  Due to their atomic-scale thickness, the resonances of 2D material membranes
show signatures of nonlinearities at amplitudes of only a few nanometers. While
the linear dynamics of membranes is well understood, the exact relation between
the nonlinear response and the resonator's material properties has remained
elusive. In this work, we propose a method to determine the Young's modulus of
suspended 2D material membranes from their nonlinear dynamic response. The
method is demonstrated by interferometric measurements on graphene and MoS2
resonators, which are electrostatically driven into the nonlinear regime at
multiple driving forces. It is shown that a set of response curves can be
fitted by the solutions of the Duffing equation using only one fit parameter,
from which the Young's modulus is extracted using membrane theory. Our method
is fast, contactless, and provides a platform for high-frequency
characterization of the mechanical properties of 2D materials.
