Bi-directional homogenization design of well-connected freeform thermal metamaterials

Thermal metamaterials hold significant promise for manipulating, controlling, and processing heat flow, primarily due to their structural configuration. The design of freeform thermal metamaterials is a long-standing challenge, with ensuring connectivity proving troublesome. In this paper, a general design framework involving three structural scales, macro-meso-micro, is presented for well-connected freeform thermal metamaterials. At first, the macroscopic design domain is divided into design cells, each of which corresponds to an anisotropic thermal conductivity tensor induced by transformation thermotics theory. Then, structures of the design cells are generated via topology optimization. To improve the connectivity between the adjacent cells, the Bi-Directional Homogenization (BDH) method is adopted, including the computational process of forward homogenization from the microscale to the mesoscale , and the inverse homogenization from the macroscale to the mesoscale. Three types of thermal metamaterials (cloak, concentrator, and rotator) are designed using both BDH method and traditional Inverse Homogenization (IH) method. Compared with the IH results, the structural connectivity of the thermal cloak, concentrator, and rotator designed using the BDH method are increased by 6%, 7%, and 3.3% respectively, the optimization time are shortened by 93.84%, 92.8%, and 92.8% respectively. Numerical tests demonstrate that the BDH design results prove significant advantages in thermal functionality and structural stiffness . • BDH method is proposed for the design of connected freeform thermal metamaterials. • Thermal cloak, concentrator, rotator are designed and analyzed. • Superior thermal/mechanical performance, and design efficiency are achieved.