BIEM-based variational principles for elastoplasticity with unilateral contact boundary conditions

Abstract

The structural step problem for elastic-plastic internal-variable materials is addressed in the presence of frictionless unilateral contact conditions. Basing on the BIEM (boundary integral equation method) and making use of deformation-theory plasticity (through the backward-difference method of computational plasticity), two variational principles are shown to characterize the solution to the step problem: one is a stationarity principle having as unknowns all the problem variables, the other is a saddle-point principle having as unknowns the increments of the boundary tractions and displacements, along with the plastic strain increments in the domain. The discretization by boundary and interior elements transforms the above principles into well-posed mathematical programming formulations belonging to the symmetric Galerkin BEM formulations (with features such as a symmetric sign-definite coefficient matrix, double integrations, and hypersingular integrals).