Nonlinear electroelasticity: material properties, continuum theory and applications

Abstract

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

Instabilities of soft dielectrics

“…This leads, in the following section, to the incremental forms of the governing equations, which are needed for analysing the instabilities of dielectrics of various configurations. For more detailed accounts, we refer to Dorfmann & Ogden [2,74,86].…”

“…fields is based on the seminal work of Toupin [1], while an up-to-date version of the theory has been summarized in the recent review article by Dorfmann & Ogden [2]. In [2], various experiments that highlight the electromechanical coupling in soft dielectrics were reviewed followed by a summary of the basic equations of the static nonlinear continuum theory of elasticity and the appropriate specialization of Maxwell's equations. The two theories were then combined to obtain the general theory of nonlinear electroelasticity, with constitutive equations introduced and specialized for the behaviour of isotropic electroelastic materials.…”

Rubber Surface Change and Static Charging under Periodic Stress

“…Rubber materials are usually subject to periodic mechanical and electrical forces, e.g., in tires and insulators. Interest in the shape changes induced by electric fields [1][2][3][4] has grown recently, driven by different applications. For instance, dielectric elastomer actuators (DEAs) [5] display intriguing attributes similar to biological muscles, including self-sensing abilities [6,7] and improving the intelligence of gripping technologies [8].…”

Electro‐Thermal model of thermal breakdown in multilayered dielectric elastomers

“…The overestimation of the possible number of layers predicted by simulations compared to experimental results may be explained by the fact that no mechanical deformation of the stack is taken into consideration in the model presented herein. Modeling the electro‐mechanical coupling of dielectric elastomers is addressed multiple times in the literature, for example, by Hoffstadt and Maas, Dorfmann and Ogden, Zhao and Suo, and Qu and Suo . If the electro‐mechanical coupling was included in the electro‐thermal model presented in this work, the electric field would increase due to compression of the elastomer layer.…”