A Study On Mechanical Properties Of Graphene Based On The Finite Element Model Of Semi Rigid Node Frame System

Graphene material is regarded as the most important material in the 21st century.The material is composed of carbon atoms form hexagonal structures according to certain sequence and form a honeycomb lattice of sheet-like carbon nanomaterials.Graphene material have good toughness,thermal conductivity,high hardness,and are widely used in biomedical,aerospace,military defense,communications,machinery,civil engineering and other fields.Because the graphene material is irreplaceable in the application process,once unstable factors occur under the reciprocating load,it will be an indelible disaster,so the study of its mechanical properties is of crucial importance.Based on the molecular structural mechanics theory,the predecessors analogized the carbon-carbon covalent bond to a beam element and considered that the nodes were rigidly connected for the study of the mechanical properties of graphene sheets.Therefore,a rigid node model was proposed and good calculation results were obtained.In this paper,the carbon-carbon covalent bond is regarded as a beam element,and adjacent covalent bonds are connected by springs,and a finite element model of semi-rigid node frame system is proposed.In this model,the spring coefficient k is introduced,including spring bending stiffness k1,tensile stiffness k2,torsional stiffness k3.According to the knowledge of structural mechanics,the space stiffness equation of beam element in the semi-rigid node frame system are deduced.Based on the large-scale finite element commercial software ABAQUS computing platform,the user unit subroutine(UEL)was developed.The finite element modeling of the semi-rigid node frame system is performed.The correctness of the finite element solution is verified by numerical examples.The influencing factors of spring coefficient k are discussed in detail,and the variation of young's modulus of the graphene structure under different influencing factors are analyzed,and the value of the spring coefficient k is determined.Based on the finite element model of semi-rigid node frame system,the young's modulus and buckling stress of graphene structure are calculated and analyzed.The influence of different sizes on the young's modulus of the ideal graphene is discussed.The numerical examples showed that the young's modulus of the ideal graphene has no relation with the size.The influence of the number and location of defect elements on the young's modulus of graphene containing defects is analyzed.As a result,it is found that the larger the number of defective elements,the smaller the young's modulus is.The defects of y direction are more destructive to the graphene structure.The effects of different boundary conditions on the ideal and defect-containing graphene buckling stress are discussed,and numerical examples show that the value of buckling stress is the largest and the structure is relatively stable on the condition of fixed support.