Molecular-continuum model for the prediction of stiffness, strength and toughness of nanomaterials

A semi-analytical method called molecular-continuum model is proposed to estimate the stiffness, strength and fracture toughness of nanomaterials. This model is developed by combining the concept of molecular dynamics and continuum mechanics, in which the potential energy describing the interactions of atoms is not restricted to the harmonic potential function, and hence its deriving stress–strain relation is not restricted to being linear. The estimated properties can therefore be the ones defined based upon the initial linear region such as stiffness, or the ones occur at the later period of the materials such as strength and toughness. By using this model, several mechanical properties of nanomaterials such as Young’s modulus, Poisson’s ratio, shear modulus, yield strength, ultimate strength, mode I and mode II fracture toughness can be predicted. For the purpose of illustration and verification, some examples of one-dimensional nanomaterials, such as carbon nanotubes and single crystal copper nanowires, and two-dimensional nanomaterials, such as graphene and single crystal copper nanofilms, are presented in this paper.