Homogenization of many-body structures in fully nonlinear elasticity: A first approach with some applied flavour
✍ Scribed by Philipp Emanuel Stelzig
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 103 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0936-7195
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✦ Synopsis
Abstract
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)