A discrete model and analysis of one-dimensional deformations in a structural interface with micro-rotations

Vasiliev, Aleksey A.; Miroshnichenko, Andrey E.; Ruzzene, Massimo

doi:10.1016/j.mechrescom.2009.11.010

Cited by 20 publications

(9 citation statements)

References 43 publications

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“…Vassiliev et al 25,26 have studied a discrete linear onedimensional micromechanics model that includes longitudinal, shear, and rotational degrees of freedom. This 1D discrete Cosserat-like lattice model consists of an infinite chain of square block elements (Cosserat elements) connected with multiple harmonic springs.…”

Section: A Model and Methodsmentioning

confidence: 99%

Rotational modes in a phononic crystal with fermion-like behavior

Deymier

Runge

Swinteck

et al. 2014

Journal of Applied Physics

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The calculated band structure of a two-dimensional phononic crystal composed of stiff polymer inclusions in a soft elastomer matrix is shown to support rotational modes. Numerical calculations of the displacement vector field demonstrate the existence of modes whereby the inclusions and the matrix regions between inclusions exhibit out of phase rotations but also in phase rotations. The observation of the in-phase rotational mode at low frequency is made possible by the very low transverse speed of sound of the elastomer matrix. A one-dimensional block-spring model is used to provide a physical interpretation of the rotational modes and of the origin of the rotational modes in the band structure. This model is analyzed within Dirac formalism. Solutions of the Dirac-like wave equation possess a spinor part and a spatio-temporal part. The spinor part of the wave function results from a coupling between the senses (positive or negative) of propagation of the wave. The wave-number dependent spinor-part of the wave function for two superposed waves can impose constraints on the integral of the spatio-temporal part that are reflected in a fermion-like lifting of degeneracy in the phonon band structure associated with in-phase rotations.

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Section: A Model and Methodsmentioning

confidence: 99%

Rotational modes in a phononic crystal with fermion-like behavior

Deymier

Runge

Swinteck

et al. 2014

Journal of Applied Physics

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“…Some rare papers (see e.g. [31,63,68]) can be found in the literature in which lattice models with enriched kinematics are used to model band-gaps without the need of introducing negative equivalent masses. Nevertheless, to the authors' knowledge, a systematic treatment of band-gap modelling based on the spirit of micromorphic continuuum mechanics is still lacking and deserves attention.…”

Section: Motivation and Originality Of The Present Workmentioning

confidence: 99%

Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps

Madeo

Neff

Ghiba

et al. 2013

Continuum Mech. Thermodyn.

147

197

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In this paper the relaxed micromorphic model proposed in [49,26] has been used to study wave propagation in unbounded continua with microstructure. By studying dispersion relations for the considered relaxed medium, we are able to disclose precise frequency ranges (band-gaps) for which propagation of waves cannot occur. These dispersion relations are strongly nonlinear so giving rise to a macroscopic dispersive behavior of the considered medium. We prove that the presence of band-gaps is related to a unique elastic coefficient, the socalled Cosserat couple modulus µc, which is also responsible for the loss of symmetry of the Cauchy force stress tensor. This parameter can be seen as the trigger of a bifurcation phenomenon since the fact of slightly changing its value around a given threshold drastically changes the observed response of the material with respect to wave propagation. We finally show that band-gaps cannot be accounted for by classical micromorphic models as well as by Cosserat and second gradient ones. The potential fields of application of the proposed relaxed model are manifold, above all for what concerns the conception of new engineering materials to be used for vibration control and stealth technology.

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“…This model is based on a discrete linear one-dimensional micromechanics model that includes longitudinal, shear and rotational degrees of freedom [11,12]. This 1D discrete lattice model consists of an infinite chain of square block elements connected with multiple harmonic springs.…”

Section: One-dimensional Discrete Micromechanics Modelmentioning

confidence: 99%

Torsional topology and fermion-like behavior of elastic waves in phononic structures

Deymier

Runge

Swinteck

et al. 2015

Comptes Rendus. Mécanique

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A one-dimensional block-spring model that supports rotational waves is analyzed within Dirac formalism. We show that the wave functions possess a spinor and a spatio-temporal part. The spinor part leads to a non-conventional torsional topology of the wave function. In the long-wavelength limit, field theoretical methods are used to demonstrate that rotational phonons can exhibit fermion-like behavior. Subsequently, we illustrate how information can be encoded in the spinor-part of the wave function by controlling the phonon wave phase.

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A discrete model and analysis of one-dimensional deformations in a structural interface with micro-rotations

Cited by 20 publications

References 43 publications

Rotational modes in a phononic crystal with fermion-like behavior

Rotational modes in a phononic crystal with fermion-like behavior

Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps

Torsional topology and fermion-like behavior of elastic waves in phononic structures

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