On the Connection between Continuum Crystal Plasticity and the Mechanics of Discrete Dislocations

Abstract

This work aims at linking the levels of the continuum crystal plasticity with that of discrete dislocations. First, some former results about the kinematics of discrete dislocations are recalled. Then the fields at the continuum level are constructed by averaging the corresponding fields at the dislocation level. Under the assumptions of small elastic strains, small lattice curvature at the dislocation level and statistical homogeneity at the scale of the representative volume element the classical forms of the balance equations for the continuous fields can be retrieved. In addition, a multiplicative decomposition the deformation gradient in an elastic part and an irreversible part is achieved. While the elastic strains are assumed to be small, the plastic strains can be arbitrarily large.