Intelligence thermotics: Correlated self-fixing behavior of thermal metamaterials

Abstract

It is a challenge to design intelligent thermal metamaterials due to the lack of suitable theories. Here we propose a kind of intelligent thermal metamaterials by investigating a core-shell structure, where both the core and shell have an anisotropic thermal conductivity. We solve Laplace's equation for deriving the equivalent thermal conductivity of the core-shell structure. Amazingly, the solution gives two coupling relations of conductivity tensors between the core and the shell, which cause the whole core-shell structure to counterintuitively self-fix a constant isotropic conductivity even when the area or volume fraction of the core changes within the full range in two or three dimensions. The theoretical findings on fraction-independent properties are in sharp contrast with those predicted by the well-known effective medium theories, and they are further confirmed by our laboratory experiments and computer simulations. This work offers two coupling relations for designing intelligent thermal metamaterials, and they are not only helpful for thermal stabilization or camouflage/illusion, but they also offer hints on how to achieve similar metamaterials in other fields.