Nonlinear elastic behavior of two-dimensional molybdenum disulfide

This research explores the nonlinear elastic properties of two-dimensional molybdenum disulfide. We derive a thermodynamically rigorous nonlinear elastic constitutive equation and then calculate the nonlinear elastic response of two-dimensional MoS${}_{2}$ with first-principles density functional theory (DFT) calculations. The nonlinear elastic properties are used to predict the behavior of suspended monolayer MoS${}_{2}$ subjected to a spherical indenter load at finite strains in a multiple-length-scale finite element analysis model. The model is validated experimentally by indenting suspended circular MoS${}_{2}$ membranes with an atomic force microscope. We find that the two-dimensional Young's modulus and intrinsic strength of monolayer MoS${}_{2}$ are 130 and 16.5 N/m, respectively. The results approach Griffith's predicted intrinsic strength limit of ${\ensuremath{\sigma}}_{\mathrm{int}}\ensuremath{\sim}\frac{E}{9}$, where $E$ is the Young's modulus. This study reveals the predictive power of first-principles density functional theory in the derivation of nonlinear elastic properties of two-dimensional MoS${}_{2}$. Furthermore, the study bridges three main gaps that hinder understanding of material properties: DFT to finite element analysis, experimental results to DFT, and the nanoscale to the microscale. In bridging these three gaps, the experimental results validate the DFT calculations and the multiscale constitutive model.