Analysis of material instability of a smooth elastic-inelastic transition model

Abstract The objective of this paper is to analyze material instability of a rate–independent smooth elastic-inelastic transition model with a finite elastic range. In contrast with standard rate-independent models for metals with a yield surface, the smooth model depends nonlinearly on the total deformation rate tensor so analysis of material instability requires special attention. Expressions are developed for the limit load, and a uniform homogeneous stress state is perturbed by a shearing velocity gradient to obtain a perturbation vector that must vanish to maintain equilibrium. It is shown that the mode for instability of this perturbation is consistent with Rice’s condition that the traction vector applied to the shearing material surface remains stationary. The analytical predictions for example problems are compared with results of numerical simulations of localization.