79
Views
5
CrossRef citations to date
0
Altmetric
Articles

On the dispersion of waves for the linear thermoelastic relaxed micromorphic model

ORCID Icon, ORCID Icon, , ORCID Icon &
Pages 3-20 | Received 09 May 2019, Accepted 26 Sep 2019, Published online: 25 Nov 2019

References

  • A. C. Eringen, “Balance laws of micromorphic mechanics,” Int. J. Eng. Sci., vol. 8, no. 10, pp. 819–828, 1970. DOI: 10.1016/0020-7225(70)90084-4.
  • R. D. Mindlin, “Micro-structure in linear elasticity,” Arch. Ration. Mech. Anal., vol. 16, no. 1, pp. 51–78, 1964. DOI: 10.1007/BF00248490.
  • E. Cosserat and F. Cosserat, Théorie des corps déformables. Paris: Librairie Scientifique A. Hermann et Fils, 2009.
  • E. Aero and E. Kuvshinskii, “Fundamental equations of the theory of elastic media with rotationally interacting particles,” Sov. Phys.-Solid State, vol. 2, no. 7, pp. 1272–1281, 1961.
  • G. Grioli, “Elasticità asimmetrica,” Annal. Matematica Pura Appl., vol. 50, no. 1, pp. 389–417, 1960. DOI: 10.1007/BF02414525.
  • W. Günther, “Zur Statik und Kinematik des Cosseratschen Kontinuums,” Abh. Braunschweig. Wiss. Ges., vol. 10, no. 213, pp. 1, 1958.
  • J. Jeong and P. Neff, “Existence, uniqueness and stability in linear Cosserat elasticity for weakest curvature conditions,” Math. Mech. Solids, vol. 15, no. 1, pp. 78–95, 2010. DOI: 10.1177/1081286508093581.
  • J. Jeong, H. Ramézani, I. Münch, and P. Neff, “A numerical study for linear isotropic cosserat elasticity with conformally invariant curvature,” Z. Angew. Math. Mech., vol. 89, no. 7, pp. 552–569, 2009. DOI: 10.1002/zamm.200800218.
  • P. Neff and J. Jeong, “A new paradigm: The linear isotropic Cosserat model with conformally invariant curvature energy,” Z. Angew. Math. Mech., vol. 89, no. 2, pp. 107–122, 2009. DOI: 10.1002/zamm.200800156.
  • R. A. Toupin, “Elastic materials with couple-stresses,” Arch. Ration. Mech. Anal., vol. 11, no. 1, pp. 385–414, 1962. DOI: 10.1007/BF00253945.
  • R. A. Toupin, “Theories of elasticity with couple-stress,” Arch. Ration. Mech. Anal., vol. 17, no. 2, pp. 85–112, 1964. DOI: 10.1007/BF00253050.
  • C. Truesdell and R. Toupin, “Principles of classical mechanics and field theory,” in Prinzipien der Klassischen Mechanik und Feldtheorie, S. Flügge, Ed. Berlin, Heidelberg: Springer, 1960, pp. 226–858.
  • A. C. Eringen and E. Suhubi, “Nonlinear theory of simple micro-elastic solids,” Int. J. Eng. Sci., vol. 2, no. 2, pp. 189–203, 1964. DOI: 10.1016/0020-7225(64)90004-7.
  • D. Iesan, “On a theory of micromorphic elastic solids with microtemperatures,” J. Therm. Stresses, vol. 24, no. 8, pp. 737–752, 2001.
  • D. Iesan, “On the micromorphic thermoelasticity,” Int. J. Eng. Sci., vol. 40, no. 5, pp. 549–567, 2002. DOI: 10.1016/S0020-7225(01)00061-1.
  • C. Galeş, “On the nonlinear theory of micromorphic thermoelastic solids,” Math. Prob. Eng., pp. 1–16, 2010. DOI: 10.1155/2010/415304.
  • P. Neff, I.-D. Ghiba, A. Madeo, L. Placidi, and G. Rosi, “A unifying perspective: The relaxed linear micromorphic continuum,” Continuum Mech. Thermodyn., vol. 26, no. 5, pp. 639–681, 2014. DOI: 10.1007/s00161-013-0322-9.
  • M. V. D'Agostino, G. Barbagallo, I.-D. Ghiba, B. Eidel, P. Neff, and A. Madeo, “Effective description of anisotropic wave dispersion in mechanical metamaterials via the relaxed micromorphic model,” J. Elast., 2019. DOI: 10.1007/s10659-019-09753-9.
