Modeling crack discontinuities without element-partitioning in the extended finite element method

International audienceIn this paper, we model crack discontinuities in two-dimensional linear elastic continua using the extended nite element method without the need to partition an enriched element into a collection of triangles or quadrilaterals. For crack modeling in the X-FEM, the standard finite elementapproximation is enriched with a discontinuous function and the near-tip crack functions. Each element that is fully cut by the crack is decomposed into two simple (convex or nonconvex) polygons, whereas the element that contains the crack tip is treated as a nonconvex polygon. On using Euler'shomogeneous function theorem and Stokes's theorem to numerically integrate homogeneous functions on convex and nonconvex polygons, the exact contributions to the stiness matrix from discontinuous enriched basis functions are computed. For contributions to the stiness matrix from weakly singular integrals (due to enrichment with asymptotic crack-tip functions), we only require a one-dimensional quadrature rule along the edges of a polygon. Hence, neither element-partitioning on either side of the crack discontinuity nor use of any cubature rule within an enriched element are needed. Structured finite element meshes consisting of rectangular elements, as well as unstructured triangular meshes, are used. We demonstrate the exibility of the approach and its excellent accuracy in stress intensity factor computations for two-dimensional crack problems