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Reduced models for linearly elastic thin films allowing for fracture, debonding or delamination

Banff International Research Station for Mathematical Innovation and Discovery

This talk is devoted to highlighting the interplay between fracture and delamination in thin films. The usual scaling law on the elasticity parameters and the toughness of the medium with respect to its thickness gives rise to traditional cracks which are invariant in the transverse direction. We will show that, upon playing on this scaling law, it is also possible to observe debonding effects (delamination as well as decohesion) through the appearance of cracks which are orthogonal to the thin direction. Starting from a three-dimensional brittle elastic thin film, we will first present how both phenomena can be recovered independently through a Gamma-convergence analysis as the thickness tends to zero. Then, working on a “toy model" for scalar anti-plane displacements, we will show how both phenomena can be obtained at the same time. Some partial results in the full three-dimensional case will be presented.
These are joint works with Blaise Bourdin, Duvan Henao, Andrès Leon Baldelli. and Corrado Maurini.

Mathematics; Mechanics of deformable solids; Calculus of variations and optimal control; optimization; Material science

video/mp4

Author affiliation: Laboratoire Jacques Louis Lions - Université Paris 6

2017-02-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59698

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/