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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≪10<ε≪1 and are periodically distributed with period ε. We also assume that the stiffness of the soft material degenerates with rate ε2γε2γ, γ>0γ>0, so that the contrast between the two materials becomes infinite as ε↓0ε↓0. We study the homogenisation limit ε↓0ε↓0 in a low energy regime, where the displacement of the stiff component is infinitesimally small. We derive an effective twoscale 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 scaleterm justifies a singlescale model for highcontrast materials, which features a nonlinear and nonmonotone effect describing a coupling between microscopic and the effective macroscopic displacements.
Original language  English 

Pages (fromto)  67102 
Journal  Asymptotic Analysis 
Volume  104 
Issue number  12 
DOIs  
Publication status  Published  14 Aug 2017 
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Projects
 1 Finished

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council