Topology-optimized thermal metamaterials traversing full-parameter anisotropic space

Abstract It is widely adopted in thermal metamaterials that mixing different materials could conveniently result in effective thermal conductivities (ETCs) beyond naturally-occurring materials. When multiple materials are isotropically mixed, the ETC is a direct average governed by their filling fractions and given bulk conductivities. That could lead to an inhomogeneous and anisotropic value within the maximal and minimal thermal conductivities of constituent materials. Usually thermal metadevices rely on anisotropic thermal conductivity tensor, whose tensorial elements are frequently inter-dependent and confined within a limited parametric space. It is thus nontrivial to establish a design recipe for advanced thermal metamaterials whose ETCs could cover full-parameter anisotropic space. We demonstrate topological functional cells (TFCs) with copper and polydimethylsiloxane, and show that the anisotropic ETCs traverse their full-parameter space. Such robust scheme based on topology-optimized TFCs unlocks unexplored opportunities for functional thermal metadevices whose parameters may not be reached in previous mixing approaches. This study also sheds light on the developments in emerging acoustic, mechanical and electromagnetic composite materials.