A Discontinuity-Enriched Finite Element Method for modeling Fracture Growth in Brittle Materials
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Enriched finite element methods such as the eXtended/Generalized Finite Element Method (XFEM/GFEM) have become popular for modeling problems with material discontinuities (e.g., composites and fracture). The main advantage as compared to the standard finite element method (FEM) remains the versatility in the choice of discretizations, since in XFEM/GFEM discontinuities are completely decoupled from the finite element mesh. However, XFEM/GFEM is no without issues, which include the need for stable formulations to bound the condition number of stiffness matrices and the shifting of enrichments to deal with nonzero essential boundary conditions. Modeling complex kinematics such as branching and merging of discrete cracks remains challenging and requires an intricate computer implementations. At worst, it is currently not possible in XFEM/GFEM to recover smooth reactive tractions from boundaries with prescribed nonzero displacements. Here we introduce the Discontinuity-Enriched Finite Element Method (DE-FEM) [1,2,3] as an alternative procedure to XFEM/GFEM for modeling crack growth in brittle materials. While DE-FEM retains the mesh-geometry decoupling virtue of XFEM/GFEM, it addresses all of its drawbacks by placing enriched nodes directly along discontinuities. Most notably, this is done with a straightforward computer implementation that enables complex kinematics, namely the modeling of multiple crack growth with branching and merging. Numerical examples show the capability of DE-FEM in obtaining accurate stress intensity factors—with an interaction integral that considers the interplay among cracks and in capturing crack patterns similar to those observed in the literature. REFERENCES [1] A.M. Aragón and Angelo Simone, The Discontinuity-Enriched Finite Element Method. Int. J. Numer. Meth. Eng, Vol. 112, pp. 1589–1613, 2017. [2] J. Zhang, S.J. van den Boom, F. van Keulen and A.M. Aragón, A stable discontinuity- enriched finite element method for 3-D problems containing weak and strong discon- tinuities. Comput. Methods Appl. Mech. Eng, Vol. 355, pp. 1097–1123, 2019. [3] A.M. Aragón and C.A. Duarte, Fundamentals of Enriched Finite Element Methods. 1st Edition, Elsevier, 2023.