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Journal Articles Journal of the Mechanics and Physics of Solids Year : 2014

A variational model for fracture and debonding of thin films under in-plane loadings

Abstract

We study fracture and delamination of a thin stiff film bonded on a rigid substrate through a thin compliant bonding layer. Starting from the three-dimensional system, upon a scaling hypothesis, we provide an asymptotic analysis of the three-dimensional variational fracture problem as the thickness goes to zero, using Gamma-convergence. We deduce a two-dimensional limit model consisting of a brittle membrane on a brittle elastic foundation. The fracture sets are naturally discriminated between transverse cracks in the film (curves in 2D) and debonded surfaces (two-dimensional planar regions). We introduce the vectorial plane-elasticity case, applying the rigorous results established for scalar displacement fields, in order to numerically investigate the typical cracking scenarios encountered in applications. To this end, we formulate a reduced-dimension, rate-independent, irreversible evolution law for transverse fracture and debonding of thin film systems. Finally, we propose a numerical implementation based on a regularized formulation of the fracture problem via a gradient damage functional. We provide an illustration of the capabilities of the formulation exploring complex crack patterns in one and two dimensions, showing a qualitative comparison with geometrically involved real life examples.
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Dates and versions

hal-00841953 , version 1 (05-07-2013)

Identifiers

  • HAL Id : hal-00841953 , version 1

Cite

Andrés Alessandro León Baldelli, Jean-François Babadjian, Blaise Bourdin, Duvan Henao, Corrado Maurini. A variational model for fracture and debonding of thin films under in-plane loadings. Journal of the Mechanics and Physics of Solids, 2014, 70, pp.320-348. ⟨hal-00841953⟩
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