Local and Global Approaches to Fracture Mechanics Using Isogeometric Analysis Method

In the present research, implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics are investigated. NURBS and Tsplines are two different computational geometry technologies which are studied in this work. 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 modeling discrete cracks. Also 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. T-splines are a kind of computational geometry technology with the possibility of local refinement and also with no topologically rectangular arrangement of control points. Therefore, T-splines can decrease superfluous control points which they do not have any major effects on the geometry. Various numerical simulations demonstrate the suitability of the isogeometric approach to fracture mechanics

Keywords:

Fracture mechanics , Isogeometric analysis method , Knot insertion , NURBS , T-spline