On the dynamic theory of elastoplastic medium with microstructure

Abstract

A model of elastoplastic medium is developed, in which plastic gliding (or, microscopically speaking, the motion of dislocations) is permitted only along three mutually normal sets of glide planes. The distance between the adjacent glide planes is an important material parameter in the model. It is assumed that it does not change in the course of plastic deformation. It is shown that both the potential and kinetic energy and the dissipative function of such a medium can be derived as functions of only macroscopic variables, namely, the vector of total displacements and the tensor of plastic distorsion in the medium together with their space and time derivatives. The derived Lagrange function accounts for the kinetic energy of macroscopic movements in the medium and microscopic movements caused by the motion of dislocations on the one hand, and for the potential energy of the macroscopic elastic stresses and microscopic fluctuations of stresses due to dislocations on the other hand. In the system with three mutually normal sets of glide planes, the energies of internal stresses and motions appearing due to presence and motion of dislocations can be interpreted and easily calculated in terms of “mesoscopic” motions and deformations of “structural elements” defined as cubic volumes placed between the neighbouring glide planes. Possibilities for generalizations of the model are discussed.