Numerical investigation of the state of stresses in bilayer composites under tensile and shear loading conditions

摘要

The bilayer composites are the fundamental structures of the single walled carbon nanotubes (SWNTs), layered graphene structures, and multi-layered composites. A finite difference numerical method had been used to analyze the stress state at the interface of the bilayer composite. A displacement potential function based method was used for the mathematical modelling of the governing equations, displacements, and stresses. Then a finite difference scheme was used for the discretization of the bi-harmonic governing equation and the associated boundary conditions. Two types of loadings were considered: (a) tensile loading, and (b) shear loading. For each case, the interface stress distribution was obtained. It was found that the interface stresses were highly dependent on the mechanical properties of the individual material. Some important aspects of the interface stress state were revealed. A sudden jump in the stresses had been observed even though the displacements were continuous along the interface. The displacement and stress distributions in the two materials are presented.