LAUSR

Understanding the deformability, flexibility, and bending mechanics of two-dimensional (2D) materials is critical for the realization of next-generation deformable electronics and nanomechanical devices. While the mechanics of few-layer graphene have been studied for more than a decade, there is still no consensus on its bending stiffness and how it scales with thickness [1-3]. Conventional measurements from mechanical resonance and nanoindentation [4] are challenging because out-of-plane deformations and pre-tension strongly impact the extraction of bending stiffness. Electron microscopy provides a powerful platform for addressing this challenge by enabling measurements of the conformation and strain of 2D materials at atomic resolution. Using aberration-corrected STEM at 80 kV, below the knock-on damage threshold of graphene [5], we investigate the bending mechanics of few-layer graphene. Using low voltages and dose rates, we probe the graphene on the atomic scale while minimizing electron beam damage in order to measure the equilibrium conformation of highly curved 2D materials. Using a combination of STEM, scanning convergent beam diffraction, geometric phase analysis, and density functional theory (DFT) we show that the bending of few-layer graphene is dominated by slip and shear rather than in-plane strain. As a result, few-layer graphene exhibits unusual, curvature-dependent mechanics that can dramatically tune its bending stiffness; for example, the stiffness of trilayer graphene changes by almost 300% when it is curved from 6 to 50 degrees.