An earlier system of rotationally invariant electroelastic equations for deformable insulators, which was derived from a well-defined macroscopic model, is extended to include the simplest mechanical and electrical viscous-type dissipation. The resulting nonlinear description satisfies the principle of material objectivity. When the resulting description is linearized, the viscous-type linear electrical dissipative variable contains the spin tensor because a biasing polarization is present in the ferroelectric ceramic.
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References
1.
. TierstenH. F.On the nonlinear equations of thermoelectroelasticity?International Journal of Engineering Science, 9, 587–604 (1971).
2.
. TierstenH. F.: On the accurate description of piezoelectric resonators subject to biasing deformations, International Journal of Engineering Science, 33, 2239–2259 (1995).
3.
. TruesdellC.NollW.: The nonlinear field theories of mechanics, in Encyclopedia of Physics, Vol. III/2, Secs. 17 and 19, ed., FlüggeS., Springer-Verlag, Berlin, 1965.
4.
. EringenA. C.: Nonlinear Theory of Continuous Media, Secs. 27 and 44, McGraw-Hill, New York, 1962.
5.
. BoleyB. A.WeinerJ. H.: Theory of Thermal Stresses, Secs. 1.8–1.12, Wiley, New York, 1960.
6.
. DeGrootS. R.MazurP.: Non-Equilibrium Thermodynamics, Ch. III, Secs. 1 and 2, North-Holland, Amsterdam, 1963.
7.
. EringenA. C.: Nonlinear Theory of Continuous Media, Secs. 36–40, McGraw-Hill, 1962.
8.
. ToupinR. A.The elastic dielectric?Journal of Rational Mechanics and Analysis, 5, 849–916 (1956).
9.
. TruesdellC.ToupinR. A.: The classical field theories, in Encyclopedia of Physics, Vol. III/1, Sec. 293, ed., FlüggeS., Springer-Verlag, Berlin, 1960.
10.
. GreenA. E.AdkinsJ. E.: Large Elastic Deformations and Nonlinear Continuum Mechanics, Ch. 8, Oxford University Press, London, 1960.
11.
. SpencerA. J. M.: Theory of Invariants, in Continuum Physics, Vol. 1, Part III, Sec. 2.1, ed., EringenA. C., Academic, New York, 1972.
12.
. BaumhauerJ. C.TierstenH. F.Nonlinear electroelastic equations for small fields superposed on a bias?Journal of the Acoustical Society of America, 54, 1017–1034 (1973).
13.
. TruesdellC.ToupinR. A.: The classical field theories, in Encyclopedia of Physics, Vol. III/1, Sec. 20, Eq. (20.8), ed., FlüggeS., Springer-Verlag, Berlin, 1960.
14.
. TruesdellC.ToupinR. A.: The classical field theories, in Encyclopedia of Physics, Vol. III/1, Secs. 17 and 18, Eq. (18.2), ed., FlüggeS., Springer-Verlag, Berlin, 1960.
15.
. IEEE Standard on Piezoelectricity. IEEE Std. 176-1978, Institute of Electrical and Electronics Engineers, New York, 1978, p. 23, Class C6v (6 mm).
16.
. TierstenH. F.Electroelastic equations for electroded thin plates subject to large driving voltages?Journal of Applied Physics, 74, 3389–3393 (1993).