A maximum principle for the analysis of elastic-plastic systems

Summary

We consider an elastic-plastic body subjected to a specific programme of static loading. In the analysis of the behaviour of the body in the course of the individual steps of the loading programme some difficulties arise if the variational principles of the theory of plasticity are applied. We then propose a maximum principle which appears suitable for the formulation of simple and direct computing procedures. For an elastic-perfectly plastic material the function to be maximized represents the differential energy dissipated in the single infinitesimal step starting from the elastic solution. In that function the variables are the plastic distortions. Since the energy dispersed by the effect of these latter must at every point be positive or zero, the maximum in question is a field maximum and therefore the property is not variational.

The principle is demonstrated both for elastic-perfectly plastic materials and for elastic—work-hardening materials. Materials with regular yield surfaces are at first considered; the demonstration is then extended to the case of singular yield surfaces.