Electro-active polymers undergo large deformations while being typically very thin; this encourages us to study the geometric nonlinear set up within the structural mechanics framework of thin plates and shells as a material surface. In this paper, the full set of three dimensional, geometric nonlinear field equations are incorporated to develop constitutive relations by introducing a generalized free energy function, which takes parts from a pure mechanical strain energy (e.g. neo-Hookean) and a mixed electro-mechanical free energy. The key feature is the multiplicative decomposition of the deformation gradient tensor, which allows for separate constitutive models for any electro-mechanic coupling phenomenon. We apply this model exemplary to the case of electrostriction and use the Gauss law of electrostatics in order to incorporate charge controlled actuation, which has been reported to omit pull-in instability. In order to translate the resulting equations to their two-dimensional geometrically nonlinear counterparts for thin plates, a plane stress condition is imposed on the total stress tensor and the effect of the electrostrictive coupling is investigated on voltage controlled as well as on charge controlled actuation, employing non-linear Finite Elements. Finally, results are compared to numerical as well as experimental results on electrostrictive coupling and charge controlled actuation.
Elisabeth Staudigl, Michael Krommer, Yury Vetyukov, and Alexander Humer, "Nonlinear electro-elastic modeling of thin dielectric elastomer plate actuators," Proc. SPIE 10594, Electroactive Polymer Actuators and Devices (EAPAD) XX, 105940F (Presented at SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring: March 06, 2018; Published: 27 March 2018); https://doi.org/10.1117/12.2295881.
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