Out-of-plane deformation patterns, such as buckling, wrinkling, scrolling, and folding, formed by multilayer van der Waals materials have recently seen a surge of interest. One crucial parameter governing these deformations is bending rigidity, on which significant controversy still exists despite extensive research for more than a decade. Here, we report direct measurements of bending rigidity of multilayer graphene, molybdenum disulfide (${\mathrm{MoS}}_2$), and hexagonal boron nitride (hBN) based on pressurized bubbles. By controlling the sample thickness and bubbling deflection, we observe platelike responses of the multilayers and extract both their Young’s modulus and bending rigidity following a nonlinear plate theory. The measured Young’s moduli show good agreement with those reported in the literature ($E_{\text{graphene}}>E_{\text{hBN}}>E_{{\text{MoS}}_2}$), but the bending rigidity follows an opposite trend, $D_{\text{graphene}}<D_{\text{hBN}}<D_{{\text{MoS}}_2}$ for multilayers with comparable thickness, in contrast to the classical plate theory, which is attributed to the interlayer shear effect in the van der Waals materials.

Monolayer two-dimensional (2D) crystals exhibit a host of intriguing properties, but the most exciting applications may come from stacking them into multilayer structures. Interlayer and interfacial shear interactions could play a crucial role in the performance and reliability of these applications, but little is known about the key parameters controlling shear deformation across the layers and interfaces between 2D materials. Herein, we report the first measurement of the interlayer shear stress of bilayer graphene based on pressurized microscale bubble loading devices. We demonstrate continuous growth of an interlayer shear zone outside the bubble edge and extract an interlayer shear stress of 40 kPa based on a membrane analysis for bilayer graphene bubbles. Meanwhile, a much higher interfacial shear stress of 1.64 MPa was determined for monolayer graphene on a silicon oxide substrate. Our results not only provide insights into the interfacial shear responses of the thinnest structures possible, but also establish an experimental method for characterizing the fundamental interlayer shear properties of the emerging 2D materials for potential applications in multilayer systems.

Nanoblisters such as nanobubbles and nanotents formed by two-dimensional (2D) materials have been extensively exploited for strain engineering purposes as they can produce self-sustained, nonuniform in-plane strains through out-of-plane deformation. However, deterministic measure and control of strain fields in these systems are challenging because of the atomic thinness and unconventional interface behaviors of 2D materials. Here, we experimentally characterize a simple and unified power law for the profiles of a variety of nanobubbles and nanotents formed by 2D materials such as graphene and ${\mathrm{MoS}}_2$ layers. Using membrane theory, we analytically unveil what sets the in-plane strains of these blisters regarding their shape and interface characteristics. Our analytical solutions are validated by Raman spectroscopy measured strain distributions in bulged graphene bubbles supported by strong and weak shear interfaces. We advocate that both the strain magnitudes and distributions can be tuned by 2D material-substrate interface adhesion and friction properties.