Enhanced stiffness characteristic and anisotropic quasi-static compression properties of a negative Poisson’s ratio mechanical metamaterial

The negative Poisson’s ratio (NPR) mechanical metamaterials exhibit excellent mechanical properties, whereas their low stiffness limits the development. In this paper, we investigated an NPR mechanical metamaterial: star-circle honeycomb (SCH), which possesses enhanced stiffness compared to the classical star-shaped honeycomb (SH). Based on the Castigliano’s second theorem and the principle of virtual work, a theoretical model was built to calculate the effective elastic properties of the SCH, and validated by the finite element method (FEM). The comparison with the SH showed that the SCH possessed a significantly enhanced elastic modulus. Also, we find that the elastic properties can be adjusted broadly and tailored to meet the engineering needs by selecting parameters reasonably. Subsequently, the anisotropic quasi-static compression responses of the SCH were studied. The results showed that the plateau stress and energy absorption capacity in the y-direction load were both better than that in the x-direction load. The parameter study indicated that θ and ψ produced a greater impact on the quasi-static responses. A reasonable combination of parameters can give full play to the mechanical properties of the structure. This work provided a new design idea for improving the stiffness and choosing the optimal in-plane loading direction of metamaterials.