To the bases of the nonlinear theory of electroelasticity

1Khoroshun, LP, 1Levchuk, OI
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 3:43-52
Section: Mechanics
Language: Russian

A new principle is proposed for constructing a nonlinear theory of coupled dynamical processes of electroelasticity. The theory is based on the equations of the two-continuum mechanics of dielectrics as a mixture of positive and negative charges in pairs, which form neutral molecules or elementary cells. The existence of an elastic potential and the linear-quadratic dependence of partial stresses on the difference of displacements of charges is accepted. Based on the definitions of a polarization vector and an associated electric field, the equations of the two-continuum mechanics are transformed into equations of electroelasticity, which describe the piezoelectric and electrostriction effects.

Keywords: dielectric, electroelasticity, electrostriction, piezoelectric, polarization vector, two-continuum mechanics
  1. Grinchenko, V. T., Ulitko, A. F. & Shulga, N. A. (1989). Mechanika Sviazannykh Polej v Elementakh Konstruktsij. Electrouprugost. 5, Kiev: Naukova Dumka (in Russian).
  2. Khoroshun, L. P., Maslov, B. P. & Leschenco, P. V. (1989). Prognozirovanie Effektivnykh Svojstv Piezoactivnykh Kompozitnykh Materialov. Kiev: Naukova Dumka, (in Russian).
  3. Panovskiy, V. & Filips, M. (1963). Klassicheskaja Electrodinamika. Moscow: Fizmatgiz (in Russian).
  4. Khorohun, L. P. (2006). General Dynamic Equations of Electromagnetomechanics for Dielectrics and Piezoelectrics. Int. Appl. Mech., 42, No. 4, pp. 407-420. doi:
  5. Wen, C.-W. & Weng, G. J. (2000). Theoretical approach to effective electrostriction in inhomogeneous materials. Phys. Rev. B., 61, No. 1, pp. 258-265. doi:
  6. Tamm, I. E. (1976). Osnovy Teorii Elektrichestva. Moscow: Nauka (in Russian).
  7. Khoroshun, L. P. & Soltanov, N. S. (1984). Termouprugost Dvukhkomponentnykh Smesej. Kiev: Naukova Dumka (in Russian).
  8. Novatskiy, V. (1975). Teorija Uprugosti. Moscow: Mir (in Russian).