End-clamp stress transfer as a mechanism for thickness-dependent Young’s modulus in multilayer graphene

To overcome the limited load-bearing capacity of monolayer graphene in practical devices, utilizing multilayer graphene is essential, which, in turn, requires an accurate evaluation of its mechanical properties. However, the thickness dependence of the effective Young’s modulus in multilayer graphene may arise, at least in part, from incomplete load transfer through weak van der Waals interfaces. In this study, we perform molecular dynamics simulations to replicate microelectromechanical systems (MEMS)-based tensile tests, comparatively analyzing the mechanical responses under two representative gripping conditions: an all-layer grip clamping all layers simultaneously, and a bottom-layer grip relying solely on interfacial adhesion. Our simulations reveal that incomplete interlayer stress transfer at the end-clamps induces strain mismatch, which causes a significant reduction in the effective Young’s modulus (Eeff) as the number of layers increases. Notably, within the simulated results, the stress transfer length remains almost independent of the gauge length, scaling up with the number of layers. Based on these mechanisms, we propose an analytical model capable of predicting Eeff at the microscale. This study provides a potential framework for quantitatively evaluating the interfacial mechanical properties of two-dimensional materials using gauge-length-dependent MEMS tensile tests.