Surface-oriented homogenization method for size-dependent thermal expansion coefficient of thermal metamaterial

This paper explores the influence of microstructures on the effective thermal expansion coefficient of thermal metamaterials, highlighting the surface-induced size-dependent effects. These effects stem from the unique porous microstructural characteristics, influenced by volume fraction and geometric configuration. Unlike nanoscale phonon-driven surface effects, comprehensive finite element numerical simulations reveal that macroscopic surface mechanisms in thermal metamaterials arise from changes in heat conduction pathways due to microstructural features. These surface regions, characterized by an intrinsic length, are determined by the microstructure itself. To accurately capture the complex size-dependent coefficients of linear thermal expansion, we developed a surface-oriented homogenization method that leverages the interaction between extrinsic and intrinsic length under surface mechanisms. Unlike classical homogenization methods, this approach does not require compliance with the principle of scale separation. The effectiveness of this surface-oriented homogenization method is demonstrated through simulations of thermal metamaterial sheet subjected to temperature variations, highlighting that this method combines the efficiency of traditional homogenization methods with the high accuracy of high-fidelity finite element methods. This paper not only provides a novel surface-oriented homogenization approach that can overcome computational challenges of thermal metamaterial structures but also offers an approach to constructing an offline dataset for the intrinsic length that is beneficial to guiding the data-driven design of thermal metamaterial structures.