Modified Young’s moduli in both directions were obtained for the two-dimensional single crystal body with a square lattice by using the continuum approach of continuum mechanics and taking into account only the interaction of neighbouring atoms. Separately, an expression was obtained taking into account the linear defects such as vacancies. The values of effective Young’s moduli compared with the same values for an infinite crystal lattice. Analyses showed that the influences of scale effects and vacancies on the Young’s moduli were considerable. In addition, it was shown that the effective Young’s moduli had three components: the macroscopic value; factors determining the scale effect; factors determining the vacancy. The last component was analogous to the parameter of the damage of the theory of fracture.

Modified Young’s Moduli of Nano-Materials Taking into Account the Scale Effects and Vacancies. A.N.Alizada, A.H.Sofiyev: Meccanica, 2011, 46[5], 915-20