Vol. 14, No. 4, 2019

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Local gradient theory for thermoelastic dielectrics: accounting for mass and electric charge transfer due to microstructure changes

Olha Hrytsyna and Vasyl Kondrat

Vol. 14 (2019), No. 4, 549–568

In this paper a complete set of nonlinear field equations of a gradient-type continuum theory for thermoelastic nonferromagnetic dielectrics is obtained. The specification of the mentioned set of equations is based on the application of electrothermomechanical balance laws and takes into consideration the polarization electric current and mass flux (of nondiffusive and nonconvective nature) associated with microstructure changes. The electric current is caused by a change of both dipole and quadrupole electric moments over time, whilst the mass flux is caused by a change of the vector of the local mass displacement over time. The obtained set of equations accounts for the electromechanical coupling for isotropic materials and describes the near-surface, size, flexoelectric and thermopolarization effects. The classical theory of piezoelectrics is incapable of describing the mentioned phenomena. For isothermal linear approximation, the proposed theory is used to investigate the effect of thin-film thickness as well as of the diameter and surface curvature of a thin fiber and a cylindrical hole in elastic dielectrics on their stationary stress-strain state, bound surface electric charge, surface energy of deformation and polarization, etc. It is shown that a disjoining pressure emerges in thin films. This pressure can affect the strength and stability of nanoscale dielectric films. The results obtained in this paper are general and can be used for designing new nanocomposite materials and devices utilizing the micro/nanoscale films, fibers, etc.

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local gradient theory, electric quadrupole moment, local mass displacement, surface and size effects.
Received: 1 April 2019
Revised: 20 August 2019
Accepted: 26 August 2019
Published: 13 December 2019
Olha Hrytsyna
Institute of Construction and Architecture
Slovak Academy of Sciences
9 Dúbravská cesta
84503 Bratislava 45
Center of Mathematical Modelling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
National Academy of Sciences of Ukraine
15 D. Dudajeva St. 15
79005 Lviv
Vasyl Kondrat
Center of Mathematical Modeling of the Institute of Applied Mathematics and Mechanics
National Academy of Sciences of Ukraine
15 D. Dudajeva St. 15
79005 Lviv