Nonlinear dynamic response of single layer graphene sheets using multiscale modelling

• Computationally efficient multiscale finite element model is employed for the nonlinear dynamic response of graphene sheet.
• Equations of motion are solved using Newmark’s time integration and shooting technique for steady state frequency response.
• Effects of material and geometric nonlinearities, size, boundary conditions, and damping on the response are investigated.
• Hardening response with the dominant effect of geometric nonlinearity compared to material nonlinearity.

In this paper, computationally efficient multiscale modelling considering material and geometric nonlinearities is employed for the first time to investigate the dynamic response of single layer graphene sheets under harmonic excitation. The constitutive relation at continuum level is derived from a strain energy density function as Tersoff–Brenner atomic interaction potential per unit area of a unit cell through Cauchy–Born rule. The governing equation of motion obtained using Hamilton's principle is solved using Newmark's direct time integration and shooting techniques to obtain steady state periodic response. The effects of material and geometric nonlinearities, size of the graphene sheet, boundary conditions, damping and loading parameters on the natural frequencies/response characteristics are investigated. The dynamic response depicts hardening nonlinearity with the dominant effect of geometric nonlinearity compared to material nonlinearity.