We consider a discrete network of a large number of infinitely thin homogeneous rods oriented along a given vector and connected by elastic springs at each point. The asymptotic behavior of small oscillations of this discrete system is studied in the case where the distances between the nearest rods tend to zero. For general nonperiodic arrays of rods, we deduce equations aimed at the description of the homogenized model of the system. It is shown that the homogenized equations correspond to the asymmetric dynamics of the elastic medium. Indeed, in this case, the stress tensor of the medium linearly depends not only on the strain tensor but also on the rotation tensor.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 6, pp. 764–785, June, 2011.
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Berezhnoi, M.A. Discrete model of the nonsymmetric theory of elasticity. Ukr Math J 63, 891–913 (2011). https://doi.org/10.1007/s11253-011-0551-7
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DOI: https://doi.org/10.1007/s11253-011-0551-7