Linear elastic deformation of the two-dimensional triangular lattice with multiple vacancies is considered. Closed-form analytical expressions for displacement field in the lattice with doubly periodic system of vacancies are derived. Effective elastic moduli are calculated. The results are compared with the ones obtained by molecular dynamics simulations of a lattice with random distribution of vacancies. At low vacancy concentrations, less than 4%, random and periodic distributions of vacancies produce the same effect on elastic moduli. One of the main goals is to examine the possibilities and limitations of modelling of the lattice with vacancies by an elastic continuum with holes. It is found that the effective elastic properties are modelled adequately, provided the shape of the holes is chosen appropriately. On the contrary, the strain field, in particular, strain concentration differs significantly. ARTICLE HISTORY

The pair force interaction potential that allows one to describe a deviation from spherical symme try, which is typical for hexagonal close packed structures, is constructed using the "spherically symmetric" Mie potential that depends only on the interatomic distance. The parameters of the considered potential, which ensure the stability of hexagonal close packed lattices, are obtained for a wide range of metals, erbium. It is shown that for this pair interaction potential the hexagonal close packed structure is energeti cally more favorable than the face centered cubic structure. The proposed potential can be used to perform computational experiments and analytical investigations.

This paper is devoted to the application of the pair torque interaction potential for the simulation of the elastic behavior of a promising two-dimensional material: single layer molybdenium disulphide (SLMoS2). It is demonstrated that both Mo–Mo and S–S interactions can be regarded as pair force interactions with sufficient accuracy. Using both experimental and calculated numerically elastic moduli, and also the phonon spectrum available in the literature, the parameters of the Morse potential are determined for Mo–Mo and S–S bonds, and the parameters of the pair torque potential are obtained for the Mo–S bond. As a result, a combination of force and torque pair potentials is proposed, which allows for the correct modelling of SLMoS2 mechanical behavior.

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