Elastic fields and effective properties of triangular lattice with vacancies

Abstract eng:
We consider linear elastic deformation of the two-dimensional triangular lattice with multiple vacancies. For the lattice with doubly periodic system of vacancies we derive closed-form analytical expressions for displacement field, and calculate effective elastic moduli. Molecular dynamics simulations of a lattice with random distribution of vacancies are carried out, and we compare the obtained elastic moduli with the analytical results. If the vacancy concentration is less than 4%, random and periodic distributions of vacancies produce the same effect on elastic moduli. We examine the possibilities and limitations of modeling of the lattice with vacancies by an elastic continuum with holes. We conclude that it is possible to model the effective elastic properties adequately, if the shape of the holes is chosen appropriately. Nevertheless, the strain field, in particular, strain concentration differs significantly.

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