Applied Mathematics and Mechanics

, Volume 20, Issue 6, pp 593–603

# The simple shear oscillation and the restrictions to elastic-plastic constitutive relations

• Chen Liangsen
• Zhao Xinghua
• Fu Minfu
Article

## Abstract

Based on the definitions of hardening, softening and ideal plastic behavior of elastic-plastic materials in the true stress tensor space, the phenomena of simple shear oscillation are shown to be relative to the oscillatory occurrence of hardening and softening behavior of elastic-plastic materials, namely the oscillation of hardening behavior, by analyzing a simple model of rigid-plastic materials with kinematical hardening under simple shear deformation. To make the models of elastic-plastic materials realistic, must be satisfied the following conditions: for any constitutive model, its response stresses to any continuous plastic deformation must be non-oscillatory, and there is no oscillation of hardening behavior during the plastic deformation.

## Key words

objective rates elastic-plastic constitutive relation simple shear oscillation

O344.1

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© Editorial Committee of Applied Mathematics and Mechanics 1999

## Authors and Affiliations

• Chen Liangsen
• 1
• Zhao Xinghua
• 2
• Fu Minfu
• 1
1. 1.Institute of Engineering MechanicsUniversity of NanchangNanchangP R China
2. 2.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP R China