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Thermoelastic Diffusion Theory for Piezoelectric Materials

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Encyclopedia of Continuum Mechanics

Synonyms

Green-Naghdi theory

; Piezoelectric

; Thermoelastic diffusion

Definitions

Piezoelectricity is the ability of some materials to generate an electric charge in response to applied mechanical stress.

Cross effects of heat and mass diffusion exchange with the environment arising from and inside nuclear reactors influence their design and operations. Thermoelastic diffusion material is an elastic deformable solid allowing for changes in temperature and mass diffusion. Diffusion can be defined as the random walk of an ensemble of particles from regions of high concentration to regions of lower concentration. Thermodiffusion in an elastic solid is due to coupling of the fields of temperature, mass diffusion, and that of strain.

Green and Naghdi theory of types I, II, and III are three thermomechanical theories of deformable continua. The type I coincides with the classical heat conduction based on Fourier’s law. The type II and III models are based on entropy balance law rather than...

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References

  • Bowen RN (1976) Theory of mixture. In: Eringen AC (ed) Continuum physics, vol III. Academic, New York

    Google Scholar 

  • Curie J, Curie P (1880) Développement, par pression, de l’électricité polaire dans les cristaux hémièdres à faces inclinées. C R Acad Sci 91:294–295

    MATH  Google Scholar 

  • Green AE, Naghdi PM (1991) A re-examination of the basic postulates of thermomechanics. Proc R Soc Lond A 432:171–194

    Article  MathSciNet  MATH  Google Scholar 

  • Green AE, Naghdi PM (1993) On thermoelasticity without energy dissipation. J Elast 31:189–208

    Article  MathSciNet  MATH  Google Scholar 

  • Green AE, Naghdi PM (1995) A unified procedure for construction of theories of deformable media, Classical continuum physics, Generalized continua, Mixtures of interacting continua. Proc R Soc Lond A 448:335–356, 357–377, 379–388

    Google Scholar 

  • Lebon G, Desaive T, Dauby P (2006) A unified extended thermodynamics descrition of diffusion, thermo-diffusion, suspension and porous media. Trans ASME 73:16–20

    Article  MATH  Google Scholar 

  • Mindlin RD (1961) On the equations of motion of piezoelectric crystals, problems of continuum. In: Muskelishvili NI (ed) Mechanics, 70th Birthday Volume. SIAM, Philadelphia, pp 282–290

    Google Scholar 

  • Mindlin RD (1979) Equation of high frequency of thermo-piezoelectric, crystals plates, interactions in elastic solids. Springer, Wein

    Google Scholar 

  • Nowacki W (1978) Some general theorems of thermo-piezoelectricity. J Therm Stresses 1:171–182

    Article  Google Scholar 

  • Nowacki W (1979) Foundation of linear piezoelectricity. In: Parkus H (ed) Interactions in elastic solids. Springer, Wein

    Google Scholar 

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Correspondence to Moncef Aouadi .

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Aouadi, M. (2018). Thermoelastic Diffusion Theory for Piezoelectric Materials. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_144-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_144-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

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