Evolution Equations for Defects in Finite Elasto-Plasticity

Abstract

The paper deals with continuous models of elasto-plastic materials with microstructural defects such as dislocations and disclinations. The basic assumptions concern the existence of plastic distortion and so-called plastic connection with metric property and the existence of the free energy function. This is dependent on the Cauchy-Green strain tensor, and its gradient with respect to the plastically deformed anholonomic configuration, and on the dislocation and disclination densities. The defect densities are defined in terms of the incompatibility of the plastic distortion and non-integrability of the plastic connection. The evolution of plastic distortion and disclination tensor has been postulated under the appropriate viscoplastic and dissipative type equations, which are compatible with the principle of the free energy imbalance. The associated small distortion model is provided. The present model and the previous ones have been also compared.