Nonlinear continuum theory of dislocations

Within the framework of mechanics of generalized continua, a principle of virtual work and a set of static equations are formulated for a body with continuously distributed dislocations at finite strain. The stored energy is supposed to depend on the elastic deformation as well as on the dislocation density. The internal dynamics of dislocations are shown to be described by the model of oriented media. Governing and constitutive equations for such material are proposed with respect to the initial and current description, using absolute tensor notation. Special attention is focused to the link with the engineering plasticity.