Stress rate and the Lagrangian formulation of the finite-strain plasticity for a von Mises kinematic hardening model
type: Item
instance of: scholarly article
title: Stress rate and the Lagrangian formulation of the finite-strain plasticity for a von Mises kinematic hardening model
zbMATH Open document ID: 0601.73047
DOI: 10.1016/0020-7683(87)90033-3
author: P. D. Kiousis
author: George Z. Voyiadjis
published in: International Journal of Solids and Structures
publication date: 1987-01-01T00:00:00Z
review text: The use of the Jaumann stress rate, in kinematic hardening finite-strain plasticity, in the case of simple shear generates oscillations in the stress field. Alternate theories have been introduced to define other stress rates by making use of the polar decomposition and consequently producing increasing shear stress. In this work, a Lagrangian formulation is introduced which, for the case of simple shear produces monotonically increasing stress-strain relationships. The yield criterion is originally expressed in terms of the Cauchy stress and subsequently transformed to the Lagrangian reference frame. The associated flow rule used here preserves the normality rule in the second Piola-Kirchhoff stress space and is equivalent to that of the Cauchy stress space. This approach preserves the accuracy of the interpretation of the material behavior in the Eulerian reference frame and it also bypasses the use of the Jaumann stress rate in the formulation of kinematic hardening finite-strain plasticity.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74D99
zbMATH DE Number: 3970203
zbMATH Keywords: Jaumann stress rate
zbMATH Keywords: kinematic hardening finite-strain plasticity
zbMATH Keywords: simple shear
zbMATH Keywords: oscillations in the stress field
zbMATH Keywords: Lagrangian formulation
zbMATH Keywords: monotonically increasing stress-strain relationships
zbMATH Keywords: yield criterion
zbMATH Keywords: terms of the Cauchy stress
zbMATH Keywords: transformed to the Lagrangian reference frame
zbMATH Keywords: flow rule
zbMATH Keywords: normality rule
zbMATH Keywords: second Piola-Kirchhoff stress space
MaRDI profile type: Publication
full work available at URL: 0020-7683(87)90033-3
OpenAlex ID: W2083426813
description: scientific article; zbMATH DE number 3970203