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Asymptotic and numerical study of fine inclusions in elastic domains

Abstract : This work focused on mathematical modeling and numerical approximation of the influence of a very thin inclusion on an elastic substrate of different stiffness. The study is motivated by applications in tires and is not based on conventional homogenization techniques. Indeed, the objective was to treat the interaction between a single inclusion and its elastic medium and not a density of inclusions. The study consisted of three parts, the first concerning mathematical modeling for linear behavior laws leading to an expression of the contribution of the inclusion in the form of the inclusion-free field corrected by correctors at different orders. These correctors are independent of the characteristic size of the inclusion. The second relates to the numerical approximation of this influence by means of the finite element method and that of the inverted finite elements. A numerical strategy for taking into account the influence of several inclusions is also presented. The last part is prospective and discusses the possibility of extending the approach for nonlinear behavioral laws.
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  • HAL Id : tel-02000262, version 1

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Mohamed Rafik Ben Hassine. Asymptotic and numerical study of fine inclusions in elastic domains. Numerical Analysis [math.NA]. Université de Lyon; École nationale d'ingénieurs de Tunis (Tunisie), 2017. English. ⟨NNT : 2017LYSEI086⟩. ⟨tel-02000262⟩

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