The problem of surface wave propagation in a reduced Cosserat medium

Kulesh, M.; Grekova, Elena F.; Шардаков, И. Н.

doi:10.1134/s1063771009020110

Cited by 23 publications

(18 citation statements)

References 3 publications

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“…This parameter can hence be seen as a discreteness quantifier which starts accounting for lattice discreteness as soon as it reaches the threshold value μ 0 c specified in Eq. (14). This fact is a novel feature of the introduced relaxed model: we claim that neither the classical micromorphic continuum model nor the Cosserat and the second gradient ones are able to predict such band-gap phenomena.…”

Section: Numerical Resultsmentioning

confidence: 89%

“…In the papers of Grekova and co-workers [7,14] the reduced Cosserat medium is analyzed. The reduced Cosserat model can be obtained by our relaxed micromorphic model by setting α c = 0 and μ h → ∞.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…It is worth noticing that in our relaxed micromorphic model the observed forbidden range of frequency is valid for every plane wave solution (compression and shear). In the papers of Grekova and co-workers [7,14] the reduced Cosserat medium is analyzed. The reduced Cosserat model can be obtained by our relaxed micromorphic model by setting α c = 0 and μ h → ∞.…”

Section: Casementioning

confidence: 99%

See 2 more Smart Citations

Band gaps in the relaxed linear micromorphic continuum

Madeo

Neff

Ghiba

et al. 2014

Z. Angew. Math. Mech.

109

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In this note we show that the relaxed linear micromorphic model recently proposed by the authors can be suitably used to describe the presence of band-gaps in metamaterials with microstructures in which strong contrasts of the mechanical properties are present (e.g. phononic crystals and lattice structures). This relaxed micromorphic model only has 6 constitutive parameters instead of 18 parameters needed in Mindlin-and Eringen-type classical micromorphic models. We show that the onset of band-gaps is related to a unique constitutive parameter, the Cosserat couple modulus μc which starts to account for band-gaps when reaching a suitable threshold value. The limited number of parameters of our model, as well as the specific effect of some of them on wave propagation can be seen as an important step towards indirect measurement campaigns.

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Section: Numerical Resultsmentioning

confidence: 89%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Casementioning

confidence: 99%

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Band gaps in the relaxed linear micromorphic continuum

Madeo

Neff

Ghiba

et al. 2014

Z. Angew. Math. Mech.

109

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“…Generalization of Lamb problems to the case of wave propagation in porous media can be found in [53]; in media with complicated properties, in [54]; and in two component media, in [55]. Reviews are given in [56,57] on the propagation of harmonic waves in multilayered media with arbitrary elastic anisotropy.…”

Section: Some Related Problemsmentioning

confidence: 99%

Planar internal Lamb problem: Waves in the epicentral zone of a vertical power source

Kuznetsov

Terentjeva

2015

Acoust. Phys.

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“…There are many models for granular media (Badanin 2012, Harris 2009, Heinrich et al 1996, Kurbatskiy et al 2011). In the recent papers (Grekova et al 2004, Kulesh et al 2009) the Reduced Cosserat Continuum was suggested as a possible model to describe granular materials. In this continuum translations and rotations are independent, the stress tensor is not symmetric, and the couple stresses are zero.…”

Section: Introductionmentioning

confidence: 99%

Reduced cosserat continuum as a possible model for granular medium

Lalin

Zdanchuk

2014

Proceedings of the International Conference „Innovative Materials, Structures and Technologies”

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Abstract. We considered a nonlinear reduced Cosserat continuum: an elastic medium, whose translations and rotations are independent, the force stress tensor is asymmetric and the couple stress tensor is zero. We suggested the reduced Cosserat continuum as a possible model for granular medium. Granular materials are ubiquitous in our daily lives. They play an important role in many industries, such as mining, agriculture, and construction. We considered a nonlinear reduced Cosserat continuum for reference and current configurations and obtained the set of equations for each configuration.

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The problem of surface wave propagation in a reduced Cosserat medium

Cited by 23 publications

References 3 publications

Band gaps in the relaxed linear micromorphic continuum

Band gaps in the relaxed linear micromorphic continuum

Planar internal Lamb problem: Waves in the epicentral zone of a vertical power source

Reduced cosserat continuum as a possible model for granular medium

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