosity, and the macroscopic deformation. Differentiation of the strain energy density function, with respect to deformation, provides an expression for the stress–strain behavior of the porous hyperelastic material. Example calculations are carried out for porous hyperelastic materials with a Neo–Hookean matrix. The constitutive model is used to predict the stress–strain behavior of the pore-containing matrix as a function of initial porosity and macroscopic loading conditions. Predictions of the dependence of the small-strain elastic response on porosity are compared to various estimates of effective elastic moduli for porous materials found in the literature. Constitutive model predictions of the small to large-strain deformation behavior compare well with results from numerical three-dimensional micromechanical multi-void cell models.

The large-strain constitutive behavior of cold-rolled 1018 steel has been characterized at strain rates ranging from $\dot \varepsilon = 10^{ - 3} $ to 5 × 104 s−1 using a newly developed shear compression specimen (SCS). The SCS technique allows for a seamless characterization of the constitutive behavior of materials over a large range of strain rates. The comparison of results with those obtained by cylindrical specimens shows an excellent correlation up to strain rates of 104 s−1. The study also shows a marked strain rate sensitivity of the steel at rates exceeding 100 s−1. With increasing strain rate, the apparent average strain hardening of the material decreases and becomes negative at rates exceeding 5000 s−1. This observation corroborates recent results obtained in torsion tests, while the strain softening was not clearly observed during dynamic compression of cylindrical specimens. A possible evolution scheme for shear localization is discussed, based on the detailed characterization of deformed microstructures. The Johnson-Cook constitutive model has been modified to represent the experimental data over a wide range of strain rates as well as to include heat-transfer effects, and model parameters have been determined for 1018 cold-rolled steel.

Purpose: This paper deals with the FEA of the sheet metal forming process that involves various nonlinearities. Our objective is to develop a parametric study that can leads mainly to predict accurately the final geometry of the sheet blank and the distribution of strains and stresses and also to control various forming defects, such as thinning as well as parameters

ABSTRACT: In this paper, a Total Lagrangian formulation based on the Logarithmic strains is developed. The
variation in these strains is based on the variation of the Engineering strains and the variation of Green strains.
The  “true”  Cauchy  stresses  thus  obtained  are  compared  with  the  Engineering  stresses  based  on  the
Engineering strains obtained from a Total Lagrangian formulation. The Cauchy stresses obtained based on the
assumption  of  small  Engineering  shear  strains  are  also  compared  with  the  above  mentioned  stresses.  A
Geometric nonlinear Total Lagrangian  formulation applied on  two-dimensional elasticity using 4-node plane
finite  elements  was  used.  The  formulation  was  implemented  into  the  finite  element  program  (NUSAP).  The
solution  of  nonlinear  equations was  obtained  by  the Newton-Raphson method.  The  program was  applied  to
obtain stresses  for  three numerical examples. The evaluation of  the accuracy of  the formulation was based on
comparing  the  stresses  obtained  with  those  from  the  other  two  formulations  as  stated  above.  The  paper
concludes that all three Total Lagrangian formulations converge to the correct solution, as expected, for small
strains. For moderate and  large strains,  there  is a clear difference between  the Cauchy and    the Engineering
stresses.  The  formulation  based  on  the Logarithmic  strains  results  in  the  accurate  evaluation  of  the “true”
Cauchy  stresses.  These  stresses  can  be  used  in  the  geometric  and  material  nonlinear  analyses  of  large
deformation problems using constitutive equations based on Logarithmic strains.

PEM fuel cell assembly pressure is known to cause large strains in the gas diffusion layer (GDL), which results in significant changes in its mechanical, electrical and thermal properties. These changes affect the rates of mass, charge, and heat transport through the GDL, thus impacting fuel cell performance and lifetime. The appropriate modeling of the inhomogeneous GDL compression process associated with the repetitive channel-rib pattern is therefore essential for a detailed description of the physical–chemical processes that take place in the cell. In this context, the mechanical characterization of the GDL is of special relevance, since its microstructure based on carbon fibers has strongly nonlinear orthotropic properties. The present study describes a new finite element model which fully incorporates the nonlinear orthotropic characteristics of the GDL, thereby improving the prediction of the inhomogeneous compression effects in this key element of the cell. Among other conclusions, the numerical results show that the linear isotropic models widely reported in the literature tend to overestimate the porosity and the partial intrusion of the GDL in the channel region, and may lead to incorrect predictions in terms of interfacial contact pressure distributions.