Mechanical anisotropy of two-dimensional metamaterials: a computational study

Metamaterials, rationally designed multiscale composite systems, have attracted extensive interest because of their potential for a broad range of applications due to their unique properties such as negative Poisson's ratio, exceptional mechanical performance, tunable photonic and phononic properties, structural reconfiguration, etc. Though they are dominated by an auxetic structure, the constituents of metamaterials also play an indispensable role in determining their unprecedented properties. In this vein, 2D materials such as graphene, silicene, and phosphorene with superior structural tunability are ideal candidates for constituents of metamaterials. However, the nanostructure-property relationship and composition-property relationship of these 2D material-based metamaterials remain largely unexplored. Mechanical anisotropy inherited from the 2D material constituents, for example, may substantially impact the physical stability and robustness of the corresponding metamaterial systems. Herein, classical molecular dynamics simulations are performed using a generic coarse-grained model to explore the deformation mechanism of these 2D material-based metamaterials with sinusoidally curved ligaments and the effect of mechanical anisotropy on mechanical properties, especially the negative Poisson's ratio. The results indicate that deformation under axial tensile load can be divided into two stages: bending-dominated and stretching-dominated, in which the rotation of junctions in the former stage results in auxetic behavior of the proposed metamaterials. In addition, the auxetic behavior depends heavily on both the amplitude/wavelength ratio of the sinusoidal ligament and the stiffness ratio between axial and transverse directions. The magnitude of negative Poisson's ratio increases from 0 to 0.625, with an associated increase of the amplitude/wavelength ratio from 0 to 0.225, and fluctuates at around 0.625, in good agreement with the literature, with amplitude/wavelength ratios greater than 0.225. More interestingly, the magnitude of negative Poisson's ratio increases from 0.47 to 0.87 with the increase of the stiffness ratio from 0.125 to 8, in good agreement with additional all-atom molecular dynamics simulations for phosphorene and molybdenum disulfide. Overall, these research findings shed light on the deformation mechanism of auxetic metamaterials, providing useful guidelines for designing auxetic 2D lattice structures made of 2D materials that can display a tunable negative Poisson's ratio.