The elastic dielectric.
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Slepian used an operational "definition" of stress and concluded that the compensating mechanical forces which must be introduced operationally are not derivable from a tensor.Abstract:
for the force on a dielectric in an electrical field E and bounded by a surface S with unit normal n. He used an operational \"definition\" of stress and concluded that the compensating mechanical forces which must be introduced operationally are not derivable from a tensor. It is suggested here that Slepian's analysis is essentially correct and that the difficulty arises because of the choice of an operationally \"defined\" stress. This choice is inconsistent with the existence of an electrical surface stress-which is familiar, in the magnetic analogue, in studies of the form effect-and it is argued here that the Euler-Cauchy definition of stress is the appropriate one. The Definition of Stress.-In authoritative works on continuum mechanics stress is introduced by means of the stress hypothesis of Euler and Cauchy,2 that is, by asserting that, acting upon any imagined closed geometrical surface a within the body, there exists a field of stress vectors t which has an equivalent effect to the (interparticle) forces exerted by the material outside aupon the material within. For a dielectric material the interaprticle (i.e., intermolecular) forces are partly long-range in character and they may therefore contribute not only to t but also to f, the body force per unit volume. For the present purpose, however, the important point to note is that ais an imagined geometrical surface and not a physical surface of separation within the material. An alternative procedure is to use the operational definition of stress in which it is imagined that a physical cut is made in the material along an internal element of surface dd = nda. If means are then introduced for keeping the strains in the material on both sides of the cut the same as they were before the cut was made, then the force introduced by these means is t'do-, where t' is the operationally defined stress vector. In adopting this operational definition, Slepian commented: \"It is not assumed that the cut and the introduced means do not disturb the microstructure and micromechanics of the material. For example, in the case of a fluid the cut and means would cause molecules to be reflected which would otherwise pass through the geometric element of surface dS. It is assumed, however, that in spite of the change in the micromechanics, there is no change in the observable macromechanics.\"' It may also be noted there is a further element of idealization involved in that the cut is imagined to be of finite extent: in practice, as discussed later in this paper, it is only possible to measure the force on an element of volume when the element is completely separated from the rest of the body. For an ordinary elastic material the stress acting at a physical surface of separa-read more
Citations
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References
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Journal ArticleDOI
A nonlinear field theory of deformable dielectrics
TL;DR: In this article, a new formulation of the field theory of dielectric solids is proposed, which does not start with Newton's laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences.
Journal ArticleDOI
Electrostatic Forces and Stored Energy for Deformable Dielectric Materials
TL;DR: In this article, an isothermal energy balance is formulated for a system consisting of deformable dielectric bodies, electrodes, and the surrounding space, which is obtained in the electrostatic limit but with the possibility of arbitrarily large deformations of polarizable material.
Journal ArticleDOI
On finitely strained magnetorheological elastomers
TL;DR: In this article, two different continuum formulations for magnetorheological elastomers (MREs) are presented: an Eulerian (current configuration) based approach using the second law of thermodynamics plus the conservation laws method of mechanics and a new, Lagrangian based formulation based on the unconstrained minimization of a potential energy functional.
Journal ArticleDOI
Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning
Yu Su,Chad M. Landis +1 more
TL;DR: In this paper, a continuum thermodynamics framework is devised to model the evolution of ferroelectric domain structures, which falls into the class of phase-field or diffuse-interface modeling approaches.
Journal ArticleDOI
Flexoelectricity in soft materials and biological membranes
TL;DR: In this article, a nonlinear theoretical framework for flexoelectricity in soft materials was developed, using the concept of soft electret materials, and illustrate an interesting nonlinear interplay between the so-called Maxwell stress effect and flexo-lectrics.