Non-standard dynamics of elastic composites

Maksym Berezhnyi; Evgen Khruslov; Maksym Berezhnyi; Evgen Khruslov

doi:10.3934/nhm.2011.6.89

Networks and Heterogeneous Media

2011, Volume 6, Issue 1: 89-109. doi: 10.3934/nhm.2011.6.89

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Non-standard dynamics of elastic composites

Maksym Berezhnyi ^{1
,},
Evgen Khruslov ^{1
,}

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

Received: 01 April 2010 Revised: 01 November 2010
Primary: 35B27, 35Q30, 74Q10; Secondary: 76M30, 76M50.

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.
- Microstructure,
- anisotropic material,
- elastic material,
- inhomogeneous material,
- asymptotic analysis
Citation: Maksym Berezhnyi, Evgen Khruslov. Non-standard dynamics of elastic composites[J]. Networks and Heterogeneous Media, 2011, 6(1): 89-109. doi: 10.3934/nhm.2011.6.89

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Abstract

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.

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