Lagrangian field theory of plasticity based on dislocation dynamics - Various Approaches

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The purpose of this paper is to give a qualitative idea of a phenomenological continuum theory of plastic deformation based on dislocation dynamics. The theory works within Lagrange formalism of fields; with regard to Thermodynamics of Irreversible Processes the fundamental field variables are mainly complex. Physically the structure of the theory follows the microstructure of dislocations and their dynamics. From the thermodynamical point of view we are dealing with internal variables, which - in contrast with tradititional approaches -really fit to the dislocation concept. Keeping in mind that plastic deformation and dislocation dynamics are running far away from thermal equilibrium Lagrange formalism is a most appropriate tool. It further allows of taking into account dissipation which is an essential feature of plastic deformation. Finally Lagrange formalism is the most concise form of a field theory which is most important from the practical point of view as well as from a sophisticated point of view of unification of physical theories. Our presentation aims at a structural survey of our approaches. For the details - especially for the mathematical ones - we refer to our preceding and forthcoming papers.