High contrast homogenisation in nonlinear elasticity under small loads

Cherdantsev, Mikhail ORCID: https://orcid.org/0000-0002-5175-5767, Cherednichenko, Kirill and Neukamm, Stefan 2017. High contrast homogenisation in nonlinear elasticity under small loads. Asymptotic Analysis 104 (1-2) , pp. 67-102. 10.3233/ASY-171430

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	High-contrast homogenisation; Nonlinear elasticity; Two-scale
Publisher:	IOS Press
ISSN:	0921-7134
Date of First Compliant Deposit:	29 June 2017
Date of Acceptance:	4 May 2017
Last Modified:	25 Nov 2024 23:15
URI:	https://orca.cardiff.ac.uk/id/eprint/101931

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