# Gradient-Type Theory for Electro-Thermoelastic Non-ferromagnetic Dielectrics: Accounting for Quadrupole Polarization and Irreversibility of Local Mass Displacement

## Abstract

A complete set of equations of the gradient-type theory for thermoelastic non-ferromagnetic polarized solids is obtained using the methods of continuum mechanics, electrodynamics, and non-equilibrium thermodynamics. The theory takes into consideration the polarization electric current and the mass flux of non-diffusive and non-convective nature associated with microstructure changes. Such mass flux is related to the process of local mass displacement. The constructed theory is characterized by the dependence of the constitutive functions on the strain tensor, the temperature, the electric field vector and its gradient, the density of induced mass, and the reversible component of the gradient of a modified chemical potential. The last three parameters are related to the electric quadrupole and mass dipole moments, which are taken into account in order to develop a general theory of dielectrics. It is shown that due to accounting for the irreversibility of the local mass displacement, we obtain rheological constitutive relations not only for electric and mass dipole moments but also for a heat flux and for the electric current. As a result, the theory generalized in such a way accounts for the electromechanical coupling for isotropic materials and describes the experimentally observed phenomena, such as surface, size, and flexoelectric and thermopolarization effects. The classical theory of dielectrics is incapable of describing the abovementioned effects. The obtained fundamental field equations within the continuum approximation make it possible to study the process of formation of a near-surface inhomogeneity of the stress-strain state of a traction-free elastic isotropic layer.

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