Abstract
In this work, we study the emergence of different crack modes in linearly elastic thin films by means of a Gamma-convergence analysis as the thickness tends to zero. We first consider a purely elastic body made of a film deposited on an infinitely stiff substrate through a bonding layer. The displacement mismatch between the film and the substrate generates a cohesive type energy depending on the displacement jump. Then, we consider a single line...
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In this work, we study the emergence of different crack modes in linearly elastic thin films by means of a Gamma-convergence analysis as the thickness tends to zero. We first consider a purely elastic body made of a film deposited on an infinitely stiff substrate through a bonding layer. The displacement mismatch between the film and the substrate generates a cohesive type energy depending on the displacement jump. Then, we consider a single linearly elastic brittle thin film. We show that the limit admissible displacements are of Kirchhoff-Love type outside the cracks, which are themselves transverse. Finally, we study the interplay between transverse cracks and debonding. We come back to the first system made of a film, a bonding layer and a substrate, but now allow it to crack. In the simplified anti-plane setting, in addition to transverse cracks, a threshold criterion acting on the displacement activates either a cohesive or a delamination energy. Some partial results in the general vectorial case are discussed. Author Keywords:Free discontinuity problems
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Journal title
Interfaces and Free Boundaries
