Reexamination of Jumps Across Quasistatically Propagating Surfaces under Generalized Plane Stress in Anisotropically Hardening Elastic-Plastic Solids

摘要

Strong discontinuities across quasistatically propagating surfaces in anisotropic elastic plastic solids under generalized plane stress have been reexamined allowing for some generality in constitutive response and taking into account the phenomenon of necking. Jumps in stresses have been ruled out on the basis of material stabiltiy postulates and a previous approach has been discussed. It has been noted that for elastic-perfectly plastic solids, sliding velocity discontinuities occur under restrictive and exceptional conditions (when both the surface and its normal are stress characteristics) for generalized plane stress as compared to plane strain. Necks may form along (stress) characteristic directions with the relative velocity vector orthogonal to the other family of characteristics.