Generalized continua and non-homogeneous boundary conditions in homogenisation methods [Plenary lecture presented at the 81st Annual GAMM Conference, Karlsruhe, 25 March 2010]
被引:140
作者:
Forest, Samuel
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MINES ParisTech, Ctr Mat, CNRS, UMR 7633, F-91003 Evry, FranceMINES ParisTech, Ctr Mat, CNRS, UMR 7633, F-91003 Evry, France
Forest, Samuel
[1
]
Duy Khanh Trinh
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MINES ParisTech, Ctr Mat, CNRS, UMR 7633, F-91003 Evry, FranceMINES ParisTech, Ctr Mat, CNRS, UMR 7633, F-91003 Evry, France
Duy Khanh Trinh
[1
]
机构:
[1] MINES ParisTech, Ctr Mat, CNRS, UMR 7633, F-91003 Evry, France
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. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
机构:
S Fed Univ, Rostov Na Donu 344090, Russia
RASci, S Sci Ctr, Rostov Na Donu 344090, RussiaUniv Halle Wittenberg, Zentrum Ingenieurwissensch, Lehrstuhl Tech Mech, D-06099 Halle, Saale, Germany
机构:
Commiss European Communities, Joint Res Ctr, IPSC, ELSA, I-21020 Ispra, VA, ItalyCommiss European Communities, Joint Res Ctr, IPSC, ELSA, I-21020 Ispra, VA, Italy
机构:
S Fed Univ, Rostov Na Donu 344090, Russia
RASci, S Sci Ctr, Rostov Na Donu 344090, RussiaUniv Halle Wittenberg, Zentrum Ingenieurwissensch, Lehrstuhl Tech Mech, D-06099 Halle, Saale, Germany
机构:
Commiss European Communities, Joint Res Ctr, IPSC, ELSA, I-21020 Ispra, VA, ItalyCommiss European Communities, Joint Res Ctr, IPSC, ELSA, I-21020 Ispra, VA, Italy