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.
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