Effective Elastic Properties And Mechanical Behavior Of Bilayer Graphene Sheets

Graphene is a member of carbon family. It is an allotrope of carbonwhose structure is a single planar sheet of sp2-bonded carbon atoms thatare densely packed in a honeycomb crystal lattice. It was first found byNovoselov et al. in2004. Due to its nano-size and special structure,graphene has exceptional thermal, electrical and mechanical properties. Ithas a wide application in nano-engineering and nano-composites, whichask for the profound study.In this paper, we study bilayer graphene sheets (BLGSs). Themolecular dynamics (MD) method and non-local elasticity theory are usedin the study. In the MD simulations, BLGSs are considered as a congeriesof individual atoms, the movement equations are established for everyatom, and the deformation behavior of BLGSs can be determined by thetrajectories of each atom. The non-local elasticity theory is the expansionand development of classical continuum mechanics, and it can account forsmall-scale effect of nanostructure.We first use MD method to simulate the deformation behavior ofsingle layer graphene sheets (SLGSs) under different loads andtemperature. Using the continuum mechanics of thin plate under lagerdeflection with the non-local elasticity theory, we can get the effectivethickness and elastic modulus.We consider BLGSs as a nonlocal orthotropic double-layer platewhich contains van der Waals interaction between layers. By the non-localelasticity theory, we can establish equations of BLGSs’ nonlinear bendingand motion. These equations can be solved by using the perturbationmethod. Simulating the nonlinear bending and vibration of BLGSs by MD method, we can get the deflections and nature frequencies. Matching theMD simulation results with the numerical results obtained from thenonlocal plate model, the small scale parameter can be determined.In this paper we can find that the effective thickness and elasticmodulus of SLGSs are size-depedent and temperature-depedent. Also thenonlinear bending and vibration of BLGSs are size-depedent andtemperature-depedent, and effected by the stacking sequence. In addition,we get the small scale parameter which provides theoretical basis forapplications of continuum elastic theory to nano-scale structures.