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

Abstract

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.

3D coupled HM–XFEM modeling with cohesive zone model and applications to non planar hydraulic fracture propagation and multiple hydraulic fractures interference

“…Advanced numerical methods have been used to overcome the well-known weaknesses of 3D quadratic XFEM elements that suffer classically from major robustness and conditioning issues. First, a robust procedure has been developed in [57] for the integration of functions discontinuous across arbitrary curved interfaces. It is combined with an improved XFEM enrichment technique proposed by [56] and well-suited for strong discontinuities.…”

“…This XFEM model is based on the previous numerical model developped by Faivre et al [34] but with the following distinguished features : (i) fully hydromechanical coupling based on an improved XFEM enrichment technique, (ii) fracture propagation on non-predefined paths, (iii) 3D configuration including complex nonplanar fracture geometries and (iv) multiple-crack junction. Besides the extension of our model to fluid-filled cohesive crack junctions, most of these new features borrow on recently published advances on the XFEM [56,57,58,59]. The assembly of all these state-of-the art techniques results in a more complete model which is a step forward to address the challenges mentioned above.…”

“…In order to overcome conditioning issues usually encountered with 3D XFEM elements, a robust XFEM enrichment technique is employed [56]. It is associated to a consistent integration technique adapted to curved cracks and branched discontinuities [57]. The stability of our model is ensured by the use of three distinct approximation spaces.…”

Challenges, Tools and Applications of Tracking Algorithms in the Numerical Modelling of Cracks in Concrete and Masonry Structures

“…The generality of some of the update schemes as well of the definitions for the level set functions allows their almost straightforward extension to 3D problems (e.g. [192,193,185,194,195]).…”

A fictitious domain method for the simulation of thermoelastic deformations in NC‐milling processes

“…Using higher‐order polynomials for the blending, isoparametric transformations are obtained. Blending techniques in the context of extended finite element methods are for instance investigated in previous works …”