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Abstract:
In this paper, the effective elastic properties of hexagonal monolayers such as graphene, boron nitride, silicon carbide, and aluminum nitride are evaluated using the asymptotic homogenization method taking into account temperature changes. The effective properties are determined analytically by considering temperature, force constants, bond lengths, and thickness, using atomic interactions within the context of the unit cell problem. The relationship between environmental temperature and the coefficient of thermal expansion is established by considering changes in the values ​​of bond stretching, bond angle bending, and torsion resistance constants at different temperatures from 0 to 1800 K. The results provided by the proposed homogeneous model are consistent with the valid findings of other researchers in the literature. It is found that these different hexagonal nanosheets exhibit isotropic temperature-dependent properties and their Young's and shear modulus decrease almost linearly as the temperature rises, considering a constant coefficient of thermal expansion. However, Poisson's ratio is found to be independent of temperature. Furthermore, the temperature-dependent elastic properties of these nanosheets become nonlinear when the variation of the coefficient of thermal expansion with temperature is taken into account. The Young and shear moduli of the nanosheets increase as the coefficient of thermal expansion decreases and vice versa. The highest elastic modulus values are obtained when the thermal expansion is close to its minimum threshold. However, it is recognized that the elastic modulus of graphene and boron nitride nanosheets is higher than that of silicon carbide and aluminum nitride at any temperature. As an alternative to lengthy computer modeling or rigorous testing, the homogeneous models provided can be used to simulate nanosheets.

Keywords:
Asymptotic homogenization method, Hexagonal nanosheets, Effective mechanical properties, Coefficient of thermal expansion