Numerical crack path selection problem based on energy profiles

Given the infinite number of possible crack paths in a material, a mathematical theory to determine a crack path has not yet been established. On this occasion, we numerically find a crack path in a variational fracture framework. Based on the variational crack propagation model by Francfort and Marigo, we numerically compare elastic energy profiles along several crack paths and determine a crack path with a minimum energy profile. We consider multiple straight crack cases and kink- and circle-shaped crack paths. For these cases, we additionally employ a variational formula for the derivative of the energy profile. Furthermore, we numerically observe that our approach's selected kink crack path exhibits good agreement with the crack propagation results in the phase field model.