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

By A. Madeo, Patrizio Neff, Ionel-Dumitrel Ghiba, Luca Placidi, Giuseppe Rosi. 2013

169 citations recorded by the source corpus.

In this paper, the relaxed micromorphic model proposed in Ghiba et al. (Math Mech Solids, 2013), Neff et al. (Contin Mech Thermodyn, 2013) 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 so-called 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.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6f8340e1d7a1668e32b5b4f49c52ed9499bca684

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Granular micromechanics based micromorphic model predicts frequency band gaps (2015, background): “In this case for a plane wave solution, all kinematic measures should be only functions of x1 [45] φ̄i = φ̄i (x1, t) ψi j = ψi j (x1, t) (46) There are altogether twelve equations of motion in terms of the three average displacement field variables, φ̄i , and nine micro-displacement gradient field v”
Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response (2015, background): “In particular, the results obtained for 1D systems [135] can be generalized by showing how to synthesize microstructures whose continuous counterparts exhibit “forbidden” frequencies for wave propagation [238], the onset of trapping boundary layers or energy trapping at the microscopic level and con”
Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements (2015, background): “…descriptors in order to account for those phenomena of energy distribution, trapping and flow which were studied – in different contexts – in the papers (Carcaterra, 2002; Carcaterra and Akay, 2004; Culla et al., 2003; Ko et al., 2005; Luongo, 2001; Neff et al., 2013b; Madeo et al., 2013).”