An introduction of the local displacements of mass and electric charge phenomena into the model of the mechanics of polarized electromagnetic solids

Abstract

Using the fundamental principles of thermodynamics of irreversible processes and continuum mechanics and electrodynamics, a complete set of equations of the thermomechanics of an electroconducting polarized medium has been obtained by taking into account the local displacements of mass and electric charge. To determine the thermodynamic state, two additional state parameters, namely the induced mass and the gradient of the energy measure of mass displacement, have been introduced. Two other parameters, the energy measure of mass displacement and the mass displacement vector, have been coupled to the aforementioned parameters. Such an extension of the state parameter space allows one to describe the near-surface inhomogeneity of the stress-strained state and the electric polarization as well as the surface charges and the electromagnetic signals induced by the surface formation.

Local gradient theory of dielectrics with polarization inertia and irreversibility of local mass displacement

“…Taking into account the process of local displacement of mass we represent the mass flux J m * as the sum of the convective term J mc = ρv * and the term J ms = ∂ m /∂t, which is caused by structural changes of the fixed body element, namely J m * = J mc + J ms [Burak et al 2008]. Here v * is a velocity of the convective displacement of the fixed body element and ρ is the mass density.…”

“…We assume that, for an arbitrary body of finite size that occupies the domain (V ), the vector of local displacement of mass and the density of the induced mass are such that [Burak et al 2008] (V )…”

“…VASYL KONDRAT AND OLHA HRYTSYNA approach to the construction of the nonlocal theory of dielectrics, proposed in [Burak et al 2008;Kondrat and Hrytsyna 2008a], is based on considering the process of local mass displacement. Burak [1987] was the first to pay attention to this process.…”

“…Later it was shown that the equations of the local gradient electromagnetothermomechanics of polarized nonferromagnetic solids describe surface inhomogeneity in the mechanical and electromagnetic fields [Burak et al 2008], a high-frequency dispersion of elastic waves [Kondrat and Hrytsyna 2009b], and the Mead anomaly [Chapla et al 2009]. It should be noted that the relations of the theory obtained in [Burak et al 2008] are based on the assumption of reversibility of the polarization process; local mass displacement and polarization inertia is not taken into account.…”

“…It should be noted that the relations of the theory obtained in [Burak et al 2008] are based on the assumption of reversibility of the polarization process; local mass displacement and polarization inertia is not taken into account. However, such an approximation may be insufficient and unacceptable for the study of transitional processes of the formation of near-surface inhomogeneities and the perturbation of electromagnetomechanical processes by shock loads, as well as for the description of acoustic and electromagnetic emission caused by the formation of surfaces, etc.…”