A Finite Element Method for Problems in Perfect Plasticity Using Discontinuous Trial Functions

Abstract

It is known (see e.g. [3],[5]) that the displacements in an elastic perfectly-plastic body may be discontinuous. Conventional finite element methods (displacement methods) for plasticity problems are based on using continuous trial functions and are thus not particularly well adapted to the nature of the true solution. In this note we propose a finite element method of displacement type for problems in perfect plasticity where we use a finite element space V_h of piecewise polynomial functions with no requirement on inter-element continuity. In order to be able to approximate a discontinuous solution u of a plasticity problem accurately with functions in V_h, the finite element mesh will have to fit the discontinuities of u. Thus, since the location of these discontinuities is in general not known in advance, one would like to use some kind of adaptive technique where according to the results of computations the finite element mesh is succesively modified. In this note we do not consider this more general problem but concentrate on analyzing the proposed method in the case of a given mesh.