Incremental elastoplastic analysis for active macro-zones

In this paper a strategy to perform incremental elastoplastic analysis using the Symmetric Galerkin Boundary Element Method for multidomain type problems is shown. The discretization of the body is performed through substructures, distinguishing the bem-elements characterizing the so-called active macro-zones, where the plastic consistency condition may be violated, and the macro-elements having elastic behaviour only. Incremental analysis uses the well-known concept of self-equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self-stress matrix). The nonlinear analysis does not use updating of the elastic response inside each plastic loop, but at the end of the load increment only. This is possible by using the self-stress matrix, both, in the predictor phase, for computing the stress caused by the stored plastic strains, and, in the corrector phase, for solving a nonlinear global system which provides the elastoplastic solution of the active macro-zones. The use of active macro-zones gives rise to a nonlocal and path-independent approach which is characterized by a notable reduction of the number of plastic iterations. The proposed strategy shows several computational advantages as is shown by the results of some numerical tests, reported at the end of this paper. These tests were performed using the Karnak.sGbem code, in which the present procedure was introduced as an additional module.