Reference : Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear...
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Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth
Chen, L. [Institute of High Performance Computing, Singapore 138632, Singapore, Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore]
Rabczuk, T. [Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße, 1599423 Weimar, Germany]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Liu, G. R. [University of Cincinnati, Cincinnati, OH 45221-0070, United States]
Zeng, K. Y. [Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore]
Kerfriden, P. [Institute of Mechanics and Advanced Materials (iMAM), Cardiff School of Engineering, Cardiff University, Queen's Buildings, Parade, Cardiff, CF24 3AA Wales, United Kingdom]
Computer Methods in Applied Mechanics & Engineering
Yes (verified by ORBilu)
[en] Convergence rate ; Edge-based smoothed finite element method ; Extended finite element method ; Fracture analysis ; Numerical method ; Stress intensity factor ; Convergence rates ; Edge-based ; Stress intensity ; Blending ; Brittle fracture ; Convergence of numerical methods ; Crack propagation ; Crack tips ; Cracks ; Numerical methods ; Stress intensity factors ; Finite element method
[en] 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.
Royal Academy of Engineering and of the Leverhulme Trust. Senior Research Fellowship entitled ‘‘Towards the next generation surgical simulators’’ ; EPSRC under grants EP/G069352/1 Advanced discretisation strategies for ‘‘atomistic’’ nano CMOS simulation ; EP/ G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method ; German Research Foundation (DFG)
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