XLME interpolants, a seamless bridge between XFEM and enriched meshless methods
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European Commission's projectREALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery (EC-FP7-279578)
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.
CitationAmiri, F., Anitescu, C., Arroyo, M., Bordas, S., Rabczuk, T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. "Computational Mechanics", Gener 2014, vol. 53, núm. 1, p. 45-57.