This paper presents a robust enrichment strategy to model weak and strong discontinuities as well as cracks for industrial applications. First, numerical issues encountered with popular extended finite element approximation spaces are pointed out. Then, the paper gives indications on how to circumvent those issues. The very originality of the paper relies on questioning the theoretical approximation spaces with respect to numerical results and to modify accordingly their design. The relationship between the new design and the previous designs is clearly established, in order to highlight the very small implementation cost of the modifications exposed here. Hence with minimal additional computational cost, gains in accuracy can be significant as shown later in the paper.
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.
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