Numerical fracture growth modeling using smooth surface geometric deformation

Numerical methods for fracture propagation model fracture growth as a geometric response to deformation. In contrast to the widely used faceted representations, a smooth surface can be used to represent the fracture domain. Its benefits include low cost, resolution-independent storage, swift generation of local tip coordinate systems, and a parametric representation. In the present work, an interaction-free deformation-informed surface modification algorithm of the fracture is presented, with localized stress intensity factor computations, and automatic resolution adjustment, which allows for geometric evolution without the need of appending or re-approximating the fracture surface. The method 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 increases only as a function of curvature, but not area, and the discretization of the parametric surface is achieved in constant time. 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. Use of the algorithm is demonstrated for a discrete finite element-based fracture propagation method.