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High contrast homogenisation in nonlinear elasticity under small loads.
- Source :
-
Asymptotic Analysis . 2017, Vol. 104 Issue 1/2, p67-102. 36p. - Publication Year :
- 2017
-
Abstract
- We study the homogenisation of geometrically nonlinear elastic composites with high contrast. The composites we analyse consist of a perforated matrix material, which we call the "stiff" material, and a "soft" material that fills the remaining pores. We assume that the pores are of size 0 < ε << 1 and are periodically distributed with period ε. We also assume that the stiffness of the soft material degenerates with rate ε2γ,γ > 0, so that the contrast between the two materials becomes infinite as ε ↓ 0. We study the homogenisation limit ε ↓ 0 in a low energy regime, where the displacement of the stiff component is infinitesimally small. We derive an effective two-scale model, which, depending on the scaling of the energy, is either a quadratic functional or a partially quadratic functional that still allows for large strains in the soft inclusions. In the latter case, averaging out the small scale-term justifies a single-scale model for high-contrast materials, which features a non-linear and non-monotone effect describing a coupling between microscopic and the effective macroscopic displacements. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09217134
- Volume :
- 104
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Asymptotic Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 124662510
- Full Text :
- https://doi.org/10.3233/ASY-171430