The variational approach to fracture
A. A. Griffith variational model of brittle fracture mechanics and crack evolution is investigated with samples in static equilibrium with the applied loads. The crack propagation criteria test is balanced between the potential energy released through a virtual increase of the crack length and the energy spent in creating additional length. The output of the minimization is not found to be a crack, as the Cantor part corresponds in effect to diffuse cracking process, with overall dimensionality higher than 1. In the traction experiment with a hard device, the elastic evolution and all admissible evolutions with a set number of jumps satisfy the weak variational evolution. The crack initiation is completely in agreement with the strong variational evolution and prohibits the pre-existence of a crack, as that would contradict the Lipschitz character of the domain.
Publication Source (Journal or Book title)
Journal of Elasticity
Francfort, G., Bourdin, B., & Marigo, J. (2008). The variational approach to fracture. Journal of Elasticity, 91 (1-3), 5-148. https://doi.org/10.1007/s10659-007-9107-3