A comprehensive lattice-stability limit surface for graphene

Abstract

The limits of reversible deformation in graphene under various loadings are examined using lattice-dynamical stability analysis. This information is then used to construct a comprehensive lattice-stability limit surface for graphene, which provides an analytical description of incipient lattice instabilities of all kinds, for arbitrary deformations, parametrized in terms of symmetry-invariants of strain/stress. Symmetry-invariants allow obtaining an accurate parametrization with a minimal number of coefficients. Based on this limit surface, we deduce a general continuum criterion for the onset of all kinds of lattice-stabilities in graphene: an instability appears when the magnitude of the deviatoric strain γ reaches a critical value γc which depends upon the mean normal strain E¯ and the directionality θ of the principal deviatoric stretch with respect to reference lattice orientation. We also distinguish between the distinct regions of the limit surface that correspond to fundamentally different mechanisms of lattice instabilities in graphene, such as structural versus material instabilities, and long-wave (elastic) versus short-wave instabilities. Utility of this limit surface is demonstrated in assessment of incipient failures in defect-free graphene via its implementation in a continuum finite elements analysis (FEA). The resulting scheme enables on-the-fly assessments of not only the macroscopic conditions (e.g., load and deflection) but also the microscopic conditions (e.g., local stress/strain, spatial location, temporal proximity, and nature of incipient lattice instability) at which an instability occurs in a defect-free graphene sheet subjected to an arbitrary loading condition.