  • M. V. D'Agostino, G. Barbagallo, I.-D. Ghiba, A. Madeo, and P. Neff, “A panorama of dispersion curves for the weighted isotropic relaxed micromorphic model,” Z. Angew. Mathem. Mech., vol. 97, no. 11, pp. 1436–1481, 2017.
  • A. Madeo, G. Barbagallo, M. V. D'Agostino, L. Placidi, and P. Neff, “First evidence of non-locality in real band-gap metamaterials: Determining parameters in the relaxed micromorphic model,” Proc. R. Soc. A, vol. 472, no. 2190, pp. 20160169, 2016. DOI: 10.1098/rspa.2016.0169.
  • P. Neff, A. Madeo, G. Barbagallo, M. V. D'Agostino, R. Abreu, and I.-D. Ghiba, “Real wave propagation in the isotropic-relaxed micromorphic model,” Proc. R. Soc. A, vol. 473, no. 2197, pp. 20160790, 2017. DOI: 10.1098/rspa.2016.0790.
  • I.-D. Ghiba, P. Neff, A. Madeo, L. Placidi, and G. Rosi, “The relaxed linear micromorphic continuum: Existence, uniqueness and continuous dependence in dynamics,” Math. Mech. Solids, vol. 20, no. 10, pp. 1171–1197, 2015. DOI: 10.1177/1081286513516972.
  • M. Hlaváćek, “A continuum theory for isotropic two-phase elastic composites,” Int. J. Solids Struct., vol. 11, no. 10, pp. 1137–1144, 1975. DOI: 10.1016/0020-7683(75)90092-X.
  • G. Barbagallo, A. Madeo, M. V. D’Agostino, R. Abreu, I.-D. Ghiba, and P. Neff, “Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics,” Int. J. Solids Struct., vol. 120, pp. 7–30, 2017. DOI: 10.1016/j.ijsolstr.2017.01.030.
  • A. Madeo, P. Neff, I.-D. Ghiba, L. Placidi, and G. Rosi, “Wave propagation in relaxed micromorphic continua: Modeling metamaterials with frequency band-gaps,” Continuum Mech. Thermodyn., vol. 27, no. 4–5, pp. 551–570, 2015. DOI: 10.1007/s00161-013-0329-2.
  • A. C. Eringen and W. D. Claus, Jr. “A micromorphic approach to dislocation theory and its relation to several existing theories,” Technical report, Princeton University NJ, Department of Aerospace and Mechanical Sciences, 1969.
  • A. Madeo, P. Neff, I.-D. Ghiba, and G. Rosi, “Reflection and transmission of elastic waves in non-local band-gap metamaterials: A comprehensive study via the relaxed micromorphic model,” J. Mech. Phys. Solids, vol. 95, pp. 441–479, 2016. DOI: 10.1016/j.jmps.2016.05.003.
  • G. Barbagallo, D. Tallarico, M. V. D'Agostino, A. Aivaliotis, P. Neff, and A. Madeo, “Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures,” Int. J. Solids Struct., vol. 162, pp. 148–163, 2019. DOI: 10.1016/j.ijsolstr.2018.11.033.
  • A. Aivaliotis, A. Daouadiji, G. Barbagallo, D. Tallarico, P. Neff, and A. Madeo, “Microstructure-related Stoneley waves and their effect on the scattering properties of a 2D Cauchy/relaxed-micromorphic interface,” Wave Motion, vol. 90, pp. 99–120, 2019. DOI: 10.1016/j.wavemoti.2019.04.003.
  • A. C. Eringen, Microcontinuum Field Theories: I. Foundations and Solids. New York, NY, USA: Springer, 2012.
  • P. Neff, B. Eidel, M. V. D'Agostino, A. Madeo. “Identification of scale-independent material parameters in the relaxed micromorphic model through model-adapted first order homogenization,” J. Elast., 2019. DOI: 10.1007/s10659-019-09752-w.
  • A. Madeo, P. Neff, I.-D. Ghiba, L. Placidi, and G. Rosi, “Band gaps in the relaxed linear micromorphic continuum,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 95, no. 9, pp. 880–887, 2015. DOI: 10.1002/zamm.201400036.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.