The formation of wrinkles in single-layer graphene sheets under nanoindentation.

We investigate the formation of wrinkles and bulging in single-layer graphene sheets using an equivalent atomistic continuum nonlinear hyperelastic theory for nanoindentation and nanopressurization. We show that nonlinear geometrical effects play a key role in the development of wrinkles. Without abandoning the classical tension field membrane theory, we develop an enhanced model based upon the minimization of a relaxed energy functional in conjunction with nonlinear finite hyperelasticity. Formation of wrinkles are observed in rectangular graphene sheets due to the combination of induced membrane tension and edge effects under external pressure.