Extension of the Upper Bound Method to Include Estimation of Stresses

Abstract

The upper bound method is a convenient tool for evaluating the rate of work in processes involving predominantly plastic deformation of rigid/perfectly plastic material. Since the rate of work for an incompressible material depends only on the deviator portion of the stress, the hydrostatic portion does not enter the formulation and the stress field is not determined. Here we show that this limitation can be overcome by adding a relatively simple postprocessing procedure. We then apply this technique to examples of rigid asperities penetrating a plastic material undergoing subsurface bulk deformation and compare our results with previous approximate solutions.