ILL-POSEDNESS OF THE INITIAL AND BOUNDARY-VALUE-PROBLEMS IN NONASSOCIATIVE PLASTICITY

Associative plasticity theories do not predict correctly the volumetri c plastic strain, in the course of plastic deformation, in the case of materials where the position and conformation of the yield surface ar e functions of the prevailing hydrostatic stress. Non-associative theo ries have been proposed and used to correct this deficiency. Such theo ries, however, lead to other serious difficulties. In this paper we es tablish clear criteria for the well-posedness of the initial, boundary /initial and boundary value problems when the plasticity theory is ass ociative as well as non-associative. We further show cases where non-a ssociativity leads to iu-posedness of these problems even when the mat erial is not at failure. Specifically we demonstrate that the initial/ boundary and boundary value problems either have no solution, or if th ey do, the solution is not unique. We also show by specific examples t hat the banding condition, i.e., the vanishing of the determinant of t he acoustic tensor, is tantamount (a) to loss of hyperbolicity of the equation of motion and (b) lack of existence or loss of uniqueness of the solution of the boundary value problem, in certain situations. Fin ally, we show the existence of a fundamental criterion that governs th e stability of infinitesimal as well as finite elastoplastic domains.