Substructuring FE–XFE approaches applied to three-dimensional crack propagation

摘要

Two substructuring methods are investigated in order to allow for the use of the eXtended Finite Element Method (X-FEM) within commercial finite element (FE) codes without need for modifying their kernel. The global FE problem is decomposed into two subdomains, the safe domain and the cracked domain based on the value of the level sets representing the crack. The safe domain is treated by the host FE software while the cracked domain is treated by an independent XFE code. The first substructuring method consists of calculating the Schur matrix of a cracked super-element with the XFE code. The second technique introduces the finite element tearing and interconnecting method (FETI) which ensures the compatibility of the displacements at the interface between the cracked and safe subdomains. The stiffness matrices and nodal forces are provided by the XFE and FE codes for the cracked and safe subdomains, respectively. The solutions obtained with these two techniques are rigorously equivalent to those computed with the stand-alone XFE code. First, the computational efficiency of the two approaches is demonstrated. Second, a validation is proposed towards comparison with reference values of the stress intensity factors in simple 3D cracked geometries. Finally, this contribution presents an application of the FE–XFE–FETI method to the computation of the stress intensity factor induced by a crack inside a hydraulic cylinder under internal pressure.