Studies On Mechanical Properties Of Singlewalled Carbon Nanotubes Based On The Nonlinear Constitutive Model

With the development of nanomechanics,the studies of mechanical properties of carbon nanotubes(CNTs)have gradually become a hot topic in recent years.Recent experiments have shown that the stress-strain relationship of graphene is nonlinear under finite deformations.Theoretically,the stress-strain relation of single-walled carbon nanotubes(SWCNTs)with big tube diameters are consistent with that of graphene because the SWCNTs are formed by rolling graphene.So far,the effect of the nonlinear constitutive model has not been used to research the mechanical properties of CNTs.In the practical application of CNTs,it is often difficult to avoid the influence of external factors,which may lead to an initial deformation of CNTs.Small deformation will have some unknown effects on the structure of CNTs,which cannot be ignored.In this paper,based on the nonlinear constitutive relationship of graphene,a new Bernoulli-Euler beam model of SWCNTs considering the nonlinear constitutive relationship and initial deformation is established.Then,the static bending and forced vibrations of SWCNTs are studied by Galerkin method and multi-scale method for the case of a hinged-hinged beam under uniformly distributed loads.For SWCNTs without initial deformation.(1)The nonlinear terms in the nonlinear constitutive soften the stiffness of the system in the case of static bending,and this effect will become more obvious with the increase of external load.(2)The nonlinear terms in the nonlinear constitutive can change the position of the amplitude bifurcation points in the case of forced vibration.For SWCNTs with initial deformation.(1)The initial deformation is consistent with the direction of external load in the case of static bending,which increases the stiffness of the system.The initial deformation is opposite to the direction of the external load,which makes the static deformation of carbon nanotubes becomes complicated.(2)The initial deformation changes the mechanical properties of SWCNTs from hard nonlinearity to soft nonlinearity in the case of forced vibration.