A solid–shell formulation based on the assumed natural inhomogeneous strains for modeling the viscoelastic response of electro-active polymers

A complete thermo-electro-viscoelastic characterization of dielectric elastomers, Part II: Continuum modeling approach

“…Finally, the coupling of the mechanical material response to the application of an electric field has to be established. For this, numerous different formulations can be found in the literature, amongst others in the publications of Ask et al [17,49], Saxena et al [50] or Jabareen [51]. The approach adopted in the context of this work originates from the ideas presented in the works of Steinmann [52] and Dorfmann and Ogden [53].…”

“…Alternatively, the parameter c 1 (E) is also multiplied with the purely mechanical first invariant I 1 , which may be interpreted as a deformation-dependent formulation of the coupling parameters. Thus, the approach chosen herein is in accordance with the concepts presented in [49,51]. Within the scope of this work, we will extend on the formulation given in [40], in which the field sensitivity is captured exclusively by additional terms in the elastic energy contribution.…”

“…which is the definition of the electric field strength in the undeformed configuration. Throughout the literature, the form of the first four invariants is consistent, see for example [62,63,18,51]. However, for the form of the two remaining invariants I 5 , I 6 that describe the coupling between the electric field and the mechanical deformation, two different options can be found.…”