Nonlinear Electroelastic Deformations of Dielectric Elastomer Composites

Abstract eng:
In this talk, we will present homogenization solutions for the macroscopic elastic dielectric response — under finite deformations and finite electric fields — of dielectric elastomer composites with two-phase isotropic particulate microstructures. Specifically, solutions will be presented for three classes of microstructures: i) an isotropic iterative microstructure wherein the particles are infinitely polydisperse in size and non-spherical in shape, ii) an isotropic distribution of polydisperse spherical particles of a finite number of different sizes, and iii) an isotropic distribution of monodisperse spherical particles. The solution for the iterative microstructure, which corresponds to the viscosity solution of a Hamilton-Jacobi equation in five “space” variables, is constructed by means of a novel high-order WENO finitedifference scheme. The solutions for the microstructures with spherical particles are constructed by means of hybrid finite elements. aimAimed at gaining physical insight into the extreme enhancement in electrostrictive properties displayed by emerging dielectric elastomer composites, various cases wherein the dielectric elastomer is non-Gaussian and the filler particles are nonlinear elastic dielectrics that exhibit polarization saturation will be discussed in detail. Contrary to an initial conjecture in the literature, it will be shown (inter alia) that the isotropic addition of a small volume fraction of stiff high-permittivity particles to dielectric elastomers does not lead to the extreme electrostriction enhancements observed in experiments. It will be posited that such extreme enhancements are the intricate manifestation of interphasial phenomena.

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