An integration technique for 3D curved cracks and branched discontinuities within the eXtended Finite Element Method

Bertrand Paul (1, 2, 3) , Marcel Ndeffo (1, 3) , Patrick Massin (3) , Nicolas Moes (4)

1 IFPEN - IFP Energies nouvelles
2 GeoRessources
3 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
4 GeM - Institut de Recherche en Génie Civil et Mécanique

In this paper, we present a robust procedure for the integration of functions discontinuous across arbitrary curved interfaces defined by means of level set functions for an application to linear and quadratic eXtended Finite Elements. It includes the possibility to have branching discontinuities between the different sub-domains. For the volume integration, integration subcells are built from the approximation mesh, in order to obtain an accurate approximation of the sub-domains. The set of subcells we get constitutes the integration mesh, which can also be used by the visualization tools. Then, we extract the faces of these integration subcells that coincide with the sub-domain boundaries, allowing us to perform surface integrations on the sub-domain boundaries. When combined with the eXtended Finite Element Method (XFEM) optimal convergence rates are obtained with curved geometries for both linear and quadratic elements.

Mots clés: XFEM; level-set-method; high order approximation; numerical integration; curved geometries

Domaines: Analyse numérique [cs.NA]

Bertrand Paul, Marcel Ndeffo, Patrick Massin, Nicolas Moes. An integration technique for 3D curved cracks and branched discontinuities within the eXtended Finite Element Method. Finite Elements in Analysis and Design, 2017, 123, pp.19-50. ⟨10.1016/j.finel.2016.09.002⟩. ⟨hal-01455394⟩