Static and dynamic fracture analysis in elastic solids using a multiscale extended isogeometric analysis

Abstract

The main objective of this paper is to develop a novel multiscale approach for simulating static and stationary dynamic crack problems in two-dimensional elastic solids through an extended isogeometric analysis using the Non-Uniform Rational B-Splines (NURBS). This multiscale strategy consists of two techniques that the Nitsche’s method is applied for coupling different length-scales meshes on one hand, and on the other hand, a local enrichment technique is taken to describe the cracks independently of the mesh in the refined region by introducing the enrichment function into the isogeometric analysis displacement approximation. This method inherits the advantage of XIGA and simultaneously improves his limitation on the local mesh refinement. The proposed approach possesses several advantages in fracture modeling: (i) the singularities of the crack-tip fields can be captured precisely and conveniently by the enrichment techniques; (ii) higher-order convergence rates is achieved and (iii) stress smoothing results are achieved owing to higher continuity of NURBS basis functions. Numerical results of static and stationary dynamic crack problems validate its accuracy and efficiency.