Spectral efficiency of engineered thermal cloaks in the frequency regime

We analyse basic thermal cloaks designed via different geometric transforms applied to thermal cloaking. We evaluate quantitatively the efficiency of these heterogeneous anisotropic thermal cloaks through the calculation of the standard deviation of the isotherms. The study addresses the frequency regime and we point out the cloak's spectral efficiencies. We find that all these cloaks have comparable efficiency irrespective of whether or not they have singular conductivity at their inner boundary. However, approximate cloaking with multi-layered cloak critically depends upon the homogenization algorithm and a large number of thin layers (at least fifty) is required to reduce substantially the standard deviation of the isotherms.Comment: 13 pages, 7 figures. The results from this article will be presented on a poster at the Metamaterials 2014 Copenhague conferenc

Homogenization of Stratified Elastic Composites with High Contrast

International audienceWe determine the asymptotic behavior of the solutions to the linear elastodynamic equations in a stratified media comprising an alternation of possibly very stiff layers with much softer ones, when the thickness of the layers tends to zero. The limit equations may depend on higher order terms, characterizing bending effects. A part of this work is set in the context of non-periodic homogenization and an extension to stochastic homogenization is presented

A notion of capacity related to elasticity. Applications to homogenization.

International audienceWe study a notion of capacity related to elasticity which proves convenient to analyze the concentrations of strain energy caused by the rigid displacements of some in nitesimal parts of an elastic body in two or three dimensions. By way of application, we investigate the behavior of solutions to initial boundary value problems describing vibrations of periodic elastic composites with rapidly varying elastic properties. More speci cally, we analyze a two-phase medium whereby a set of heavy sti tiny particles is embedded in a softer matrix. This task is set in the context of linearized elasticity