An Alternative Framework for Developing Material Models for Finite-Strain Elastoplasticity

Abstract

Contemporary plasticity theories and their related material models for finite deformations are either based on additive decomposition of a strain-rate tensor or on multiplicative decomposition of a deformation gradient tensor into an elastic part and a plastic part. From the standpoint of the nonlinear continuum mechanics, the former theories, which are used to model hypoelastic-plastic materials, are rather incomplete theories, while the latter theories, which are used to model hyperelastic-plastic materials, are not even continuum-based theories, while none of their related material models are thermodynamically consistent. Recently, a nonlinear continuum theory for finite deformations of elastoplastic media was proposed, which allows for the development of objective and thermodynamically consistent material models. Therefore, the analysis results of the models are independent of the description and the particularities of their mathematical formulation. Here by the description we mean total or updated Lagrangian description and by the particularities of formulation, the ability to describe the model in various stress spaces using internal mechanical power conjugate stress measures and strain rates. In this chapter, an alternative framework for developing objective and thermodynamically consistent hypoelastic-plastic-and hyperelastic-plastic-based material models is presented using the first nonlinear continuum theory of finite deformations of elastoplastic media. Keywords: nonlinear continuum theory for finite deformations of elastoplastic media, objective and thermodynamically consistent formulation, J 2 generalised plasticity with isotropic hardening, hypoelastic-plastic-and hyperelasticplastic-based material models with internal damping

Investigating the Effect of Cementite Particle Size and Distribution on Local Stress and Strain Evolution in Spheroidized Medium Carbon Steels using Crystal Plasticity‐Based Numerical Simulations

“…[ 35,36 ] It uses finite‐strain theory coupled with the continuum mechanical description of deformable bodies to calculate the material response. [ 35,37 ] This tool has been used successfully to solve many problems, as detailed in the previous studies. [ 19,31,38–45 ] The recent steel matrix analysis with ceramic particles by Qayyum et al [ 46 ] has shown the viability of the DAMASK code to conduct a local deformation behavioral analysis.…”

A Study on the ‘Compatiblity Assumption’ of Contemporary Multiplicative Plasicity Models

“…that the material model can be formulated in whatever stress space in terms of internal power conjugate stress measures and strain or deformation rates without influencing the analysis results. This is achieved by two postulates, namely that the force acting on the surface of an infinitesimal volume element and the rate of the change of the internal mechanical energy accumulated in the element in the body's initial and current configurations be the same [8,9], which was later on extended by Écsi and Élsztős and their associates to cover constitutive equations in rate forms [10][11][12]. Upon using the same procedure, the Cauchy's stress theorem ,…”

“…As a result, the assumption of a stress-free or locally unstressed intermediate configuration is not justified physically from the nonlinear continuum theory point of view. However, it should be noted, that all the problems herein except for the stress-free/locally unstressed configuration with contemporary plasticity models can be eliminated by modifying the kinematics of elastoplastic deformations in accordance with the theory of nonlinear continuum mechanics, which then will result in the entirely new nonlinear continuum theory for finite-deformations of elastoplastic media already published by Écsi and Élesztős and their associates [10][11][12].…”