The two-continuum mechanics of dielectrics as a basis of the theory of piezoelectricity and electrostriction

Abstract

The paper proposes a new principle for setting up the theory of coupled dynamic electroelasticity of dielectrics that have piezoelectric and electrostrictive properties. The theory is based on the purely mechanical two-continuum description of dielectrics as a mixture of positive and negative charges coupled into neutral molecules or elementary cells. It is assumed that an elastic potential exists and that the partial stresses are in quadratically nonlinear dependence on the difference of the displacements of charges. Based on the definition of the polarization vector of an elementary dielectric volume and the electric field it generates, the equations of two-continuum mechanics are reduced to coupled dynamic equations for the macrodisplacements of neutral molecules and the electric-field intensity, which describe the piezoelectric and electrostrictive effects

The Triple-Continuum Mechanics of Conductors as the Basis for the Theory of Electromagnetic Waves and Conduction

“…The new principle of deriving the equations of electromagnetomechanics of dielectrics [14,15] and conductors allows proving and explaining the physical sense of Maxwell's displacement-current term. For dielectrics, it is double-continuum mechanics describing the deformation of a dielectric as a mixture of positive and negative charges paired into neutral formations.…”

“…A new principle of the theory of linear and nonlinear electroelasticity was formulated in [14,15]. It is based on the two-continuum mechanics of dielectrics as mixtures of positive and negative charges coupled into neutral molecules or cells.…”

“…The double-continuum mechanics of dielectrics [14,15] uses the definition of the polarization vector and electric field generated by it to arrive at coupled equations for the macrodisplacements of neutral molecules and electric-field strength. In the case of a fixed dielectric, Maxwell's equations follow from them as a special case.…”