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Sur la rupture des couches minces : une approche variationnelle

Abstract : We study the problem of fracture in thin film systems subject to tensile stresses originated by mechanical loading or inelastic phenomena, due e.g. to thermal or moisture couplings. In such systems, homogeneous loads lead to the nucleation of interacting transverse and debonding cracks, producing auto-structuration of quasi-periodic crack networks and propagation of complex patterns showing robust morphological features. We tackle the problem of describing the irreversible evolution of fractures, covering the phases of crack nucleation, path selection and irreversible evolution in space and time. Available literature results rely upon phenomenological models lacking rigorous derivation and are limited to simple geometrical settings. In addition, problems of nucleation of new cracks, mechanisms of path selection and irreversible, non-smooth evolution in space and time are not explored, due to the limitations of to classical theory of fracture mechanics. We propose the derivation of a limit, asymptotic, reduced-dimension, global, varia- tional, theory for fracture of thin films starting from three-dimensional brittle elasticity within the framework of variational fracture, using notions of variational convergence. We then introduce a regularization of the limit fracture problem, by the means of a damage gradient functional, suitable to the numerical solution by finite elements. The proposed work allows to obtain a systematic understanding of the competition between various mechanisms including fracture and debonding; to rigorously establish a reduced, variational, asymptotic model, valid for thin films that is rich enough to capture the important physics of failure; and to tackle a detailed numerical study of the complex cracking and debonding patterns observed in thin film systems.
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https://tel.archives-ouvertes.fr/tel-00921907
Contributor : Andrés Alessandro León Baldelli <>
Submitted on : Sunday, December 22, 2013 - 5:36:48 PM
Last modification on : Friday, January 8, 2021 - 9:48:03 AM
Long-term archiving on: : Monday, March 24, 2014 - 9:30:12 AM

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  • HAL Id : tel-00921907, version 1

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Andreés Alessandro León Baldelli. Sur la rupture des couches minces : une approche variationnelle. Mécanique des solides [physics.class-ph]. Université Pierre et Marie Curie - Paris VI, 2013. Français. ⟨NNT : 391⟩. ⟨tel-00921907⟩

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