Meshless finite volume method for the analysis of fracture problems in orthotropic media

In this paper, a meshless finite volume (MFV) formulation is developed for analyzing fracture problems in orthotropic media. In this approach, Delaunay triangular scheme is utilized to discretize the domain based on the set of nodes with arbitrary distribution. For approximating the field variables, the moving least square (MLS) approximation is used. Stress singularity at the crack tips is considered by enrichment functions in the vicinity of the crack tips and also the interaction M-integral is used to compute the stress intensity factor (SIF). To illustrate the effectiveness and accuracy of the proposed method several problems with different shapes, load conditions, crack positions and different inclinations of the axes of orthotropy, are studied in the computation of the SIF. The obtained results of the presented method reveal that using either regular basis functions or enriched functions can lead to highly accurate and stable results even by using significantly fewer degrees of freedom in comparison with the other available numerical methods.