Energy conservation during remeshing in the analysis of dynamic fracture

The analysis of (dynamic) fracture often requires multiple changes to the discretisation during crack propagation. The state vector from the previous time step must then be transferred to provide the initial values of the next time step. A novel methodology based on a least-squares fit is proposed for this mapping. The energy balance is taken as a constraint in the mapping, which results in a complete energy preservation. Apart from capturing the physics better, this also has advantages for numerical stability. To further improve the accuracy, Powell-Sabin B-splines, which are based on triangles, have been used for the discretisation. Since C1 continuity of the displacement field holds at crack tips for Powell-Sabin B-splines, the stresses at and around crack tips are captured much more accurately than when using elements with a standard Lagrangian interpolation, or with NURBS and T-splines. The versatility and accuracy of the approach to simulate dynamic crack propagation are assessed in two case studies, featuring mode-I and mixed-mode crack propagation.