Three-dimensional metamaterials with a negative Poisson's ratio and a non-positive coefficient of thermal expansion

Four types of three-dimensional (3-D) metallic metamaterials with tailorable thermo-mechanical properties are designed. For the first three types, the structure-property relations are studied by adjusting design parameters including two length parameters, one angle parameter and two material combinations. For the fourth type, one additional angle parameter is involved. It is shown that each of the four types of metamaterials designed exhibits the cubic symmetry and thus needs three independent elastic constants to characterize its elastic behavior and one coefficient of thermal expansion to describe its isotropic thermal expansion. The effects of the design parameters on the effective Poisson's ratio (PR), coefficient of thermal expansion (CTE), Young's modulus, shear modulus and the relative density are systematically investigated for each of the four types of designed metamaterials by using unit cell-based finite element simulations that incorporate periodic boundary conditions. It is found that 3-D metallic metamaterials with positive, near-zero or negative PR and CTE can be obtained by tailoring the bi-material lattice structures and material combinations. Also, it is revealed that metamaterial # 1 can achieve both a negative PR and a non-positive CTE while maintaining a high stiffness and a low relative density (and thus a lightweight). The good tunability of thermo-mechanical properties of the four types of metamaterials provides an avenue of enabling the expansion of Ashby's material chart to produce more material options for engineering applications.