Journal of Mathematical Sciences

, Volume 238, Issue 2, pp 129–138 | Cite as

Equations of the Local Gradient Electromagnetothermomechanics of Polarizable Nonferromagnetic Bodies with Regard for Electric Quadrupole Moments

  • V. F. Kondrat
  • O. R. Hrytsyna

We formulate a complete system of relations of the local gradient electromagnetothermomechanics of electrically conductive nonferromagnetic polarizable solid media. The nonlocal character of the constitutive relations of the proposed mathematical model is explained by the presence of electric quadrupole moments in the polarization current. As a result of taking into account these moments, the space of parameters of the thermodynamic state of the body is expanded by including a pair of additional conjugate parameters, namely, the quadrupole moment and the gradient of the vector of electric-field intensity. It is shown that the developed model takes into account the electromechanical interaction for materials with high level of symmetry (isotropic materials) and describes the flexoelectric and thermopolarization effects. We also present the key system of equations for a physically and geometrically linear medium.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • V. F. Kondrat
    • 1
  • O. R. Hrytsyna
    • 2
  1. 1.Sahaidachnyi Academy of Army Ground ForcesLvivUkraine
  2. 2.Center of Mathematical Modeling, Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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