On the computational aspects of a symmetric multidomain BEM for elastoplastic analysis

The symmetric boundary element method (SBEM) is applied to the elasto-plasticanalysis of bodies subdivided into substructures. This methodology is based on the use of: amultidomain SBEMapproach, for the evaluation of the elastic predictor; a return mapping algorithmbased on the extremal paths theory, for the evaluation of inelastic quantities characterizing theplastic behaviour of each substructure; and a transformation of the domain inelastic integrals of eachsubstructure into corresponding boundary integrals. The elastic analysis is performed by using theSBEM displacement approach, which has the advantage of creating system equations that onlyconsist of nodal kinematical unknowns at the interface boundary among substructures. The elastoplasticsolution utilizes a strain-driven strategy that is characterized by the evaluation of the elasticpredictor that is a function of the initial conditions and the load increment. The predictor phase isfollowed by the use of a returnmapping algorithm defined by introducing the extremal paths theoryto remove the time integration. Then the computed plastic strains are considered to be constantinelastic actions imposed inside the substructure in a step-by-step procedure. Their presenceinvolves domain integrals with singular kernels. These integrals are considered as Cauchy principalvalues with which the related free term is associated. In order to compute these domain integrals, theradial integral method is applied to remove the strong singularity.