A Notion of Strain and Stress Tensor for Finite Deformation of Elastic-Plastic Continua

Abstract

As a notion of strain compatible with the theory of plasticity having the plastic potential of von Mises type with the normality principle as flow rule, the strain tensor is defined by integrating the rate of deformation tensor considering the material spin with the rotation tensor. For a group of elastic-plastic continua exhibiting infinitesimal elastic and finite plastic deformation, elastic-plastic decomposition of the strain tensor is established, and it is proved that the elastic strain tensor has the exact physical meaning and that the stress tensor can be calculated through the generalized Hooke's law with the elastic strain tensor without any ambiguity.