Selected issues in the upper bound theorem of plasticity

The paper reviews the upper bound theorem in rigid plasticity, emphasizing its application to analyzing and designing metal forming processes. Two formulations of the theorem are considered. The peculiarities in applying the theorem to non-stationary and stationary processes are discussed. Special attention is devoted to friction boundary conditions. General methods of constructing trial velocity fields are presented. On the other hand, routine upper bound solutions based on the von Mises yield criterion are not reviewed, though their applied significance is not questionable. The article ends with a simple numerical example that illustrates all qualitative features of the theorem considered.