Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver

Abstract

A Local/Global non-intrusive coupling algorithm is proposed for the analysis of mixed-mode crack propagation. It is based on a three scale multigrid and extended finite element method, that was proposed recently for the direct estimation of stress intensity factors of static cracks. The algorithm couples a linear elastic global model (possibly performed by a industrial software) with an enhanced local model capable of modeling a crack and accurately estimating SIFs (performed by a separate research code). It is said non-intrusive since it does not modify the global mesh, its connectivity and solver. For the global model, the contribution of the local patch consists in additional nodal efforts near the crack, which makes it compatible with most softwares. Further the shape of the domain over which the local model is applied is automatically adapted during propagation.Keywords nested models · mixed mode · localized multigrid · williams · stress intensity factors 1 IntroductionThe question of the inclusion of a crack and its propagation in a finite element model initially not expected for this, is a question which is still today the subject of numerous

Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture

“…We undertake to study a multi-domain model characterized by a physical domain Ω ∈ R d , d = 2 or 3, which is divided into two disjoint, open and bounded subsets Ω 11 and Ω 2 such that Ω = Ω 11 ∪ Ω 2 and Ω 11 ∩ Ω 2 = ∅. Those two non-overlapping subdomains share a common interface denoted Γ (see Fig.…”

“…The basic strategy may involve a re-parametrization of the NURBS model, including the splitting of the new geometry into several patches with C 0 continuity at the boundaries. This may apply not only for geometric details but to all situations of local models different from the global NURBS patch model (e.g., local refinement, inclusion [9], local fracture [10,11], local plasticity [12], etc.). This entails a considerable modelling effort that is often as complex and time consuming as standard mesh generation and so is opposed to the core idea of IGA, which advocates a direct link between geometry and analysis.…”

“…An iterative coupling technique is used to perform the substitution in an exact but non-intrusive way: only interface data are transmitted from one model to the other and the global stiffness operator remains unchanged (independently of the shape of the local domain). This strategy has been applied in FEM for the modelling of crack propagation [11], for the modelling of localized uncertainties [28], for 3D-plate coupling [29] and for nonlinear domain decomposition [30]. Let us note that this methodology, involving the coupling of a global model and a local model in an iterative manner, has similarities with some hierarchical global/local methods in FEM: for example, the Chimera method [31], the method of finite element patches [32], numerical zoom [33] or the hp − d method [34][35][36].…”

“…In this paper, we propose an application of the non-intrusive technique [27,12,11,[28][29][30] to the NURBS context. The idea is to take the NURBS patch to be enriched as the global model.…”

“…For this purpose, an exact NURBS domain is simply constructed from the NURBS trimming curve in the case of a geometric detail while the quadrature rule used for the local model is transposed within the global NURBS patch in the case of real (covered) local models. With regard to coupling, an application of the conventional Lagrange multiplier approach to non-conforming geometries is employed to meet the non-intrusive constraint in the sense of [11,29,30]. Acceleration techniques, such as techniques based on Aitken's Delta Squared method or a Quasi-Newton method (see, e.g., [30]), are also implemented in the present situation, which results in a significant reduction of the number of iterations of the non-intrusive algorithm.…”