Lagrangian field theory of plasticity and dislocation dynamics. Attempts towards unification with thermodynamics of irreversible processes

Abstract

Within the Lagrange formalism, a mechanical continuum theory of dislocation dynamics is presented, which results in a phenomenological, unified description of elastic and plastic deformations of a crystal. Further developments towards a thermo-mechanical theory including dissipation are methodically envisaged. The theory is based on complex matter fields and vortex potentials as fundamental field variables. Especially the dislocation network is divided into different classes of equal dislocations, giving rise to a more refined description of the dislocation dynamics as traditionally can be done by the well-known dislocation density tensor. Each class of dislocations is associated with a complex dislocation field. The elastic interaction between dislocations of different classes results in correlational effects which cannot be described by means of the traditional continuum theory of dislocations. Whereas in traditional approaches the plastically deforming body is formally looked upon as an elastic solid with inherent flow properties, we are looking at such a system in a reverse manner: The plastically deforming body is formally regarded as a fluid with inherent solid properties. Formally the plastically deforming body is associated with a generalized Cosserat fluid based on matter and dislocation fields. In this way we overcome the difficulties due to the deformation chaos produced by dislocation motion.