Vol. 7, No. 3, 2012

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ISSN: 1559-3959
Local gradient theory of dielectrics with polarization inertia and irreversibility of local mass displacement

Vasyl Kondrat and Olha Hrytsyna

Vol. 7 (2012), No. 3, 285–296
Abstract

A complete system of equations of the local gradient theory of electromagnetothermomechanics of polarized nonferromagnetic isotropic solids is obtained with regard to polarization inertia and the irreversibility of the processes of local mass displacement and polarization. It is shown that in this case the constitutive relations for specific vectors of the local mass displacement and polarization are rheological and contain time derivatives of the first and higher orders. A corresponding key system of equations for the isothermal approximation is obtained. This system is also written relatively to scalar and vector potentials of the displacement vector, vectors of the electromagnetic field, and a reduced energy measure μπ of the effect of the mass displacement on the internal energy. The Lorentz gauge is generalized in such a way that equations for the vector potential of the electromagnetic field and for the generalized scalar potential are not coupled and have similar structures. The effect of polarization inertia and the above-mentioned irreversibility of processes on the interaction of the fields is analyzed.

Keywords
coupled electromagnetothermomechanical processes, local displacement of mass, dielectrics, nonlocal theory, irreversibility, inertia of polarization
Milestones
Received: 24 January 2011
Revised: 4 July 2011
Accepted: 15 December 2011
Published: 6 May 2012
Authors
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
Ukraine
Olha Hrytsyna
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
Ukraine
http://cmm.lviv.ua/hrytcyna.html