Dislocation dynamics by means of Lagrange formalism of irreversible processes—Complex fields and deformation processes

Abstract

Conventional approaches to a phenomenological theory of plasticity suffer from the fact that they are based on the concept of a “material manifold”. In this way the dislocation dynamics are structurally eliminated from the very beginning. We propose an alternative method within the framework of Lagrange formalism. With regard to thermodynamics of irreversible processes all degrees of freedom being involved in dissipation are associated with complex field variables. A plastically deformed crystal is modelled as a Cosserat fluid based on complex matter and vortex fields and on a real field of Cosserat triads representing the solid properties of the crystal. Using complex dislocation fields the dislocation network is described in more detail than conventionally is done by the well known dislocation density tensor. Especially the model allows for correlations within the dislocation network which is most essential for plasticity. Our model implies a methodical unification of elasticity and plasticity. The paper is mainly concerned with the mechanical aspects of the theory.