On the Solution of the 3D Crack Surface Contact Problem Using the Boundary Element Method

Abstract

The efficient solution of the 3D crack surface contact problem utilizing the boundary element method (BEM) is presented. The dual discontinuity method (DDM), a special formulation of the BEM, is applied. This method deals directly with the relative displacements and the discontinuities of the tractions at the crack. For the normal behavior a unilateral contact is assumed and for the description of the tangential behavior Coulomb’s frictional law is utilized. The hard contact formulation is regularized by the application of the penalty method. An incremental iterative procedure based on a radial return mapping algorithm is applied for the solution of this non-linear problem. Based on the stress field the fracture mechanical parameters are determined by an extrapolation method for all increments of a characteristic load cycle. By the analysis of this load cycle the cyclic fracture mechanics values are obtained. Due to the non-linear nature of crack growth the simulation is implemented in the framework of a predictor-corrector scheme. For the investigation of the influence of the crack surface roughness on the behavior of cracks two numerical examples are presented.