Analysis of the elastic–plastic problem involving finite plastic strain using the boundary element method

Abstract

This paper presents a formulation of the static problem of metallic solids undergoing both material and geometrical non-linearities. The plastic constitutive relations are based on the von Mises yield criterion with associated flow rule and isotropic hardening. The plastic strains can be large. The numerical approach is based on the boundary element method (BEM) but, since it is not possible to take all the integrals to the boundary, both domain and boundary discretization are needed. A material description is adopted together with an updated Lagrangian approach. The generalized midpoint algorithm is used for the computation of the large scale plastic strains. The displacement gradients are obtained, in order to avoid singularities, from polynomial differentiation of the displacement field in each domain element from the nodal values. The resulting method is incremental and iterations are needed in each increment. The two-dimensional plane strain case has been implemented and one example is presented, to show the applicability of the method proposed.