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Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth

  • This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting “edge-based” smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, “super-convergence” and “ultra-accurate” solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction.

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Document Type:Article
Author: Lei Chen, Timon RabczukORCiDGND, G.R. Liu, K.Y. Zeng, Pierre Kerfriden, Stéphane Pierre Alain Bordas
DOI (Cite-Link):https://doi.org/10.1016/j.cma.2011.08.013Cite-Link
Parent Title (English):Computer Methods in Applied Mechanics and Engineering
Date of Publication (online):2017/08/26
Year of first Publication:2012
Release Date:2017/08/26
Publishing Institution:Bauhaus-Universität Weimar
Institutes:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
GND Keyword:Angewandte Mathematik; Strukturmechanik
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften
500 Naturwissenschaften und Mathematik / 510 Mathematik / 519 Wahrscheinlichkeiten, angewandte Mathematik
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
50 Technik allgemein / 50.31 Technische Mechanik
Licence (German):License Logo Copyright All Rights Reserved - only metadata