Non-linear elastic moduli of Graphene sheet-reinforced polymer composites

• The linear and non-linear elastic moduli of the Graphene sheet are computed based on the modified Morse potential.
• The Eshelby’s tensor is obtained for a rectangular aspect ratio.
• The non-linear stiffness tensor of the Graphene sheet-reinforced polymer composite is derived using the Mori–Tanaka micro-mechanics scheme.
• The anisotropic degree is analysed for different aspect ratio and mass fractions.

The non-linear elastic moduli of the Graphene sheet-reinforced polymer composite are investigated using a combined molecular mechanics theory and continuum homogenisation tools. Under uni-axial loading, the linear and non-linear constitutive equations of the Graphene sheet are derived from a Taylor series expansion in powers of strains. Based on the modified Morse potential, the elastic moduli and Poisson’s ratio are obtained for the Graphene sheet leading to the derivation of the non-linear stiffness tensor. For homogenisation purpose, the strain concentration tensor is computed by the means of the irreducible decomposition of the Eshelby’s tensor for an arbitrary domain. Therefore, a mathematical expression of the averaged Eshelby’s tensor for a rectangular shape is obtained for the Graphene sheet. Under the Mori–Tanaka micro-mechanics scheme, the effective non-linear behaviour is predicted for various micro-parameters such as the aspect ratio and mass fractions. Numerical results highlight the effect of such micro-parameters on the anisotropic degree of the composite.