Crack growth adaptive XIGA simulation in isotropic and orthotropic materials

Abstract

Reliable prediction and thorough understanding of crack growth in engineering materials and structures are of challenging problems, but scientific and technical community has been continuously pursuing an efficient numerical approach to crack propagation simulation. We present in this paper 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 accurately 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 sub-triangle 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. Several crack growth numerical examples for both isotropic and orthotropic media are studied in different scenarios to show the performance and accuracy of the developed approach. 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.