# American Institute of Mathematical Sciences

March  2011, 6(1): 89-109. doi: 10.3934/nhm.2011.6.89

## Non-standard dynamics of elastic composites

 1 Institute for Low Temperature Physics and Engineering, Ukrainian Academy of Sciences, Lenin Ave 47, Kharkiv 61164, Ukraine

Received  April 2010 Revised  November 2010 Published  March 2011

An elastic medium with a large number of small axially symmetric solid particles is considered. It is assumed that the particles are identically oriented and under the influence of elastic medium they move translationally or rotate around symmetry axis but the direction of their symmetry axes does not change. The asymptotic behavior of small oscillations of the system is studied, when the diameters of particles and distances between the nearest particles are decreased. The equations, describing the homogenized model of the system, are derived. It is shown that the homogenized equations correspond to a non-standard dynamics of elastic medium. Namely, the homogenized stress tensor linearly depends not only on the strain tensor but also on the rotation tensor.
Citation: Maksym Berezhnyi, Evgen Khruslov. Non-standard dynamics of elastic composites. Networks & Heterogeneous Media, 2011, 6 (1) : 89-109. doi: 10.3934/nhm.2011.6.89
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