Variational formulations and numerical analysis of elastoplastic problems

Prof. Weimin Han

Department of Mathematics, University of Iowa, Iowa City, IA 52242

We consider quasistatic problems of elastoplasticity with hardening. The problems are formulated in two alternative forms: the primal form and the dual form. The primal formulation uses the flow law expressed in terms of the dissipation function while the dual formulation makes use of the yield function form of this law. Both forms are quasistatic evolutionary variational inequalities of mixed kind. For each formulation, we give a detailed analysis of the well-posedness of the problem, and error estimations for various numerical schemes. We also review some popular solution algorithms and discuss their properties, in particular their convergence properties.