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

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

Differential Geometry Approach to Continuous Model of Micro-Structural Defects in Finite Elasto-Plasticity

This paper concerns finite elasto-plasticity of crystalline materials with micro-structural defects. We revisit the basic concepts: plastic distortion and decomposition of the plastic connection. The body is endowed with a structure of differential manifold. The plastic distortion is an incompatible diffeomorphism. The metric induced by the plastic distortion on the intermediate configuration (considered to be a differential manifold) is a key point in the theory, in defining the defects related to point defects, or extra-matter. The so-called plastic connection is metric, with plastic metric tensor expressed in terms of the plastic distortion and its adjoint. We prove an appropriate decomposition of the plastic connection, without any supposition concerning the non-metricity of plastic connection. All types of the lattice defects, dislocations, disclinations, and point defects are described in terms of the densities related to the elements that characterize the decomposition theorem for plastic connection. As a novelty, the measure of the interplay of the possible lattice defects is introduced via the Cartan torsion tensor. To justify the given definitions, the proposed measures of defects are compared to their counterparts corresponding to a classical framework of continuum mechanics. Thus, their physical meanings can be emphasized at once