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Research Article

On thermo-electro-viscoelastic relaxation functions in a Green–Naghdi type theory

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Pages 1205-1233 | Received 25 Feb 2019, Accepted 02 Jul 2019, Published online: 13 Jul 2020

References

  • B. D. Coleman and W. Noll, “Foundations of linear viscoelasticity,” Rev. Mod. Phys., vol. 33, no. 2, pp. 239–249, 1961. DOI: 10.1103/RevModPhys.33.239.
  • B. D. Coleman, “On thermodynamics, strain impulses, and viscoelasticity,” Arch. Ration. Mech. Anal., vol. 17, no. 3, pp. 230–254, 1964. DOI: 10.1007/BF00282439.
  • C. Galeş and S. Chiriţǎ, “On spatial behavior in linear viscoelasticity,” Quart. Appl. Math., vol. 67, no. 4, pp. 707–723, 2009. DOI: 10.1090/S0033-569X-09-01149-0.
  • M. Fabrizio and A. Morro, “Viscoelastic relaxation functions compatible with thermodynamics,” J. Elast, vol. 19, no. 1, pp. 63–75, 1988. DOI: 10.1007/BF00041695.
  • M. Fabrizio and A. Morro, Mathematical Problems in Linear Viscoelasticity. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics, 1992.
  • Z. P. Huang, “A constitutive theory in thermo-viscoelasticity at finite deformation,” Mech. Res. Commun., vol. 26, no. 6, pp. 679–686, 1999. DOI: 10.1016/S0093-6413(99)00078-6.
  • Y. Zeng, “Large time behavior of solutions to nonlinear viscoelastic model with fading memory,” Acta Math. Sci., vol. 32B, no. 1, pp. 219–236, 2012. DOI: 10.1016/S0252-9602(12)60014-9.
  • X. Chen, “Nonlinear electro-thermo-viscoelasticity,” Acta Mech., vol. 211, no. 12, pp. 49–59, 2010. DOI: 10.1007/s00707-009-0217-9.
  • N. S. Wilkes, “Thermodynamic restrictions on viscoelastic materials,” Q. J. Mech. Appl. Math., vol. 30, no. 2, pp. 209–221, 1977. DOI: 10.1093/qjmam/30.2.209.
  • B. D. Coleman and W. Noll, “An approximation theorem for functionals, with applications in continuum mechanics,” Arch. Ration. Mech. Anal., vol. 6, no. 1, pp. 355–370, 1960. DOI: 10.1007/BF00276168.
  • B. D. Coleman and W. Noll, “Thermodynamics of materials with memory,” Arch. Ration. Mech. Anal, vol. 13, no. 1, pp. 167–146, 1963. DOI: 10.1007/BF01262690.
  • W. A. Day, “Restrictions on relaxation functions in linear viscoelasticity,” Q. J. Mech. Appl. Math., vol. 24, no. 4, pp. 487–497, 1971. DOI: 10.1093/qjmam/24.4.487.
  • W. A. Day, The Thermodynamics of Simple Materials with Fading Memory. Berlin, Heidelberg, Germany/New York, NY, USA: Springer-Verlag, 1972.
  • A. E. Green and P. M. Naghdi, “On thermomechanics and the nature of the second law,” Proc. Roy. Soc. London Ser. A, vol. 357, pp. 253–270, 1977.
  • A. E. Green and P. M. Naghdi, “A re-examination of the basic postulates of thermomechanics,” Proc. Roy. Soc. London Ser. A, vol. 432, pp. 171–194, 1991.
  • A. E. Green and P. M. Naghdi, “On undamped heat waves in an elastic solid,” J. Therm. Stress., vol. 15, no. 2, pp. 253–264, 1992. DOI: 10.1080/01495739208946136.
  • A. E. Green and P. M. Naghdi, “A unified procedure for construction of theories of deformable media. I. Classical continuum physics,” Proc. Roy. Soc. London Ser. A: Math. Phys. Sci., vol. 448, no. 1934, pp. 335–356, 1995.
  • D. Ieşan, “Thermopiezoelectricity without energy dissipation,” Proc. R. Soc. A, vol. 464, no. 2091, pp. 631–656, 2008. DOI: 10.1098/rspa.2007.0264.
  • C. Giorgi and A. Montanaro, “Constitutive equations and wave propagation in Green–Naghdi type II and III thermo-electroelasticity,” J. Therm. Stress., vol. 39, no. 9, pp. 1051–1073, 2016. DOI: 10.1080/01495739.2016.1192848.
  • A. Montanaro, “On thermo-electro-mechanical simple materials with fading memory – restrictions of the constitutive equations in a Green–Naghdi type theory,” Meccanica, vol. 52, no. 13, pp. 3023–3031, 2017. DOI: 10.1007/s11012-017-0640-2.
  • H. F. Tiersten, “On the nonlinear equations of thermoelectroelasticity,” Int. J. Eng. Sci., vol. 9, no. 7, pp. 587–604, 1971. DOI: 10.1016/0020-7225(71)90062-0.
  • R. A. Toupin, “The elastic dielectrics,” Indiana Univ. Math. J., vol. 5, no. 6, pp. 849–915, 1956. DOI: 10.1512/iumj.1956.5.55033.
  • J. B. Alblas, “General theory of electro- and magneto-elasticity,” in Electromagnetic Interactions in Elastic Solids (CISM Course), H. Parkus, Ed. Wien, Austria: Springer-Verlag, 1979, pp. 1–104.
  • V. J. Mizel and C. C. Wang, “A fading memory hypothesis which suffices for chain rules,” Arch. Rational Mech. Anal., vol. 23, no. 2, pp. 124–134, 1966. DOI: 10.1007/BF00251728.
  • J. S. Yang and R. C. Batra, “A second-order theory for piezoelectric materials,” J. Acoust. Soc. Am., vol. 97, no. 1, pp. 280–288, 1995. DOI: 10.1121/1.412312.
  • B. Babaei, A. J. Velasquez-Mao, K. M. Pryse, W. B. McConnaughey, E. L. Elson, and G. M. Genin, “Energy dissipation in quasi-linear viscoelastic tissues, cells, and extracellular matrix,” J. Mech. Behav. Biomed. Mater., vol. 84, pp. 198–207, 2018. DOI: 10.1016/j.jmbbm.2018.05.011.
  • S. Rionero and S. Chiriţǎ, “New reciprocal and continuous dependence theorems in linear theory of viscoelasticity,” Int. J. Eng. Sci., vol. 27, no. 9, pp. 1023–1036, 1989. DOI: 10.1016/0020-7225(89)90081-5.

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