Nonlinear elasticity of monolayer hexagonal crystals: Theory and application to circular bulge test

Graphene and graphene-like materials possessing monolayer hexagonal crystals have become one of the focal points of scientific researches. In this paper, an elasticity peculiar to these materials is formulated that is capable of taking both geometrical and material nonlinearities into consideration. A thin plate is proposed as a continuum model for such materials but, after postulating certain assumptions consistent with their physical nature, it is revealed that the thin plate behaves analogous to a membrane with nonzero bending rigidity. By making use of concepts from differential geometry of surfaces, interesting properties related to deformation field of the thin plate are proved. As an application to the proposed theory, the elastic behavior of a circular specimen of a monolayer hexagonal crystal subjected to bulge test is examined and, through a perturbation analysis, a series solution is obtained for its deformation field.