Reexamination of Jumps Across Quasi-Statically Propagating Surfaces Under Generalized Plane Stress in Anisotropically Hardening Elastic-Plastic Solids

Abstract

Strong discontinuities across quasi-statically propagating surfaces in anisotropic elastic-plastic solids under generalized plane stress are reexamined allowing for some generality in constitutive response and taking into account the phenomenon of necking. Jumps in stresses are ruled out on the basis of material stability postulates and a previous approach (by Pan, 1982) is discussed. It is 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.