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 [1 ]
Duy Khanh Trinh [1 ]
机构
[1] MINES ParisTech, Ctr Mat, CNRS, UMR 7633, F-91003 Evry, France
来源
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2011年 / 91卷 / 02期
关键词
Generalized continua; homogenization methods; micromorphic; second gradient; COUPLE-STRESS MODEL; HETEROGENEOUS MATERIALS; GRADIENT ELASTICITY; 2-PHASE COMPOSITE; COMPUTATIONAL HOMOGENIZATION; MICROMORPHIC CONTINUUM; MICROSTRUCTURE; IDENTIFICATION; MICROPOLAR; PLASTICITY;
D O I
10.1002/zamm.201000109
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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
引用
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页码:90 / 109
页数:20
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