TS2d3 - KINEMATICS AND RATE-TYPE ELASTIC CONSTITUTIVE EQUATIONS FOR FINITE RATE DEPENDENT INELASTIC DEFORMATION OF MATERIALS WITH SMALL ELASTIC STRAINS

Abstract

In this paper the kinematics of finite inelastic deformation are considered from a manifold theoretical point of view. Using the multiplicative decomposition of the deformation gradient into an elastic and a plastic part and the concept of a stress free intermediate configuration in a systematic manner deformation tensors, strain tensors, velocity gradients and rate of deformation tensors can be derived. In the second part of the paper two formulations for rate-type elastic constitutive equations are established. A St.Venant-Kirchhoff type formulation given in the intermediate configuration is transformed to the current configuration. The rate-type formulations are obtained by taking Lie derivatives with respect to the intermediate configuration and the reference configuration, respectively. In a systematic manner simplifications for small elastic strains are obtained.