Structure-dependent mechanical properties of self-folded two-dimensional nanomaterials.

The design of self-folded two-dimensional nanomaterials (SF-2DNMs) has been proposed to greatly enhance the ductility of two-dimensional material assemblies. However, the dependences of the mechanical properties of SF-2DNMs on the folded geometries have not been fully clarified. In this paper, we develop a theoretical model to describe the mechanical properties of SF-2DNMs based on the shear-lag analysis. With this model, the load transfer behaviors in SF-2DNMs are demonstrated. The Young's modulus and tensile strength of SF-2DNMs are found to increase and then converge with the fold length, which agree well with the results of molecular dynamics simulations. Moreover, the phase diagrams of failure modes are obtained for SF-2DNMs and their stacked assemblies, providing design criteria for the geometries of SF-2DNMs. The structure-property relationship revealed in our study will provide useful guidelines for the structure design and property optimization of SF-2DNMs.