A Primal-Dual Finite Element Approximation for a Nonlocal Model in Plasticity

We study the numerical approximation of a static in nitesimal plasticity model of kinematic hardening with a nonlocal extension involving the curl of the plastic variable. Here, the free energy to be minimized is a combination of the elastic energy and an additional term depending on the curl of the plastic variable. In a rst step, we introduce the stress as dual variable and provide an equivalent primal-dual formulation resulting in a local ow rule. To obtain optimal a priori estimates, the nite element spaces have to satisfy a uniform inf-sup condition. Finally, we show that the associated nonlinear mixed formulation can be solved iteratively by a classical radial return algorithm. Numerical results illustrate the convergence of the applied discretization and the solver.