Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework

Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing, as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains (Int. J. Nuttier Meth. Engng 2009; 80(1):103-134. DOI: 10.1002/nme.2589) to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code. Copyright (C) 2010 John Wiley & Sons, Ltd.