Electroelastic constitutive model for dielectric semilinear hyperelastic solids with application to radial deformation of a rotating tube

This paper develops a new thermodynamically consistent electroelastic constitutive model for dielectric semilinear hyperelastic solids. It shows effects of externally applied electric field and angular speed on displacement function of radially deforming rotating tubes. The Frechet derivative and laws of thermodynamics are employed to derive the constitutive model. Electro-mechanical field equations, together with the obtained constitutive model, are used to provide solution to the problem of radial deformation of a rotating tube. The obtained electric field-dependent stress response and deformation-sensitive electric field function show that at points within electroactive solids, deformation of material gives rise to redistribution of electric displacement field, and this in turn yields redistribution of stresses. Furthermore, in the absence of externally applied electric field, the constitutive model gives mechanical behaviour of the solids; and when the stretch tensor equals unit tensor, the model gives electrical behaviour of the solids. Finally, and among other things, the presence of charge generates negative radial displacement field (towards the center) in the tube which gets nullified as the angular speed increases.