Variational principles in thermoplasticity. Part 1: Heat transfer and plasticity

Variational principles in plasticity and in the theory of heat transfer are considered in order to complete and unify their mathematical theory. An extremal variational principle for the heat transfer processes based on a variational principle of virtual energy transfer is proposed. For the theory of plasticity, a unitary exposition of the stress rate variational principles and of the extremal variational principles based on the theory of convex analysis is presented. For plastic materials for which the convex analysis supplies no extremal variational principle, a two criterion extremal variational principle which is suited for a application in coupled thermomechanical processes is suggested.