Study On Mechanical Properties Of Carbon Nanotubes/Graphene Reinforced Composites

In this paper,the nonlocal Timoshenko theory of plane beam element is deduced based on the Timoshenko theory and nonlocal theory.It can be applied to the calculation of mechanical properties of carbon nanotubes,graphene sheet and its reinforced composites.The nonlocal theory is introduced into the Hamilton equation of beam,and the motion differential equation is derived by combining the strain displacement relation of Timoshenko beam.The stiffness matrix and mass matrix extracted from this equation will be written as a program for subsequent finite element calculations.Nonlocal parameter in nonlocal theory is the key parameter which is different from the stress-strain relationship in classical mechanics theory.This parameter links the stress of one node to the strain of its adjacent nodes.When the nonlocal parameter is zero,the nonlocal theory will degenerate into the classical mechanics theory.This paper use ABAQUS finite element software,Visual Studio and Intel Visual Fortran to establish a simulation platform,introducing the nonlocal theory by external subroutine:User Defined Element.The feasibility and accuracy are verified by operation verification,unit verification and example verification.Then,in order to test the capacity of computing and assembling the stiffness matrix of complex model,the mechanical properties and dynamic characteristics were calculated and verified by establishing a finite element model of graphene sheet and carbon nanotubes,including the Young's modulus of grapheme sheet,Young's modulus and vibration characteristic of carbon nanotubes are calculated.The effect of tube diameter and nonlocal parameter on Young's modulus and vibration characteristics of carbon nanotubes were investigated.For the propose of studying the mechanical properties of carbon nanotubes/graphene sheet reinforced composites,multi-scale models containing macroscopic and microscopic features are established.In this model,the matrix is modeled as conventional solid elements,graphene sheet and carbon nanotubes are modeled as nonlocal Timoshenko beam element.In addition,based on the double layer graphene sheet structure and the bonding principle of Van der Waals' force,the microscopic connection between matrix and reinforced phase is studied,and the properties of nonlinear spring element are given by INP file.Finally,modal analysis of multi-scale finite element model of composite material after meshing is carried out.