Thermal metamaterials have exhibited great potential on manipulating, controlling and processing the flow of heat, and enabled many promising thermal metadevices, including thermal concentrator, rotator, cloak, etc. However, three long-standing challenges remain formidable, i.e., transformation optics-induced anisotropic material parameters, the limited shape adaptability of experimental thermal metadevices, and a priori knowledge of background temperatures and thermal functionalities. Here, we present robustly printable freeform thermal metamaterials to address these long-standing difficulties. This recipe, taking the local thermal conductivity tensors as the input, resorts to topology optimization for the freeform designs of topological functional cells (TFCs), and then directly assembles and prints them. Three freeform thermal metadevices (concentrator, rotator, and cloak) are specifically designed and 3D-printed, and their omnidirectional concentrating, rotating, and cloaking functionalities are demonstrated both numerically and experimentally. Our study paves a powerful and flexible design paradigm toward advanced thermal metamaterials with complex shapes, omnidirectional functionality, background temperature independence, and fast-prototyping capability.

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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.

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Manipulating heat with thermal metamaterials has garnered increasing attention for enabling underlying physics and promising applications. However, the frequently adopted strategy to fabricate thermal metamaterials is using layered structures, whose design space is limited and, thus, other strategies demand further exploring. Here, we propose the holey engineering strategy as an alternative to design thermal metamaterials based on genetic algorithm optimization. The design procedures are introduced in detail, and two metadevices including the thermal cloak and thermal concentrator, are designed and verified to demonstrate the feasibility and convenience of this strategy. This work proposes a new design method for thermal metamaterials and paves an efficient way for macroscopic heat flow manipulation.