Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

Abstract

Computationally efficient multiscale modelling based on Cauchy–Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green–Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy–Born rule. The atomic interactions between carbon atoms are modelled through Tersoff–Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton–Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.