Bulging and Poking of 2D Materials

Bulging and poking of thin films are widely used mechanical tests. They became particularly popular for characterizing atomically thin 2D materials, together with spontaneously formed nano-bubbles and nano-tents. This is because they are able to induce in-plane strains in 2D materials via easy-to-apply out-of-plane deformations. We measure their profiles through atomic force microscopy (AFM) and adopt the membrane limit of the Föppl-von Kármán (FvK) theory to unveil what sets the in-plane strains in terms of their shape characteristics and boundary conditions. 2D materials are sensitive to elasto-capillarity, which can be leveraged to quickly estimate 2D-material-to-substrate work of adhesion through the profiles of spontaneously formed nano-bubbles. Through a parent-satellite bubble system, we are able to determine the transition from membrane theory to plate theory and from Griffith-type interface to cohesive-zone-type interface formed with the supporting substrate. With coarse-grained molecular dynamics (CGMD) simulations, we can reveal when continuum mechanics ultimately breaks down. Moreover, we find that recent indentation results on suspended 2D materials do not follow the well-known load-cubic-deflection relation that is widely accepted for linear elastic sheets, which can be attributed to the slippage of atomically smooth 2D materials against their supporting substrates. We identify a single dimensionless governing parameter—the sliding number—defined by comparing the sheet tension (that drives the slippage) with the interfacial traction (that resists the slippage). I will showcase several useful asymptotic behaviors emerging at small and large sliding numbers.