Convergence Analysis of Discrete Approximations of Problems in Hardening Plasticity

The initial boundary value problem of quasistatic elastoplasticity is considered here, as a vari-ational inequality and equation in the displacement and stress. A variational inequality for the stress only may be obtained by eliminating the displacement. Semidiscrete approximations of the stress problem and fully discrete nite element approximations of the full problem are considered, under assumptions of minimum regularity of the solution. It is shown that the resulting families of approximations converge to the solution of the original problem.