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

*(English)*Zbl 1193.74153Summary: Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh [T. Belytschko, T. Black, Int. J. Numer. Methods Eng. 45, No. 5, 601–620 (1999; Zbl 0943.74061)]. 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 [the authors, Int. J. Numer. Methods Eng. 80, No. 1, 103–134 (2009; Zbl 1176.74190)] 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.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74G70 | Stress concentrations, singularities in solid mechanics |

##### Keywords:

Schwarz Christoffel; conformal mapping; numerical integration; extended finite element method; quadrature; generalized finite element method; partition of unity finite element method; strong discontinuities; weak discontinuities; open-source MATLAB code##### References:

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