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Homogenization of many‐body structures in fully nonlinear elasticity: A first approach with some applied flavour
Author(s) -
Stelzig Philipp Emanuel
Publication year - 2011
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201110017
Subject(s) - homogenization (climate) , nonlinear system , anisotropy , kinematics , nonlinear elasticity , mechanics , computer science , materials science , mathematics , mathematical analysis , physics , classical mechanics , optics , biodiversity , ecology , quantum mechanics , biology
We expose and discuss a model for certain “cord‐belt like” many‐body structures in a geometrically and constitutively nonlinear regime that accounts for noninterpenetration of matter in the sense of Ciarlet and Nečas. As the structures compose of more and simultaneously smaller bodies, we state homogenization limits for the respective models based on a Γ‐convergence analysis. Depending on the structures' geometries, the homogenization process may result in different mechanical effects, ranging from anisotropy to completely new kinematic constraints. The homogenization results pose moreover as first rigorous evidence that appropriately arranged and laminated structures composed of mechanically low dimensional objects can have the same properties as if they were composed of higher dimensional objects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)