Systematic Exploration on the Effective Mechanical Properties of Three-Dimensional Chiral Auxetic Mechanical Metamaterials

Chiral mechanical metamaterials have unusual mechanical and physical properties due to the chiral geometry, for example, chirality-induced auxeticity and normal-twisting coupling. In order to fully understand the deformation mechanisms of chiral mechanical metamaterials, we need to systematically explore the structural-property relationships of them and quantify their effective mechanical properties. To meet this need, a family of two-phase three-dimensional periodic chiral mechanical metamaterials are designed. Based on a monoclinic anisotropic model, an integrated numerical-analytical method is developed to model the constitutive behavior of chiral mechanical metamaterials. The effective mechanical properties of them, including effective stiffness in three different directions, the effective Poisson’s ratios, and the coupling coefficients are numerically evaluated. Our results show that the addition of the second phase can significantly increase the effective stiffness of chiral mechanical metamaterials and decrease the overall auxeticity and the chirality-induced twist under normal loadings. By jointly tailoring the chiral geometry and material combination, the effective mechanical properties and the deformation mechanisms can be effectively tuned in a large range.