Fracture evolution based on Griffith's criterion
Christopher J. Larsen (WPI)
Tuesday 4th March, 2008 16:00-17:00 515
There has been much recent mathematical work on quasi-static fracture, triggered by the Francfort-Marigo approach. The main idea is to turn the classical Griffith criterion for crack growth into a model for predicting crack paths, and there has been much success. The main drawback of the Francfort-Marigo model is its reliance on global minimization, which in particular results in violations of Griffith's criterion. I will discuss some efforts towards creating a variational model based on local minimization that also predicts crack paths, and why a fully satisfactory (variational) approach seems impossible. One possible fix, naturally, is to instead consider dynamics. A computational model, based only on elastic dynamics away from the crack and a localized Griffith's criterion at the crack tip, will be described, along with a corresponding (speculative) analytical model for fracture dynamics.