Anisotropic thermal expansion based on a novel metamaterial

Abstract

Metamaterials exhibiting exceptional thermoelastic properties are emerging as promising candidates for scientific and engineering applications. Previous studies on mechanical metamaterials with negative thermal expansion (NTE) have primarily focused on enhancing isotropic NTE, often resulting in a high coefficient of thermal expansion (CTE) but low stiffness that characterizes bending-dominated NTE metamaterials. In this study, we proposed a novel mechanical metamaterial with significant anisotropic thermal expansion behavior and substantial stiffness based on the cross structure, re-entrant structure, and triangular structure with NTE. The programmable CTE and effective elastic modulus were analytically derived using the unit load method and stiffness matrix method, respectively, which were validated by numerical results obtained from finite element analysis (FEA). Drawing inspiration from the body-centered cubic and face-centered cubic strategies, two types of extended three-dimensional metamaterials can be obtained. The results demonstrate that a larger length ratio λ and angle θ3 can enhance the NTE effect, while reducing the Young's modulus. The maximum magnitudes of NTE and positive thermal expansion (PTE) are achieved at approximately θ2 = 90°, resulting in a decreased stiffness and slight negative Poisson's ratio (NPR). By adjusting the angles θ2 of re-entrant structures, six distinct anisotropic thermal expansion behaviors can be obtained in this planar metamaterial. Furthermore, a wider range of isotropic CTE as well as an extended range of anisotropic CTE can be achieved in the present metamaterial compared to its original metamaterials. The proposed metamaterial can be combined with traditional triangle metamaterials to enhance thermoelastic properties. The analysis also provides valuable insights into designing metamaterials with large CTE, optimal stiffness, and lightweight properties simultaneously for engineering applications.