Rate-independent elasto-plastic materials—a brief history and some new developments

The aim of this paper is to briefly discuss the history of the development of modern small deformation elasto-plasticity and its gradual evolution from a model for metal working to dealing with a variety of different responses ranging from fatigue to metal forming. In the process, we will also distinguish what we consider as the “essential” features of plasticity from “useful but perhaps inessential features”. We also summarize an approach to plasticity that incorporates only the essential features of plasticity (namely rate independence and hysteresis). The model exhibits a “diffuse yielding behavior” where there is a gradual transition from elastic to inelastic response which is more in keeping with many inelastic materials. The model shows considerable promise in modeling microplasticity and fatigue behavior. The approach is very computationally “friendly,” and it is possible to use a simple forward Euler with small time steps to integrate. We also describe a numerical implementation using a predictor–corrector approach that is very efficient in simulating the response. Classical plasticity with a sharp yield point is recoverable as a special case.