A study of two finite strain plasticity models: An internal time theory using Mandel's director concept, and a general isotropic/kinematic- hardening theory
type: Item
instance of: scholarly article
title: A study of two finite strain plasticity models: An internal time theory using Mandel's director concept, and a general isotropic/kinematic- hardening theory
zbMATH Open document ID: 0633.73051
DOI: 10.1016/0749-6419(87)90005-2
author: Satya N. Atluri
author: Seyoung Im
published in: International Journal of Plasticity
publication date: 1987-01-01T00:00:00Z
review text: Using Mandel's director concept, the internal time theory for small deformation deviatoric plasticity is extended to the case of finite elastoplasticity. The introduction of the material director triad together with an isoclinic configuration makes possible an integral representation of the induced stress tensor in terms of the deformation history [referred to the relaxed intermediate configuration]. For a class of deformations in which elastic strains are small, this leads to rate- type constitutive equations similar to those in the small deformation theory. The model retains the characteristics of the original internal time theory, such as the existence of a von Mises type of yield surface that undergoes translation (nonlinear kinematic hardening), as well as uniform expansion in the stress space, and of the normality of the tensor of plastic rate of deformation to the yield hypersurface. In modeling finite uniaxial compression and finite torsion test data, the present internal time theory is found to lead to results very similar to those from a phenomenological theory with a priori postulated evolution equation for an arbitrary objective rate (say, the Jaumann rate) of the back stress using the general representation for the symmetric tensor function. This latter phenomenological theory is a slight modification of the one proposed earlier by \textit{K. W. Reed} and the second author [ibid. 1, 63-87 (1985; Zbl 0612.73050)] and accounts for large plastic rotations in finite strain deformations. Both models are shown (1) to lead to nonoscillatory shear stresses for all magnitudes of shear in a simple shear deformation, (2) to predict the correct magnitude (as found in experiments) of axial stresses/strains in a finite-strain torsion test, and (3) to correctly model the experimentally noted differences in the von Mises equivalent Cauchy stress (or \(J_ 2)\) values in uniaxial compression test and torsion test, respectively, at large values of equivalent strains. Both…
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74D99
Mathematics Subject Classification ID: 74C15
Mathematics Subject Classification ID: 74C20
zbMATH DE Number: 4031139
zbMATH Keywords: Mandel's director concept
zbMATH Keywords: internal time theory
zbMATH Keywords: small deformation deviatoric plasticity
zbMATH Keywords: finite elastoplasticity
zbMATH Keywords: rate-type constitutive equations
zbMATH Keywords: arbitrary objective rate
zbMATH Keywords: phenomenological theory
zbMATH Keywords: large plastic rotations
zbMATH Keywords: finite strain deformations
zbMATH Keywords: Jaumann rates
zbMATH Keywords: Cauchy stress
zbMATH Keywords: Cauchy back stress
MaRDI profile type: Publication
full work available at URL: 0749-6419(87)90005-2
OpenAlex ID: W2038182311
description: scientific article; zbMATH DE number 4031139