A continuum model for the static pull-in behavior of graphene nanoribbon electrostatic actuators with interlayer shear and surface energy effects

Based on multi-beam shear model theory, a continuum mechanics model is developed to investigate the pull-in instability of wedged/curved multilayer graphene nanoribbon (MLGNR) cantilever nanobeams subjected to electrostatic and Casimir forces. The first-order fringing-field correction, the interlayer shear between neighboring graphene nanoribbons (GNRs), surface elasticity, and residual surface tension are incorporated into the analytical model. An explicit closed-form analytical solution to the governing fourth-order nonlinear differential equation of variable coefficients is introduced for the static pull-in behavior of electrostatic nanoactuators using a Fredholm integral equation of the first kind. A comparison study for a [001] silver electrostatic nanoactuator indicates that the proposed analytical closed-form solution yields an improved accuracy over other analytical and numerical methods existing in literature. The results indicate that the interfacial slip between GNRs and the surface material parameters play a significant role in static pull-in behavior of MLGNR electrostatic nanoactuators. From the experimental data and atomistic simulations available in the literature, the value of interlayer shear modulus at the graphene/graphene interface is estimated to be in the order of magnitude of 10−1 GPa. The continuum model proposed in this study will be helpful for characterizing the mechanical properties of GNRs and the design of graphene-based nanoelectromechanical system devices.