▎ 摘　　要

We handshake statistical mechanics with continuum mechanics to develop a methodology for consistent evaluation of the continuum scale properties of two-dimensional materials. The methodology is tested on pristine graphene. Our scope is kept limited to elastic modulus,E, which has been reported to vary between 0.912 TPa and 7 TPa, Poisson's ratio,nu, which has been reported to vary from being negative to a value as large as 0.46, and effective thickness,q, whose value varies between 0.75 angstrom and 3.41 angstrom. Such a large scatter arises due to inconsistent evaluation of these properties and making assumptions that may not be valid at atomistic scales. Our methodology combines three separate methods: uniaxial tension, equibiaxial tension, and flexural out-of-plane free vibrations of simply supported sheets, which, when used in tandem in molecular dynamics, can provide consistent values ofE,nu andq. The only assumption made in the present study is the validity of the continuum scale thin plate vibration equation to represent the free vibrations of a graphene sheet. Our results suggest that-(i) graphene is auxetic in nature, (ii)Edecreases with increasing size and temperature, and (iii) the effective thicknessqincreases with increasing size and temperature. Further, a robustness study of the computed mechanical properties shows consistent results, with differences varying between 1.4% and 6%.