Discrete model of the nonsymmetric theory of elasticity

  • M. A. Berezhnoi Технол. ун-т, Дармштадт, Германия; Физ.-техн. ин-т низких температур НАН Украины, Харьков


We consider a discrete network of a large number of pin-type homogeneous rods oriented along a given vector and connected by elastic springs at each point. The asymptotic behavior of small oscillations of the discrete system is studied in the case where the distances between the nearest rods tend to zero. For generic non-periodic arrays of rods, we deduce equations describing the homogenized model of the system. It is shown that the homogenized equations correspond to a nonstandard dynamics of an elastic medium. Namely, the homogenized stress tensor in the medium depends linearly not only on the strain tensor but also on the rotation tensor.
How to Cite
Berezhnoi, M. A. “Discrete Model of the Nonsymmetric Theory of Elasticity”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 6, June 2011, pp. 764-85, https://umj.imath.kiev.ua/index.php/umj/article/view/2761.
Research articles