On the finite element analysis of crack and inclusion problems in elastic-plastic materials

A finite element method for treating plane strain, elastic-plastic boundary value problems is described. Constant strain triangular elements are used. The material is assumed to obey the von Mises yield criterion and its associated flow rule. In order to test the accuracy of the method the deformation of a pressurized circular tube is investigated and the results are compared with a finite-difference solution. The applicability of the method to problems involving two different materials is demonstrated for the case of a uniaxially loaded plate containing a circular inclusion. Finally some crack problems are analysed. Special attention is devoted to the case of small scale plasticity.