Application of convex analysis concepts to the numerical solution of elastic-plastic problems by using an internal variable approach

Stepwise holonomic elastic-plastic problems are considered both at the material level and at the structural level by using an internal variable formulation (in which a free energy and a dissipation function play a central role). Under convenient hypotheses concerning the material behaviour, some extremal properties are proved, which imply that the elastic-plastic response can be determined by solving non-linear (mostly unconstrained) programs. The paper also discusses the links with extremum theorems previously demonstrated by other authors on the basis of a different approach, which explicitly consider yield surfaces and sometimes plastic multipliers, leading to non-linear constrained optimization problems. Finally, limit analysis and shakedown problems are briefly discussed within the context of the same internal variable formulation.