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Modélisation des instabilités liées au frottement sec des solides élastiques, aspects théoriques et numériques

Abstract : A first part present a bibliographical study on the modelization of dry friction, where different laws of friction, results on elastic problem with those laws and some links with micro-mechanical models are introduced. A second part deals with the analysis of a dynamical model : the sliding with Coulomb friction and a slip velocity dependent coefficient of a parallelepiped linearly elastic in unilateral contact with a flat rigid foundation. The framework of differential inclusions is introduced, including theoretical and numerical analysis results. This framework allows the mathematical study of finite degrees of freedom systems in a rigorous way. The latter give a first look of the instabilities due to the friction. After that, a one dimensional model is considered. Existence and uniqueness results are proven when the friction coefficient is monotonous. If it is not, generally there is a infinite number of solutions. The introduction of a perturbed friction condition, which is equivalent to the addition of a slight surface mass on the contact boundary, allows to regain the uniqueness. In a more restrictive framework, it is proven that a particular solution of the initial problem is approached when the perturbation parameter goes to zero. This solution is compared with the one selected by an already known criterion, called perfect delay criterion. At last, numerical schemes and stability and convergence results are also presented. Concerning the problem in dimension two or three, we present a numerical scheme based on an alternating direction method, and on the perturbed friction condition. Significant numerical simulations are shown.
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Yves Renard. Modélisation des instabilités liées au frottement sec des solides élastiques, aspects théoriques et numériques. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1998. Français. ⟨tel-00004903⟩

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