Multiscale Problems in Brittle Fracture

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Blaise Bourdin, [email protected]
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.
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