Time discretization procedures for elastoplastic problems of continuum mechanics (Q2781761)

In this PhD thesis the author investigates different time discretization methods for elastoplastic problems. The quasi-static balance of linear momentum is used together with an elastic-plastic material law, which takes into account isotropic and kinematic hardening. The equations of Prandtl-Reuss plasticity are given in a weak primal and dual formulation, and are spatially discretized by conform finite elements of lowest order. In addition to standard methods for time discretization, such as implicit Euler and Crank-Nicholson methods, discontinuous Galerkin methods of zeroth and first order are analyzed theoretically and numerically for well chosen two-dimensional test examples. This thesis has a clear structure which leads the reader into this active field of research of mathematicians and engineers. In the framework of solid mechanics, the approach based on discontinuous Galerkin methods is an interesting and novel suggestion. The solutions and the convergence behavior of numerical (adaptive) methods are documented by a number of diagrams. Unfortunately, many of the diagrams are printed by far too small, and thus are hardly readable.