Nonlinearity induced negative Poisson's ratio of two-dimensional nanomaterials

Materials exhibiting a negative Poisson's ratio have garnered considerable attention due to the improved toughness, shear resistance, and vibration absorption properties commonly found in auxetic materials. In this work, the nonlinear effect on the Poisson's ratio was derived theoretically and verified by first-principle calculations and molecular dynamics simulations of two-dimensional nanomaterials including graphene and hexagonal boron nitride. The analytic formula explicitly shows that the Poisson's ratio depends on the applied strain and can be negative for large applied strains, owing to the nonlinear interaction. Both first-principle calculations and molecular dynamics simulations show that the nonlinear effect is highly anisotropic for graphene, where the nonlinearity-induced negative Poisson's ratio is much stronger for the strain applied along the armchair direction. These findings provide valuable insights into the behavior of materials with negative Poisson's ratios and emphasize the importance of considering nonlinear effects in the study of the Poisson's ratio of two-dimensional materials.