Endommagement discret et continu : application aux materiaux quasi-fragiles

Abstract : In this thesis, some fundamental considerations of the modeling of failure are addressed for discrete damage systems. The goal is to establish, starting with simple structural problems, a bridge between the Discrete Damage Mechanics (DDM) and that of the non-local Continuum Damage Mechanics (CDM). It is currently accepted that DDM systems must be considered in a non-local framework to obtain consistent results, especially during numerical modeling of softening phenomena based on damage laws. We support this non- locality on the scale of the microstructure of the material. Using a continualisation procedure and with the use of the Padé approximant, we were able to obtain the analytic expression of the non-local continuous approximation offering an accurate simulation of the discrete problem for the whole damage process. We study the systems of the discrete axial chain under traction, the discrete bending beam and the microstructured membrane under uniform pressure. The discrete system is first solved, then the discrete equations are continualised to obtain a non-local continuum model. For each of these problems, careful attention is paid to the boundary conditions of the continual problem, the importance of which is illustrated throughout this manuscript.
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Benjamin Hérisson. Endommagement discret et continu : application aux materiaux quasi-fragiles. Mécanique des matériaux [physics.class-ph]. Université de Bretagne Sud, 2018. Français. ⟨NNT : 2018LORIS483⟩. ⟨tel-02273159⟩

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