On the deformations of an electroactive solid subject to a uniform electric field in an orthogonal rheometer

In this short paper, we extend the seminal study by Berker [4] of pseudoplanar flows that occur in an orthogonal rheometer, essentially two parallel disks rotating about non-coincident axes at the top and bottom, to the case of an electroactive elastic solid. We obtain the expression for the stress, which is a function of the deformation as well as the electric field, in an electroactive elastic solid using standard representation theorems. We show that in the case of elastic solids, pseudoplanar displacements can take place, with each layer z = constant rotating about a distinct center of rotation. We determine the nature of the locus of the centers of rotation, which can take on profiles that are distinctly different, based on the nature of the electric field, the applied pressure gradient and the rotation of the top and bottom plates.