NURBS-Based Isogeometric Analysis Method Application to Mixed-Mode Computational Fracture Mechanics

An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis functions, the possibility of enhancing a B-spline basis with discontinuities by means of knot insertion makes isogeometric analysis method a suitable candidate for modelling discrete cracks. Moreover, the repetition of two different control points between two patches can create a discontinuity and also demonstrates a singularity in the stiffness matrix. In the case of a pre-defined interface, non-uniform rational B-splines are used to obtain an efficient discretization. Various numerical simulations for edge and center cracks demonstrate the suitability of the isogeometric analysis approach to fracture mechanics.