Dielectric elastomer composites: small-deformation theory and applications

Abstract

We provide estimates for the effective response of Electro-Active Polymer Composites (EAPCs) consisting of aligned ellipsoidal inclusions of a stiff dielectric material which are distributed randomly in an soft elastomeric matrix with “ellipsoidal” two-point statistics. The derivation of the results for the electro-mechanical response assumes linearized deformations, but includes non-linear (quadratic) terms in the electric fields. We investigate three different physical mechanisms contributing to the macroscopic electro-mechanical response of the composite: the intrinsic effect of the particles on the Maxwell stress, the inter-particle (dipole) interactions which are accounted for by evaluating the effect of changes in the “shape” of the two-point probability functions with the deformation, and the effect of particle rotations and torques when the geometric and/or anisotropy axis of the particles are not aligned with the applied electric field. Several illustrative examples are provided to emphasize the relative importance of the different effects on the overall electrostriction of the composites. In particular, for the “compliant electrode” boundary conditions that are widely used in applications, it is shown that inter-particle interactions are synergistic with the intrinsic effect of the particles on the Maxwell stress, leading to significant enhancements in the electro-mechanical coupling of the EAPCs, especially at high particle concentrations. On the other hand, the effect of electric torques on non-aligned particles is generally deleterious for electrostriction.