Objective Constitutive Equation and Numerical Algorithm in Finite Deformation

Abstract

The present paper discusses rate-type elastic-plastic constitutive equations with the stress rates being taken as the Jaumann derivative and the Green derivative from the viewpoint of reference configuration and spin tensors. These equations are shown to be transformed in the rate-type forms so as to exclude the effects of rigid rotation. The obtained ordinary differential equations can be implemented to ensure objective numerical integration during finite deformation increment. The simple shear problem is taken for an example to demonstrate the accuracy of the present formulations based on the Euler method or the Runge-Kutta method of the second order.