Powell-Sabin B-splines for smeared and discrete approaches to fracture in quasi-brittle materials

For discrete fracture approaches, the degree of continuity of T-splines is reduced to C0 at the crack tip. Hence, stresses need to be evaluated and weighted at the integration points in the vicinity of the crack tip in order to decide when the critical stress is reached. In practice, stress fields are highly irregular around crack tips. Furthermore, aligning a T-spline mesh with the new crack segment can be difficult. Powell-Sabin B-splines also remedy these drawbacks as they are C1-continuous at the crack tip and stresses can be directly computed, which vastly increases the accuracy and simplifies the implementation. Moreover, re-meshing is more straightforward using Powell-Sabin B-splines. A current limitation is that, in three dimensions, there is no procedure (yet) for constructing Powell-Sabin B-splines on arbitrary tetrahedral meshes.