A Multiscale Model to Study the Mechanical Properties of the Graphene, Boron Nitride and Silicon Carbide Hexagonal Nanosheets

Abstract

Background: It is very important to precisely comprehend nanosheet’s mechanical properties for their future application, and the continuum-based methods play a vital role in this research domain. But, most of continuum models doesn’t provide a systematical theory, and just display certain property of nanostructures. The Cauchy-Born rule provides an alternative multiscale method, the resulted model is not only less accurate, and but also doesn’t describe the bending effect. Methods: A nanosheet is viewed as a higher-order gradient continuum planar sheet, and the strain energy density is thus a function of both the first- and second-order deformation gradient. The higher- order Cauchy-Born rule is used to approximate the bond vectors in the representative cell, the multiscale model is established by minimizing the cell energy, and the structural and mechanical properties are thus obtained. Results: The obtained bond lengths are respectively 0.14507 nm, 0.14489 nm, 0.1816 nm for the graphene, boron nitride and silicon carbide hexagonal nanosheets. The elastic constants, including Young’s modulus, shear modulus, Poisson’s ratio and bending rigidity, are calculated by analyzing the physical meaning of the first- and second-order strain gradients. The developed model can also be used to study the nonlinear behavior of nanosheets under some simple loading situations, such as the uniform tension, torsion and bending. The stress-strain relationship of nanosheets is presented for the uniform tension/compression, and the three types of nannosheets exhibit better compressive resistance far greater than tensile resistance. Conclusion: A reasonable multiscale model is established for the nanosheets by using the higherorder Cauchy-Born rule that provides a good interlinking between the microscale and continuum descriptions. It is proved that all three types of nannosheets shows the isotropic mechanical property. The current model can be used to establish a global nonlinear numerical modeling method in which the bending rigidity is the basic elastic constants same as the elastic modulus and Poisson’s ratio.