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-

The elastic dielectric.

Mechanics of dielectric elastomer structures: A review

In the last decade, there has been a growing trend towards flexible body wave energy converters (WECs) enabled by rubber-like elastomeric composite membrane structures that can simplify all aspects of WEC design. Currently, there are few literature studies detailing the implementations of membranes into WEC design. This paper aims to overcome this by reviewing the developments, material selection and modelling procedures for novel membrane based wave energy converters (mWECs), providing the reader with a comprehensive overview of the current state of the technology. In the first half of this paper, all of the possible WEC implementation areas are reviewed which include the primary mover, power take-off (PTO) and other sub-assembly systems. For the primary mover, the review has identified three main working surface approaches using membranes, these are: air-filled cells, water filled tubes and tethered carpets; which aim to reduce peak loads for enhanced reliability and survivability. In other areas, the PTO of WECs can benefit from using soft dielectric elastomer generators (DEGs) which offer a simpler designs compared with conventional mechanical turbomachinery. These have been implemented into the membrane working surface as well as replacing the PTO in existing WEC architectures. In the second half of the paper, a discussion is made on the material selection requirements with a few possible compositions presented. Following this, the potential modelling procedures for these devices is detailed. The device numerical models have altered existing procedures to take into account the non-linearities caused by the membrane interface and membrane PTO damping.

Flexible membrane structures for wave energy harvesting: A review of the developments, materials and computational modelling approaches

The basic modern theory of nonlinear electroelasticity and its use in the formulation of constitutive laws governing the behaviour of dielectric elastomer materials was summarized in a recent revie...

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2018.0077

Instabilities of soft dielectrics

Dielectric elastomer transducers are often subject to large tensile stretches and are susceptible to rupture. Here we carry out an experimental study of the rupture behavior of membranes of an acrylic dielectric elastomer. Pure-shear test specimens are used to measure force-displacement curves, using samples with and without pre-cracks. We find that introducing a pre-crack into a membrane drastically reduces the stretch at rupture. Furthermore, we measure the stretch at rupture and fracture energy using samples of different heights at various stretch-rates. The stretch at rupture is found to decrease with sample height, and the fracture energy is found to increase with stretch-rate.

https://absimage.aps.org/image/MAR12/MWS_MAR12-2011-004460.pdf

Rupture of a highly stretchable acrylic dielectric elastomer

This paper reports an energy-based method for the dynamic pull-in instability analysis of a spherical dielectric elastomer (DE) balloon subjected to a quasi-statically applied inflation pressure and a Heaviside step voltage across the balloon wall. The proposed technique relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle, followed by the imposition of an instability condition for extracting the threshold parameters. The material models of the Ogden family are employed for describing the hyperelasticity of the balloon. The accuracy of the critical dynamic pull-in parameters is established by examining the saddle-node bifurcation in the transient response of the balloon obtained by integrating numerically the equation of motion, derived using the Euler–Lagrange equation. The parametric study brings out the effect of inflation pressure on the onset of the pull-in instability in the DE balloon. A quantitative comparison between the static and dynamic pull-in parameters at four different levels of the inflation pressure is presented. The results indicate that the dynamic pull-in instability gets triggered at electric fields that are lower than those corresponding to the static instability. The results of the present investigation can find potential use in the design and development of the balloon actuators subjected to transient loading. The method developed is versatile and can be used in the dynamic instability analysis of other conservative systems of interest.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2017.0900

Atul Kumar Sharma

Papers

DC dynamic pull-in instability of a dielectric elastomer balloon: an energy-based approach

A numerical framework for modeling anisotropic dielectric elastomers

Effect of viscoelasticity on the nonlinear dynamic behavior of dielectric elastomer minimum energy structures

Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

A computationally efficient locking free numerical framework for modeling visco-hyperelastic dielectric elastomers