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Article Dans Une Revue Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Année : 2011

Generalized continua and non-homogeneous boundary conditions in homogenisation methods

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Samuel Forest

Résumé

Extensions of classical homogenization methods are presented that are used to replace a composite material by an effective generalized continuum model. Homogeneous equivalent second gradient and micromorphic models are considered, establishing links between the macroscopic generalized stress and strain measures and the fields of displacement, strain and stress inside a volume element of composite material. Recently proposed non-homogeneous boundary conditions to be applied to the unit cell, are critically reviewed. In particular, it is shown that such polynomial expansions of the local displacement field must be complemented by a generally non-periodic fluctuation field. A computational strategy is introduced to unambiguously determine this fluctuation. The approach is well-suited for elastic as well as elastoplastic composites.

Dates et versions

hal-00585332 , version 1 (12-04-2011)

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Samuel Forest, Duy-Khanh Trinh. Generalized continua and non-homogeneous boundary conditions in homogenisation methods. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2011, 91, pp.90-109. ⟨10.1002/zamm.201000109⟩. ⟨hal-00585332⟩
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