Symmetry constraints on the orientation dependence of high-order elastic constants for the hexagonal boron nitride monolayer.

Group theory is a powerful tool to explore fundamental symmetry constraints for the physical properties of crystal structures, e.g. it is well-known that only a few components of the elastic constants are independent due to the symmetry constraint. This work further applies group theory to derive constraint relationships for high-order elastic constants with respect to the orientation angle, where the constraint relationships are more explicit than the traditional tensor transformation law. These analytic symmetry constraints are adopted to explain the molecular dynamics simulation results, which disclose that the high-order elastic constants are highly anisotropic with an anisotropy percentage of up to 25% for the hexagonal boron nitride monolayer. The elastic constant is a basic quantity in the mechanics field, so its high anisotropy shall cause strong anisotropy for other mechanical properties. Based on the anisotropic high-order elastic constants, we demonstrate that Poisson's ratio is highly anisotropic for the hexagonal boron nitride at large strains. These findings provide fundamental insights into the symmetry dependence of high-order elastic constants and other mechanical properties.

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.