Asymptotic Homogenization of Materials with Artificial Periodic Structuresстатья
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Дата последнего поиска статьи во внешних источниках: 2 сентября 2020 г.
Аннотация:Some types of metamaterials are designed to provide coupling between classical degrees of freedom and
rotations. For modeling such materials, it is suggested in literature to exploit Cosserat non-classical elastic medium. The periodic structure of those materials makes the asymptotic averaging method a convenient tool for studying metamaterials. In the paper it is shown that the application of the averaging technique up to the second approximation order to a 3D composite medium leads to constitutive relations of a non-classical type similar to gradient elasticity theory. Moreover, it is proved that the coupling moduli are reciprocal to the number of the periodicity cells. Therefore, these moduli vanish for a large amount of the metamaterial. The same conclusion appeared to be true for tension-bending coupling. Numerical examples are given to support this theoretical conclusion.