53 / 2021-03-30 10:22:42

Simulation of crack growth using adaptive XIGA

Crack growth; Fracture; XIGA; LR B-splines; Adaptivity; Orthotropic media; Isotropic media

We present a significant extension and development of the adaptive extended isogeometric analysis (XIGA) based on LR B-splines (locally refined B-splines), which facilitates the local refinement, for modeling crack growth in isotropic and orthotropic media. The discontinuity and singularity of displacements and stresses induced by cracks are locally captured by special enrichment functions, for both isotropic and orthotropic media. This allows the representation of crack to be independent of the computational mesh and avoids the requirement for re-meshing in crack growth simulation. The numerical integration accuracy is improved with the use of the almost-polar integration and subtriangle technique for the crack-tip and cut elements, respectively. The posteriori error estimator based on Zienkiewicz–Zhu error estimation is employed to define refinement domains, and thereby, drives the adaptivity. On the other hand, the maximum circumferential stress criterion is adopted to determine the direction of crack growth. Numerical results reveal that the present approach integrated with the adaptive local refinement scheme offers higher accuracy and convergence rate than the standard XIGA. Furthermore, the adaptive XIGA in a tandem with Nitche's method is applied to simulate the crack growth of complicated structures. We additionally explore the effects of some numerical aspects or factors on crack path. Smaller crack growth increment could be used to improve the accuracy of crack path within a finer mesh in the adaptive XIGA.