Blaise Bourdin, bourdin@lsu.edu
Multiscale Problems in Brittle Fracture
The Variational Approach to Fracture has now emerged as a versatile yet rigorous model of fracture in brittle materials. Its natural ability to handle crack propagation along complex unknown geometry in two and three dimensions is allowing unprecedented numerical investigations of problems involving very complex fracture systems. I will focus on two such situations: the morphogenesis of complex cracks induced by thermal shocks, and fracture of heterogeneous materials. In the first situation, we will show how the regularized fracture energies used in the numerical simulations can be seen as ad-hoc graduent damage models in order to faithfully reproduce crack nucleation then propagation over many order of magnitude in scale. In the later one, we will show how the intuitive concept of “effective toughness” of an heterogeneous material may be inappropriate. We present a new formalism based on a “surfing experiment” for the determination and numerical computation of this effective toughness.