124 NURBS-based geometric fracture growth representation

Numerical methods for fracture propagation model fracture growth as a geometric response to deformation. In contrast to the widely used faceted representations, a smooth Non-Uniform Rational B-Spline (NURBS) surface can be used to represent the fracture domain. Its benefits include low cost, resolutionindependent storage, and a parametric representation of a smooth domain. In the present work an interaction-free, deformation-informed, Gaussian-based modification algorithm of the fracture surface is presented, with localized stress intensity factor computations, and automatic resolution adjustment, which allow for geometric evolution without the need of appending or re-approximating the fracture surface. It is based on the movement of surface control points and on the systematic editing of weights and knots. It does not require trimming, and is able to shift fracture shape and capture its path evolution efficiently. Throughout growth, the number of points required for fracture representation remains fixed, and the discretization of the fracture surface is implicitly defined by the underlying parametric space. The proposed algorithm can be incorporated into any fracture propagation code that keeps track of fracture geometry and updates it as a function of deformation. The algorithm is demonstrated for a discrete finite element-based fracture propagation method.