Elastoplastic analysis by active macro-zones with linear kinematic hardening and von Mises materials

In this paper a strategy to perform elastoplastic analysis with linear kinematic hardeningfor von Mises materials under plane strain conditions is shown. The proposed approachworks with the Symmetric Galerkin Boundary Element Method applied to multidomainproblems using a mixed variables approach, to obtain a more stringent solution. The elastoplasticanalysis is carried out as the response to the loads and the plastic strains, the latterevaluated through the self-equilibrium stress matrix. This matrix is used both, in the predictorphase, for trial stress evaluation and, in the corrector phase, for solving a nonlinearglobal system which provides the elastoplastic solution of the active macro-zones, i.e. thosezones collecting bem-elements where the plastic consistency condition has been violated.The simultaneous use of active macro-zones gives rise to a nonlocal approach which ischaracterized by a large decrease in the plastic iteration number, although the proposedstrategy requires the inversion and updating of Jacobian operators generally of big dimensions.A strategy developed in order to reduce the computational efforts due to the use ofthis matrix, in a recursive process, is shown.