Nonlinear softening and hardening nonlocal bending stiffness of an initially curved monolayer graphene

Highlight
• A study is presented for evaluating the nonlinear bending stiffness of rippled graphene.
• It is assumed that the material properties of graphene vary based on the chiral angle.
• The effect of initial curvature on the bending stiffness of the monolayer graphene is discussed.

In the present article, the governing nonlinear nonlocal elastic equations are obtained for a monolayer graphene with an initial curvature and the related softening and hardening bending stiffness is analytically calculated. The effects of large deformation, initial curvature, discreteness and direction of chiral vector on the bending stiffness of the monolayer graphene are discussed in detail. A behavior more complex than previously reported in the literature emerges. It is found that the bending stiffness of graphene strongly depends on the initial configuration, showing not obvious maxima and minima, and suggesting the possibility of a smart tuning.