A new principle for constructing the theory of coupled dynamic electroelasticity of dielectrics that have piezoelectric and electrostrictive effects is expounded. This theory is based on the purely mechanical two-continuum description of the deformation of dielectrics as a mixture of positive and negative charges coupled into pairs neutral molecules or elementary cells provided that an elastic potential exists and the partial stresses are in linear quadratic relationship with the difference of displacements of charges. Based on the definition of the vector of polarization of an elementary dielectric macrovolume and the electric field generated by it, the equations of two-continuum mechanics are transformed into coupled dynamic equations for the macrodisplacements of neutral molecules and electric-field strength that describe the piezoelectric and electrostrictive effects. Maxwell’s equations follow from these equations as a particular case.
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V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity, Vol. 5 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1989).
W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, Van Nostrand, New York (1950).
W. Nowacki, Theory of Elasticity [in Polish], PWN, Warsaw (1970).
W. K. H. Panofsky, and M. Phillips, Classical Electricity and Magnetism, Addison-Wesley, Reading MA (1962).
I. E. Tamm, Fundamentals of the Theory of Electricity, Mir, Moscow (1979).
L. P. Khoroshun and N. S. Soltanov, Thermoelasticity of Two-Component Mixtures [in Russian], Naukova Dumka, Kyiv (1984).
L. P. Khoroshun, B. P. Maslov, and P. V. Leshchenko, Predicting the Effective Properties of Piezoelecritc Composites [in Russian], Naukova Dumka, Kyiv (1989).
I. S. Shapiro, “On the history of the discovery of the Maxwell equations,” Soviet Physics Uspekhi, 15, No. 5, 651–659 (1973).
W. Haywang, K. Lubitz, and W. Wersing, Piezoelectricity. Evolution and Technology, Springer (2008).
S. A. Kaloerov and A. A. Samodurov, “Problem of electromagnetoviscoelasticity of multiply connected plates,” Int. Appl. Mech., 51, No. 6, 623–639 (2015).
V. G. Karnaukhov, V. I. Kozlov, A. V. Zavgorodnii, and I. N. Umrykhin, “Forced resonant vibrations and self-heating of solids of revolution made of viscoelastic piezoelectric material,” Int. Appl. Mech., 51, No. 6, 614–622 (2015).
S. Katzir, The Beginning of Piezoelectricity, Springer, Berlin (2006).
L. P Khoroshun, “General dynamic equations of electromagnetomechanics for dielectrics and piezoelectrics,” Int. Appl. Mech., 42, No. 4, 407–420 (2006).
J. C. Maxwell, A Treatise on Electricity and Magnetism, Vol. 2, Clarendon Press, Oxford (1873).
L. V. Molchenko and I. I. Loos, “Axisymmetric magnetoelastic deformation of flexible orthotropic shells of revolution,” Int. Appl. Mech., 51, No. 4, 434–442 (2015).
Z. K. Wang, “A general solution and the application of space axisymmetric problem in piezoelectric material,” Appl. Math. Mech. Engl. Ed., 15, No. 7, 615–626 (1994).
C.-W. Wen and G. J. Weng, “Theoretical approach to effective electrostriction in inhomogeneous materials,” Phys. Rev. B, 61, No. 1, 258–265 (2000).
Y. Yamamoto, Elektromagnetomechanical Interactions in Deformable Solids and Structures, Elsevier Science–North Holland, Amsterdam (1987).
J. Yang, An Introduction to the Theory of Piezoelectricity, Springer, New York (2005).
Z. G. Ye, Handbook of Advanced Dielectric, Piezoelectric and Ferroelectric Materials. Synthesis, Properties and Applications, CRC Press, Boca Raton (2008).
T. Y. Zhang, “Fracture behaviors of piezoelectric material,” Theor. Appl. Fract. Mech., 41, No. 1–3, 339–379 (2004).
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Translated from Prikladnaya Mekhanika, Vol. 54, No. 2, pp. 29–41, March–April, 2018.
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Khoroshun, L.P. Two-Continuum Mechanics of Dielectrics as the Basis of the Theory of Piezoelectricity and Electrostriction. Int Appl Mech 54, 143–154 (2018). https://doi.org/10.1007/s10778-018-0866-2
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DOI: https://doi.org/10.1007/s10778-018-0866-2