Strong ellipticity and progressive waves in elastic materials with voids

Chiriţă, Stan; Ghiba, Ionel–Dumitrel

doi:10.1098/rspa.2009.0360

Cited by 34 publications

(21 citation statements)

References 44 publications

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“…A direct identification of the coefficients gave us that the coefficient of the Cowin-Nunziato theory [12], the Mindlin-Eringen theory [42,19] and the microstretch theory [19,32] can be expressed in terms of our constitutive coefficients (see also [57,49]). Using these identifications one could compare all the qualitative results obtained using our relaxed micromorphic model with those already available in the literature (see for instance [42,19,26,8,9,10,27,28,29] and references therein) concerning classical theories of elastic materials with microstructure.…”

Section: Motivation and Originality Of The Present Workmentioning

confidence: 88%

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

Madeo

Neff

Ghiba

et al. 2013

Continuum Mech. Thermodyn.

143

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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Section: Motivation and Originality Of The Present Workmentioning

confidence: 88%

“…Analogously, the classical micromorphic continuum can be obtained from Eringen's model by means of the parameter identification (10) to which one must add the conditions…”

Section: Comparison With the Mindlin And Eringen Modelsmentioning

confidence: 99%

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

Madeo

Neff

Ghiba

et al. 2013

Continuum Mech. Thermodyn.

143

197

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“…b; a; n and x. By taking advantage of the positive definiteness properties of the constitutive laws and local positivity of the total strain energy density or so-called strongly ellipticity principle, one comes to realize the following restrictions (See for example Chirita and Ghiba (2010b), Ramézani et al (2012b) and Appendix A in Jeong et al (2013b)):…”

Section: D-fem Modeling Of the Nonlinear Constitutive Laws Of Microdmentioning

confidence: 99%

Non-linear elastic micro-dilatation theory: Matrix exponential function paradigm

Ramézani

Jeong²

2015

International Journal of Solids and Structures

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a b s t r a c tIn the present paper, the micro-dilatation theory or void elasticity is extended to both large displacement and large dilatation. Firstly, the deformation gradient tensor has been freshly defined by means of the matrix exponential function. The newly defined relation for the deformation gradient has painstakingly investigated for the uniqueness, decomposition issues as well as objectivity and isotropy considerations. The relation of the displacement gradient and deformation gradient tensor is brought via the matrix logarithm function. The micro-dilatation theory constitutive laws are derived using the thermodynamic principles under the zero-centrosymmetric, weakly-centrosymmetric and fully-centrosymmetric cases. These cases have been derived and scrutinized by the numerical experiments. To achieve this assignment, the basic loadings are taken into account, e.g. the hydrostatic loading, simple traction and shear. Some conclusions and outlook pertaining to the above-mentioned cases and variable bulk density have thereafter discussed.

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“…in [6] and for elastic materials with voids in [7]. For the isotropic micromorphic model, results can be found with respect to positive-definite energy and/or real wave velocity in Nowacki [8], Smith [9], Mindlin [10,11] and Eringen [12, pp.…”

Section: Introductionmentioning

confidence: 99%

Real wave propagation in the isotropic-relaxed micromorphic model

et al. 2017

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For the recently introduced isotropic-relaxed micromorphic generalized continuum model, we show that, under the assumption of positive-definite energy, planar harmonic waves have real velocity. We also obtain a necessary and sufficient condition for real wave velocity which is weaker than the positive definiteness of the energy. Connections to isotropic linear elasticity and micropolar elasticity are established. Notably, we show that strong ellipticity does not imply real wave velocity in micropolar elasticity, whereas it does in isotropic linear elasticity.

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Strong ellipticity and progressive waves in elastic materials with voids

Cited by 34 publications

References 44 publications

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

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

Non-linear elastic micro-dilatation theory: Matrix exponential function paradigm

Real wave propagation in the isotropic-relaxed micromorphic model

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