Metamaterials with remarkable thermal–mechanical stability and high specific modulus: Mechanical designs, theoretical predictions and experimental demonstrations

In the fields of aerospace, flexible electronics, intelligent manufacturing, and MEMS, the mechanical metamaterials with remarkable zero thermal expansion of coefficient (CTE) are of increasing interest due to their advantages in maintaining their original shapes upon a temperature change. Though recently published researches have demonstrated several designs in achieving a desirable CTE, it is still very challenging to develop the mechanical metamaterial with high-level thermal–mechanical stability (i.e., CTE < 0.5 ppm/°C). Additionally, most of these studies only focused on obtaining a remarkable zero CTE through optimizing the geometrical parameters, and did not provide enough performances in consideration of their mechanical behaviors (e.g., lightweight, high specific modulus), imposing certain limitations on their operation in devices that require combined thermal–mechanical attributes. This paper demonstrates a mechanical metamaterial design concept with lightweight, high specific modulus properties and high-level thermal–mechanical stability. Each of the unit cell in our designs composed of two or four bilayer beams filled by hourglass lattices in Al and Ti materials offers a tunable CTE from negative to positive, revealing its capability to offer remarkable zero CTE. A theoretical model that preciously predicts the design's thermal and mechanical performances provides a clear understanding of the effects of geometric parameters on their corresponding effective properties, facilitating the design of metamaterials with desired mechanical and thermal expansion performances. Excellent agreements between theoretical predictions, FEAs, and experiments demonstrate the advantages of our design in achieving the combined attributes of lightweight (i.e., relative density ρ¯_Uniaxial < 0.123 for the design with uniaxial thermal–mechanical stability and ρ¯_Biaxial < 0.069 for the one with biaxial thermal–mechanical stability), high specific modulus (i.e., 1104 kN⋅ mm/kg and 1203 kN⋅ mm/kg for the designs with uniaxial and biaxial thermal–mechanical stability), and a remarkable zero CTE (α_effective < 0.32 ppm/°C). Ashby plot of the effective CTE with respect to density, serving as an especially useful tool in selecting materials according to the requirements of practical applications, provides quantitative evidences for our design's outstanding thermal–mechanical performances as compared to the previously reported studies.