Constitutive Model and Incremental Shakedown Analysis in Finite Elastoplasticity

Abstract

For the deformation analysis of structures undergoing finite elastic-plastic strains, an appropriate constitutive model is presented for isotropic elastic and plastic material behavior with isotropic and kinematic hardening. The model is based on the unique decomposition of the deformation gradient into a plastic stretch, a back-rotated elastic stretch and a rotation, which can be considered as macroscopic substructure rotation. Elastic and plastic spin are determined exactly as functions of the elastic and plastic strain rate, respectively, which enables the calculation of the macroscopic substructure spin. This spin is used to define the objective corotational rate adequate to formulate the constitutive equations of finite elastoplasticity with an appropriate evolution law for kinematic hardening.