A qualitative phenomenological continuum theory of plastic deformation was based upon dislocation dynamics, and was couched in a Lagrangian field formalism. The fundamental field variables were mainly complex with regard to the thermodynamics of irreversible processes. In practice, the structure of the theory mirrored a dislocation microstructure and its dynamics. From the thermodynamic point of view, it was necessary to deal with internal variables. This, in contrast to traditional approaches, was more in tune with the dislocation concept. In view of the fact that plastic deformation and dislocation dynamics were processes that were far from thermal equilibrium, the Lagrangian formalism was a very appropriate tool. It was further possible to take account of the dissipation which was an essential feature of plastic deformation. The Lagrangian formalism was also the most concise form of field theory from both the practical and theoretical points of view.

Lagrangian Field Theory of Plasticity Based on Dislocation Dynamics - Various Approaches. K.H.Anthony, A.Azirhi, M.Scholle: Journal de Physique IV, 1998, 8[8], 1-12