The Elastic Dielectric Response of Elastomers Filled with Liquid Inclusions: From Fundamentals to Governing Equations

Over the past decade, soft solids containing electro-and magneto-active liquid—as opposed to solid—inclusions have emerged as a new class of smart materials with promising novel electro- and magneto-mechanical properties. In this context, a recent contribution has put forth a continuum theory that describes the macroscopic elastic behavior of elastomers filled with liquid inclusions under quasistatic finite deformations from the bottom up, directly in terms of their microscopic behavior at the length scale of the inclusions. This chapter presents the generalization of that theory to the coupled realm of the elastic dielectric behavior of such an emerging class of filled elastomers when in addition to undergoing quasistatic finite deformations they are subjected to quasistatic electric fields. The chapter starts with the description of the underlying fundamentals in the continuum—id est, kinematics, conservation of mass, Maxwell’s equations, balance of momenta, and constitutive behavior of both the bulk (the solid elastomer and the liquid inclusions) and the solid/liquid interfaces—and ends with their combination to formulate the resulting governing equations.