| Carbon nanomaterials(CNMs),with outstanding physical properties and chemical properties,are widely used in civil engineering,aerospace engineering,machinery manufacturing and biomedical fields.The research on mechanical properties is of great significance to the marketing of CNMs.At the nanometer scale,the dispersion of the results obtained by existing experimental methods is great,and the theoretical solution method of mechanical parameters is still lacking.Therefore,numerical method is one of the effective ways to study the mechanical properties of CNMs.Many scholars replaced the molecular structure of CNMs with the equivalent rigid-node frame model to calculate the elastic properties of CNMs and good results have been obtained.However,the rigid-node bar can’t generate bending angle at the end,and it fail to perfectly reflect the change of covalent bond angle in the molecular structure that leads to significant error between the computational results and the real situation.In order to optimize the numerical model and improve the numerical accuracy,the finite element model of semi-rigid-node bar is proposed in this paper.By equating the covalent bond to the circular crosssection bar element whose ends are connected to generalized springs,the bar,when subjected to the bending moment,appears a bending angle at the ends,which better expresses the change of the bond angle under different load conditions.Firstly,the stiffness matrix of the semi-rigid-node element is derived by the finite element method.Based on the theory of molecular mechanics,the bond energy generated by the elongation of the covalent bond,the change of bond angle and the dihedral angle torsion in the carbon atom system are respectively equivalent to the strain energy generated by the bar in the process of stretching,bending and torsion,so as to determine the mechanical parameters of bar by using the constants of molecular mechanics.Secondly,using the secondary development function of Abaqus,we compile Subroutine UEL of semi-rigid-node bar and practice finite element modeling of CNMs.For ideal and atom-missing CNMs,we calculat the Young’s modulus and Poisson’s ratio of graphene and carbon nanotubes by applying uniaxial normal strain.The shear modulus of graphene is calculated by applying transverse strain.The shear modulus of carbon nanotubes are measured by applying a certain torque.Finally,we,comparing with experimental values given in references,determine the value of semi-rigid coefficient that most conforms to the real model,and the semi-rigid-node bar system is closer to the molecular structure of CNMs.The results show that the mechanical properties of single-layer graphene sheet(SLGS)and single-walled carbon nanotube(SWCNT)are similar.Their Young’s modulus is above 1.0TPa,poisson’s ratio is about 0.08,and their shear modulus is up to 400GPa.However,CNMs are highly susceptible to size effects.The increase of the boundary length will enhance the mechanical properties of SLGS.Similarly,the increase of length and diameter will enlarge the mechanical properties of SWCNTs.Although the size effect has little effect on the models whose size is large,it is very significant for the models with little difference between boundary size and covalent bond length.As there are defects in the material itself,the degree weakening of Young’s modulus and shear modulus,which depends on the missing position of carbon atoms or the direction of cracks,is from 15 to 150GPa.The nodal stiffness of element,with the decrease of semirigid coefficient,will weaken correspondingly,and the decrease of Young’s modulus and shear modulus will be more drastic.According to this rule,we modified the numerical accuracy by adjusting the semi-rigidity of the model,and the computational results of mechanical properties were closer to the experimental values.Therefore,the finite element simulation of CNMs with semi-rigid-node bar system would become more feasible and reasonable. |
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