A new gradient theory of plasticity for modeling metal forming processes

The objective of the present paper is to show qualitative and quantitative differences in predictions based on three models of gradient theory of plasticity using a simple analytic solution. One of the models adopted is a conventional model. Its gradient term contains a space derivative of the equivalent plastic strain. The other models contain gradient terms involving a space derivative of the equivalent plastic strain rate. It is hypothesized that the latter models are more suitable for application to metal forming processes since rigid plastic models based of the flow formulation of plasticity theory are often adopted to describe such processes. The approach is pure phenomenological. In particular, it is supposed that the adequacy of the models should be solely evaluated by the coincidence of some general qualitative features of solutions to boundary value problems and general expectations concerning the effect of gradient terms on theoretical predictions.