New predictor-corrector method used as a solver for decohesion problem

Abstract

In certain problems of loading of elastic-perfectly plastic thin sheets a continuous displacement solution may not exist. The evolution of plastic zone is then connected with the evolution of discontinuity lines in both velocity and displacement fields. In the present paper it is assumed that in the presence of discontinuity lines the localized plastic zones start to proceed. A numerical study of decohesion within thin elastic-plastic sheets is conducted to total collapse. It is shown, that the localized plastic flow may develop simultaneously with the diffuse plastic zones. The structural softening caused by decohesive cracks is coupled with a complex elasto-plastic deformation process, where the previously developed diffuse plastic zones are subjected to unloading. The post-critical analysis is performed using a new reliable algorithm of a continuation method. The algorithm is based on a rank analysis of the rectangular matrix of the homogeneous set of incremental equations.