Determination of rigidities, stiffness coefficients and elastic constants of multi-layer graphene sheets by an asymptotic homogenization method

Abstract

This work is concerned with the analysis of bending and torsional rigidities of multi-layer graphene sheets (MLGSs) based on the Kalamkarov’s general asymptotic homogenization composite shell model. Also, the effective stiffness coefficients and elastic constants of MLGSs are estimated with this analytical method. The unit cell with both in-plane and out-of-plane interactions is assumed in this model. A MLGS as a homogeneous honeycomb network sheet with the periodic hexagonal unit cell is considered here in which the layers are held together by different densities of van der Waals interactions. The stiffness coefficients, elastic constants and rigidities of MLGS are found by considering different densities of the van der Waals forces and different number of layers. The results show good agreements in comparison with other experiments and numerical solutions. It is found that the homogenization method gives the ability to create promise analytical approach that can be used for other nanostructures.