A VARIATIONAL PRINCIPLE OF MAXIMUM PLASTIC WORK IN CLASSICAL PLASTICITY

Abstract

The classical equations of Lévy-Mises and Prandtl-Reuss for an ideally plastic material are reviewed. A variational principle of maximum plastic work is derived for plastic states of stress satisfying the Lévy-Mises relation and the Huber-Mises yield criterion. Uniqueness theorems are established for a completely plastic body under prescribed boundary conditions. The variational principle is applied to the problem of a uniform bar of arbitrary section deformed in combined tension, torsion, and bending