Indentation response of freestanding two-dimensional materials with an adhesive boundary condition

Abstract

An apparent paradox is found in freestanding (FS) indentation tests of 2D materials: Although the assumption of pre-stretched 2D materials with a clamped condition in FS indentation tests is contradicted with both numerical and experimental observations, the measured relationships between the indentation load and indentation displacement agree very well with the existing indentation model of a clamped, pre-stretched FS membrane. Here, we perform theoretical and finite element analyses to address this apparent paradox, and show that the conventional assumption of a clamped boundary condition in existing models of such tests can induce significant errors and should be replaced with an adhesive boundary condition in which the 2D material can be partially detached from the substrate. A new model that accounts for the adhesive boundary condition is developed and shown capable of describing the indentation response of FS 2D materials. Finally, a tentative approach is proposed on the basis of the new model to effectively obtain the Young’s moduli of 2D materials from their FS indentation response.

Publication
under review