A modified direct measurement of shear moduli of two-dimensional materials

Abstract

A direct measurement of shear moduli of two-dimensional (2D) materials is still a challenge in experiments. A commonly used method is to apply a tangential displacement on one side of a square specimen sheet for each 2D material, while its opposite side is fixed. Afterwards, the shear modulus can be obtained by fitting a linear stage of its total shear stress-strain curve. However, the obtained shear modulus can be defined as the nominal shear modulus which is much lower than that of its true value. The difference between the two shear moduli is independent of the 2D isotropic material and strongly depends on aspect ratios of the specimens. In this work, explicit equations of the nominal shear moduli of 2D materials for different aspect ratios are derived by continuum modeling. The analytical model is then verified by the finite element method and molecular dynamics simulation as well as experiments. It suggests that the true shear moduli of 2D materials can be directly and accurately measured using the specimens with high aspect ratios (≥3.6) in experiments. The present study provides key insights into a direct measurement of shear moduli for 2D materials.