Numerical study on sequential period-doubling bifurcations of graphene wrinkles on a soft substrate

A compressed stiff film on a soft substrate may exhibit wrinkles and, under increased compressive strain, post-buckling instabilities as well. We numerically analyze wrinkling behaviors of graphene attached on a polydimethylsiloxane (PDMS) substrate under lateral compression. The finite element method is used to simulate the equilibrium shape of the wrinkles as a function of compressive strain. Two-dimensional stretching and bending properties of graphene are obtained by density functional theory analysis, which are then converted to equivalent elastic properties of a continuum film with finite effective thickness. The PDMS is described using an Ogden or a neo-Hookean material model. Wrinkles first appear at extremely small strain. As the lateral compression increases, due to the nonlinear elasticity of the PDMS, sequential period-doubling bifurcations of the wrinkle mode are activated until the bifurcation stops and the film folds. We show that the bifurcations are consequences of a delicate balance between the deformations of the film and the substrate to minimize the total energy.