Combining SGBEM and FEM for modeling 3D cracks

The SGBEM-FEM alternating method suitable for the solution of elastic and elasticplastic three-dimensional fracture mechanics problems is presented. The crack is modeled by the symmetric Galerkin boundary element method (SGBEM), as a distribution of displacement discontinuities in an infinite medium. The finite element method (FEM) is used for stress analysis of the uncracked finite body. The solution for the structural component with the crack is obtained in an iterative procedure, which alternates between FEM solution for the uncracked body, and the SGBEM solution for the crack in an infinite body. Both elastic and elastic-plastic alternating procedure are developed. In the elastic alternating procedure residual forces on the surface of the finite element model are sought in order to balance tractions induced by presence of the crack. Elastic-plastic alternating procedure is based on volume residuals due to presence of the crack and elastic-plastic material behavior. Initial stress approach is used inside alternating iterative procedure for elastic-plastic problems. Computational procedure for fatigue crack growth of nonplanar cracks is presented. It is assumed that crack growth rate and the direction of crack growth are determined by the ∆J-integral.