An RP-adaptive finite element method for elastoplastic problems

In this paper we present an rp-discretization strategy for physically non-linear problems that is based on a high order finite element formulation. In order to achieve convergence, the p-version leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or globally, whereas the r-method moves the nodes of an existing FE-mesh. The basic idea of our rp-version approach is to adjust the finite element mesh to the shape of the elastic-plastic interface in order to take the loss of regularity which arises along the shape of the plastic front into account. A numerical example will demonstrate that this approach leads to very accurate results.