The equivalent Young's modulus prediction for vacancy defected graphene under shear stress

Abstract

The uncertain and unavoidable vacancy defects in graphene have the inevitable influence in the extraordinary intrinsic in-plane strength. In this paper, the equivalent Young's modulus is derived from the strain energy as an important factor to evaluate the stiffness of the entire graphene based on the mechanical molecular theory. The location of vacancy defects in graphene is discussed in the regular deterministic and uncertain patterns. In terms of the boundary condition, shear stress is loaded in armchair and zigzag edges, respectively. The results show that the center concentrated vacancy defects evidently deteriorate the elastic stiffness under shear stress. The influences of periodic and regular vacancy defects are sensitive to the boundary condition. By the Monte Carlo based finite element method, vacancy defects are dispersed randomly and propagated. The results of the equivalent Young's modulus are compared with the original values in pristine graphene. The interval and mean values of Young's modulus, total strain and energy density are also provided and discussed. Compared with the results of graphene with vacancy defects under uniaxial tension, the enhancement effects of vacancy defects are less evident in the graphene under shear stress.