Modulating mechanical anisotropy of two-dimensional materials by controlling their defects

Most two-dimensional (2D) materials (such as graphene and black phosphorus (BP)) exhibit the strong anisotropy in their nonlinear mechanical properties. However, it is still a tremendous challenge to modulate their anisotropy for some special applications. In this study, the mechanical anisotropy of graphene and BP can be regulated by controlling their defects (such as circular holes, elliptic holes and cracks) using molecular dynamics simulations, which is reasonable by comparison with available continuum models. For circular-hole defects, the isotropic ratios (λ) of fracture stresses and strains in both graphene and BP are lower than 0.4 when D/L ≥ 0.2 (D and L are the diameter of the circular hole and the boundary length of 2D materials, respectively.), where λ = 0 and λ = 1 represent the complete isotropy and the original anisotropy without defects, respectively. For elliptic-hole and crack defects, λ in both graphene and BP can be close to zero by controlling their sizes and oblique angles. In particular, modulating mechanical anisotropy of 2D materials is further proven by measuring the nonlinear mechanical properties of open-hole paper napkins. This study should be of great help for providing physical insights into the origins of defect-control isotropy of 2D materials.