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Analyse mathématique et numérique de la propagation des fissures par le modèle de multi-couronnes

Abstract : The energy release rate is required for crack initiation analysis, and a great deal of effort has been devoted to its numerical evaluation. In this thesis, it is shown that the post-initiation assessment, such as the crack growth stability, crack propagation rate, etc., is related with the second derivatives of potential energy with respect to crack length. However accurate estimate of this quantity encounters considerable difficulty because of higher order singularity near the crack tip region, and little attention has been given in the literature to this problem. The work presented here is to have assess techniques, based on a sound mathematical consideration, for calculating accurately the second variations of energy. In the present inverstigation, our attention is focused on the lagrangian representation which is recognized to be the most effective and efficient tool for solving linear and non-linear fracture problems. Using perturbation domain technique, an analytical expression of the second derivatives of potential energy with respect to crack length is derived for the following situations: 1) thermal loading case; 2) loading accomplished by surface tractions applied on crack face; 3) axisymetric structure case. All obtained analytical expressions are put in form suitable for numerical analysis of an arbitrary three-dimensional crack configuration. A variety of example computations are performed for elastic bodies containing either one single crack or several interacting cracks in tension. Close agreement between numerical results given by the proposed approach and reference solutions as well as some theoretical properties about the second variations of potential energy has been found in all cases.
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https://pastel.archives-ouvertes.fr/pastel-00574056
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Submitted on : Monday, March 7, 2011 - 10:07:52 AM
Last modification on : Sunday, December 3, 2017 - 1:50:49 PM
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Xiao-Zheng Suo. Analyse mathématique et numérique de la propagation des fissures par le modèle de multi-couronnes. Mécanique des structures [physics.class-ph]. Ecole nationale des ponts et chaussées - ENPC PARIS / MARNE LA VALLEE, 1990. Français. ⟨pastel-00574056⟩

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