Elasto-viscoplastic Models with Non-Schmid Law and Non-local Evolution of Dislocations in Crystal Lattice

Abstract

The paper deals with elasto-plastic materials with crystalline structure, which contain continuously distributed defects as dislocations, within the constitutive framework of second order deformations finite elasto-plasticity. The non-Schmid flow rule describes the evolution of the plastic distortion and the model is dependent on the tensorial measure of dislocation G which is related to the non-zero torsion of plastic connection. A new formula for the time derivative of the G is derived. The key point to formulate constitutive and evolution laws is the imbalance free energy postulate and the expression of the free energy function. The evolution for the plastic components in the slip systems is described in terms of the generalized stress vector associated with the appropriate Mandel’s stress measure, micro momentum defined for plastic mechanism, and gradient of the scalar dislocation densities.