Linear theory of micropolar media with internal nonlocal potential interactions

Abstract

This paper proposes a mathematical model that can be used to quantify the effects of a polarized electric field on the mechanical properties of a polar dielectric in the framework of mechanics of deformable solids. The physical essence of the phenomenon is known. However, its direct use in practical calculations may cause difficulties due to the complexity of the composition and structure of materials used in the design and manufacture of specific products whose operation regimes are based on polarization effects. A continuum description of the polarization phenomenon makes it possible to circumvent these difficulties.The basis of the generalized model is a micropolar linearly elastic medium. The generalization consists in taking into account the initial stress state of the material, as well as cross effects under the mutual influence of translational and rotational deformations, the possibility to calculate the characteristics of micropolar material properties based on a special nonlocal model of micropolar media with internal nonlocal potential interactions. It takes into account translational and rotational potential interactions of particles of a continuous medium at finite distances. The kinematic characteristics of the material are the same as those used by the traditional model of a micropolar elastic medium ‐ the gradients of translational displacements of the medium's particles, their rotations independent of the medium's rotation and rotations of the particles relative to the medium. Generalized forces performing work on these generalized displacements are volumetrically and surface‐distributed forces and moments. To determine the values of the parameters of the interparticle potentials of the nonlocal model, a method is proposed using data from experiments to determine the material constants of isotropic linearly elastic materials and the dispersion law for plane acoustic waves of high frequency. The paper considers and quantifies the effects of anisotropy in an initially isotropic material, as well as anharmonic effects that cause dielectric heating by a periodically changing polarizing field. The results are compared qualitatively and quantitatively with known experimental data and physical notions of the phenomena in question.