Incremental elastoplastic analysis for active macro‐zones

Abstract

SUMMARY 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 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.Copyright © 2012 John Wiley & Sons, Ltd.

Active macro‐zone approach for incremental elastoplastic‐contact analysis

“…A brief description of the strategy utilized for incremental elastoplastic analysis via multidomain SGBEM, called elastoplastic macro-zone analysis, is provided in this section. The complete version can be found in [8]. For each loading step and at each bem-elements, this analysis uses Equation (34) both to evaluate the trial stresses in the predictor phase and to compute the plastic strains in the corrector phase.…”

“…The novelty in the elastoplastic analysis introduced in [8] is that in the present paper and in other papers on the same topic, a substructuring is employed through which the structure is subdivided into elements, called bem-elements, having the following:…”

“…Elastoplastic problem. This research uses an approach for active macro-zones shown by the present authors as an incremental elastoplastic analysis problem in [8] and as a limit analysis in [9]. The approach for active macro-zones shows a more rational and innovatory strategy regarding both the theoretical and computational aspects of the symmetric Galerkin boundary element method (SGBEM).…”

“…In the plastic analysis carried out using the symmetric BEM, it is necessary to distinguish a computing phase for the elastic response to all the actions, including the volumetric ones (body forces and plastic strains), and a subsequent phase for plastic strain evaluation, stored during the loading process [8].…”

“…Equation (34) provides the stress at the Gauss points of each bem-elements as a function of the plastic strains p and of the external actions O ¢ s , the latter amplified byˇ. K is defined as a self-stress influence matrix, fully populated, not symmetric and semidefined negative [8,9]. The evaluation of this matrix only involves the elastic characteristic of the material and the structure geometry.…”