Hidden area and mechanical nonlinearities in freestanding graphene

TL;DR

This study explores how out-of-plane crumpling affects the mechanical behavior of freestanding graphene, revealing nonlinear responses linked to hidden crumpled areas.

Contribution

It introduces a method to quantify crumpling in graphene and demonstrates its impact on mechanical response, including nonlinear elasticity.

Findings

Graphene with zero hidden area exhibits linear elasticity.

Crumpled graphene shows anomalous nonlinear Hooke's law behavior.

Quantification of hidden area correlates with mechanical response.

Abstract

We investigated the effect of out-of-plane crumpling on the mechanical response of graphene membranes. In our experiments, stress was applied to graphene membranes using pressurized gas while the strain state was monitored through two complementary techniques: interferometric profilometry and Raman spectroscopy. By comparing the data obtained through these two techniques, we determined the geometric hidden area which quantifies the crumpling strength. While the devices with hidden area $\sim0~\%$ obeyed linear mechanics with biaxial stiffness $428\pm10$ N/m, specimens with hidden area in the range $0.5-1.0~\%$ were found to obey an anomalous Hooke's law with an exponent $\sim0.1$.