Extra-gradient method for the variational inequality formulation of discontinuous deformation analysis

Abstract

In the conventional discontinuous deformation analysis (DDA) method the contact conditions are enforced by the penalty function method. Improperly selected penalty parameters might incur numerical instability. In order to evade the introduction of the penalty parameters and to avoid open-close iteration that can not assure convergence, in this study the contact forces are taken as independent variables, the normal and tangential contact conditions of one angle-edge contact are expressed as two variational inequalities, then DDA is reformulated as a variational inequality problem which is solved by the extra-gradient method. The proposed computation scheme is more compact and robust, the solution of large-scale nonlinear equations is avoided and only simple projection is executed in the new scheme. Some typical examples originally designed by Shi are reanalyzed, suggesting the effectiveness of the Extra-Gradient Method and contact conditions could be satisfied more strictly.