Comprehensive analysis of thermal–mechanical properties of assembled heterogeneous polyhedral metamaterials: mechanical design, theoretical prediction, and experimental verification

Metamaterials with tunable thermal–mechanical properties offer advantages in maintaining dimensional stability under thermal shocks. Previous studies relied on empirical finite element analyses (FEA) and simplified models, limiting design flexibility to specific directions and causing significant prediction errors for extreme deformations. This paper introduces a universal design methodology and a novel theoretical prediction method to analyze the isotropic, transversely isotropic, and orthotropic thermal–mechanical properties of the heterogeneous polyhedral metamaterial. Through the coordinate transformation of the theoretical model and the accumulation of its thermal–mechanical deformations, the accurate predictions of the coefficient of thermal expansion, specific compression modulus, and specific shear modulus along X-, Y-, Z- directions of representative polyhedral metamaterials are realized simultaneously. The fixed support incorporating the Timoshenko beam model to account for shear deformations during the construction of the mechanical model, more consistent with the actual boundary conditions but weaker assumption, leverages the significant agreements between the theoretical results, FEAs, and experiments in predicting thermal–mechanical performances of polyhedral metamaterials. Furthermore, the design principles for complex 3D metamaterials with isotropic, transverse isotropic, and orthotropic thermal–mechanical properties are presented, highlighting the advantages of our method in achieving the targeted thermal–mechanical properties along the X-, Y-, and Z-directions of complex 3D metamaterials.