Existence and Regularity of Solutions for Plasticity Problems

ABSTRACT This work examines the problem of the quasi-static evolution of perfectly plastic bodies. In a first section a variational formulation is given in an adequate functional framework. The elements of the space of admissible velocity fields have a tensor of deformation which is composed of measures. An existence theorem is stated. A second section deals with the regularity of the elements of this new space and it is shown that discontinuities (slip lines) might appear in the body. In the last section, a mathematical formalism is developed in order to consider the boundary as part of the body, and to explain the noncompliance of boundary conditions as a slip line phenomenon.