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A multiple level-set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within XFEM

Abstract : In this paper, we highlight that, when the eXtended Finite Element Method (XFEM) is employed to model a microstructure in which inclusions are involved and the distance between two inclusions is small enough to be comparable with the mesh size, three numerical artefacts are induced, significantly affecting the convergence and accuracy of the numerical solution to the problem with such a microstructure. These artefacts are: a) an artificial percolation of nearby inclusions; b) an artificial distortion of phase domains; c) an enrichment deficiency. We propose to improve the XFEM/Levelset method so as to avoid these artefacts. The new technique leading to this improvement uses one level-set function for each inclusion and adds additional enrichment in an element whose support is cut by several interfaces. A local description of the multiple level-sets is provided to avoid the storage of all level-set functions. A simple integration rule is employed for numerical quadrature in elements cut by several interfaces. We show that the artefacts mentioned hereinbefore are circumvented in this framework. The performances of the method are demonstrated through benchmarks and examples applied to the homogenization of concrete materials in 2D and 3D cases.
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A. B. Tran, Julien Yvonnet, Qi-Chang He, C. Toulemonde, J. Sanahuja. A multiple level-set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within XFEM. International Journal for Numerical Methods in Engineering, Wiley, 2011, 85 (11), pp.1436-1459. ⟨10.1002/nme.3025⟩. ⟨hal-00692223⟩

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