New insights into the structure-nonlinear mechanical property relations for graphene allotropes

A vast array of two-dimensional (2D) graphene allotropes have been reported to possess remarkable electronic, thermal, and magnetic properties. However, our understanding of their structure-mechanical-property relationship is far from complete. In this study, we performed extensive density functional theory calculations to evaluate the mechanical properties of 11 different graphene allotropes, comprising structures with solely sp2 hybridized bonds and both sp and sp2 hybridized bonds. A complete set of nonlinear anisotropic elastic constants up to the fifth order are determined for these structures. Energetics of the deformation of these allotropes have been analyzed to mathematically establish a relationship between the sum of the second order nonlinear elastic constants and the area density. Empirical relationships have been obtained for predicting theYoung's moduli, Poisson's ratios and the ultimate tensile strengths (UTS) of the allotropes using their area densities and the sizes of the carbon rings. Furthermore, comparison with traditional engineering materials reveals that 2D graphene allotropes expand the available material-property space by occupying a new region with both high Young's modulus and a high UTS, as well as a high UTS and low density.