Theory and Application of the Mechanics of Graphene Sheets

Abstract: Starting from an atomistic approach, I derive a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. It is shown that graphene sheets with clamped edges have an intrinsic nonlinear mechanical response due to a variable tension induced by stretching. The elasticity theory quantitatively agrees with molecular dynamics simulations and experimental data on graphene resonators. The dynamics of graphene sheets is investigated by means of a modal decomposition. In this approach, the vibrational modes are described by a system of coupled Duffing oscillators where the nonlinear coupling terms are of cubic order. A single-particle mass spectrometry scheme is developed based on the dynamical features of interacting modes in the nonlinear regime. It is shown that simultaneous determination of the mass and position of an added particle is possible. Moreover, in this scheme only measurements in a narrow band centered at the fundamental mode resonance frequency are needed. This avoids the need for measurements at different frequencies and makes possible the realization of on-chip single-particle mass spectrometry.