Modeling Viscoelastic Dielectrics

Dielectric elastomer, as an important category of electroactive polymers, is known to have viscoelastic properties that strongly affect its dynamic performance and limit its application. Very few models accounting for the effects of both electrostatics and viscoelasticity exist in the literature, and even fewer are capable of making reliable predictions under general loads and constraints. Based on the principals of nonequilibrium thermodynamics, this paper develops a field theory that fully couples the large inelastic deformations and electric fields in deformable dielectrics. Our theory recovers existing models of elastic dielectrics in the equilibrium limit. This paper proposes, in a general nonequilibrium state, the mechanism of instantaneous instability which corresponds to the pull-in instability often observed on dielectric elastomers. Most finite-deformation constitutive relations and evolution laws of viscoelastic solids can be directly adopted in the current theoretical framework. As an example, a specific material model is selected and applied to the uniform deformation of a dielectric elastomer. This model predicts the stability criteria of viscoelastic dielectrics and its dependence on loading rate and the effect of pre-stress and relaxation. The dynamic response and the hysteresis behavior of a viscoelastic dielectric elastomer under cyclic electric fields are also studied.