XLME interpolants, a seamless bridge between XFEM and enriched meshless methods

By F. Amiri, Cosmin Anitescu, Marino Arroyo, Stéphane P.A. Bordas, Timon Rabczuk. 2014

217 citations recorded by the source corpus.

In this paper, we develop a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method at a comparable computational cost. In addition, we keep the advantages of the LME shape functions, such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes near the crack such as blending or shifting.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/085bd0925939049aeea5955236a99d075ea7f8a2

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In Mechanics of Materials

Citations in the corpus

Phase-field modeling of fracture in linear thin shells (2014, unknown): “However, despite the advances made in modeling fracture for solid bodies [1, 2, 3, 4, 5], fracture in thin bodies remains a challenge due to the complex interplay between cracks and the shell kinematics and geometry.”
A peridynamics formulation for quasi-static fracture and contact in rock (2017, methodology): “…include the extended finite element method (XFEM) (Belytschko and Black, 1999; Moes et al., 1999), numerical manifold method (NMM), efficient remeshing techniques (Areias et al., 2013, 2015) and certain meshless methods (Amiri et al., 2014; Rabczuk and Belytschko, 2004a; Zhuang and Augarde, 2010).”