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E. Hansy-Staudigl, M. Krommer:
"Charge-controlled actuation of dielectric elastomers";
Talk: 3rd Seminar on Ferroic Functional Materials / 13th International Workshop on Direct and Inverse Problems in Piezoelectricity, Kassel; 2017-10-04 - 2017-10-06.

In this talk we study dielectric elastomer actuators in the form of a thin layer with two compliant electrodes. In such actuators two main sources of electro-mechanical coupling are present - electrostatic forces acting between the electric charges and electrostriction due to intramolecular forces of the material, see [1]. In [2] we have accounted for electrostatic forces for the case of voltage-controlled actuators only. In voltage-controlled dielectric elastomer actuators the electric field is known to cause a pull-in instability at a so-called breakdown voltage. This penomenen is not observed in charge-controlled actuators. However, a different instability, named charge local- ization instability has been reported in the literature for the case of electro-mechanical coupling by means of electrostatic forces, see [3]. In this talk we extend our formula- tion from [2] to electrostriction as well as to the case of charge-controlled actuators to study the necking instability in more detail. Basically, the free energy is additively decomposed into a purely mechanical part and an electrical part. The mechanical free energy, for which we use a neo-Hookean strain energy function, is a function of the mechanical right Cauchy-Green tensor, and the electrical free energy depends on the material electric field and the total right Cauchy-Green tensor. Moreover, the mechanical right Cauchy-Green tensor follows from a multiplicative decomposition of the deformation gradient tensor into an elastic deformation gradient tensor and an electric deformation gradient tensor; by means of the latter we account for electrostriction. Charge-controlled actuation is finally introduced through the Gauss law of electrostatics.