Fracture modeling with the adaptive XIGA based on locally refined B-splines

Abstract

This paper aims at investigating fracture behavior of single and multiple cracks in two-dimensional solids by an adaptive extended isogeometric analysis (XIGA) based on locally refined (LR) B-splines. The adaptive XIGA is capable of modeling cracks without considering the location of crack faces due to the local enrichment technique based on partition-of-unity concept. The XIGA approximation is locally enriched by Heaviside function and crack tip enrichment functions to capture the discontinuity across crack faces and singularity in the vicinity of crack tips. The LR B-splines, which are generalized by B-splines and NURBS, not only inherent desirable properties of the B-splines and NURBS but also can be locally refined, ideally suitable for adaptive analysis. Structured mesh refinement strategy is applied to perform local refinement for LR B-splines based on a posteriori error estimator. According to the recovery technique proposed by Zienkiewicz and Zhu, the smoothed strain field is obtained to construct the posteriori error estimation based local refinement. The stress intensity factors (SIFs) are evaluated using the contour interaction integral technique. Several benchmark numerical examples are illustrated in comparison to analytical or reference solutions to verify the accuracy and efficiency of the developed approach. The proposed adaptive XIGA method is also applied to a curved crack, multiple cracks and complicated structure with a crack, which sufficiently presents the applicability of the proposed method in crack modeling. In addition, the convergence rate of the adaptive local refinement strategy is numerically studied and compared with that of the global refinement approach. The convergence rate of the adaptive local refinement is shown to be faster than that of the global refinement.