Nouvelle approche pour la modélisation des problèmes multi-échelles en mécanique : la méthode 95/5

Abstract : We propose a new micro/macro modelling approach for mechanical problems involving microstructure. This approach is an appealing choice for the treatment of problems involving materials with two behaviour lengths of variation, where it is impossible to define and to apply a single low describing the behaviour of both micro and micro scales. We propose a discretization for which the major part of the studied field is modelled exclusively on a macroscopic scale. Only some relatively small zones, called microscopic patterns, are modelled on a microscopic scale. The implementation of the modelling method rests on: an extension of the behaviour principle from the microscopic scale, in order to deduce a numerical behaviour for the macroscopic scale; the method of constrained natural elements CNEM, in order to be able to insert the microscopic patterns in a macroscopic discretization; and a solver introducing domain decomposition and model reduction to accelerate calculation and to take benefit from the parallel calculators. We proved the effectiveness of our approach on some benchmarks with a good estimation of the solution, and a homogeneous error distribution over the microscopic and macroscopic scales even on the edges. That enables us to consider the use of the suggested approach for the simulation of phenomena located on the edge and affecting the response of the mechanical system (friction, cutting process ...).
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Contributor : Ecole Arts Et Métiers Paristech <>
Submitted on : Tuesday, July 10, 2007 - 8:00:00 AM
Last modification on : Thursday, January 11, 2018 - 6:22:21 AM
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Djamel Missoum Benziane. Nouvelle approche pour la modélisation des problèmes multi-échelles en mécanique : la méthode 95/5. Sciences de l'ingénieur [physics]. Arts et Métiers ParisTech, 2007. Français. ⟨NNT : 2007ENAM0007⟩. ⟨pastel-00002617⟩

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