The Overall Elastic Dielectric Properties of Fiber-Strengthened/Weakened Elastomers

By employing recent results (Lopez-Pamies, O., 2014, “Elastic Dielectric Composites: Theory and Application to Particle-Filled Ideal Dielectrics,” J. Mech. Phys. Solids, 64, p. 6182 and Spinelli, S. A., Lefèvre, V., and Lopez-Pamies, O., “Dielectric Elastomer Composites: A General Closed-Form Solution in the Small-Deformation Limit,” J. Mech. Phys. Solids, 83, pp. 263–284.) on the homogenization problem of dielectric elastomer composites, an approximate solution is generated for the overall elastic dielectric response of elastomers filled with a transversely isotropic distribution of aligned spheroidal particles in the classical limit of small deformations and moderate electric fields. The solution for such a type of dielectric elastomer composites is characterized by 13 (five elastic, two dielectric, and six electrostrictive) effective constants. Explicit formulae are worked out for these constants directly in terms of the elastic dielectric properties of the underlying elastomer and the filler particles, as well as the volume fraction, orientation, and aspect ratio of the particles. As a first application of the solution, with the objective of gaining insight into the effect that the addition of anisotropic fillers can have on the electromechanical properties of elastomers, sample results are presented for the case of elastomers filled with aligned cylindrical fibers. These results are confronted to a separate exact analytical solution for an assemblage of differential coated cylinders (DCC), wherein the fibers are polydisperse in size, and to full-field simulations of dielectric elastomer composites with cylindrical fibers of monodisperse size. These results serve to shed light on the recent experimental findings concerning the dielectric elastomers filled with mechanically stiff fibers. Moreover, they serve to reveal that high-permittivity liquid-like or vacuous fibers—two classes of filler materials yet to be explored experimentally—have the potential to significantly enhance the electrostriction capabilities of dielectric elastomers.