Modeling of Inhomogeneous Deformation in a Dielectric Elastomer Generator for Energy Harvesting

Dielectric elastomer transducers promise to combine high energy density at low cost and lightweight when used as actuators or for energy harvesting generators. A cornucopia of possible applications have been demonstrated over the last years including soft matter based actuators for robotics, tunable optics, medical devices, space robotics and energy harvesters. Prestretch effects and the electromechanical instability have been shown to highly influence the performance of dielectric elastomer transducers. Nevertheless only sparse research has been done on instability and prestretch effects of dielectric elastomer membranes under inhomogeneous deformation. Dielectric elastomer transducers consist of an elastomer membrane sandwiched between a pair of compliant electrodes and can be considered as deformable capacitors with variable capacitance. Here we focus on a specific experimental setup well suited to study the performance of dielectric elastomer materials for energy harvesting. In this setup an elastomer membrane is equibiaxially prestretched and fixed on top of an air chamber which is connected to a compressed air reservoir, the source of mechanical energy for thegenerator. From the electrical point of view the compliant electrodes on the elastomer membrane can be connected to both a high and low voltage charge reservoir. Thus the change in capacitance during deformation can be used to boost charges from the low voltage reservoir to the high voltage reservoir. Experimentally, different constant voltages are applied to the elastomer membrane during inflation and the air chamber pressure is recorded together with the shape and the volume of the balloon for different initial prestretches. The usual instability in the pressure-volume curves of ballon inflation experiments are shown to be influenced by applied voltage and prestretch. Theoretically, the setup is modeled as a thermodynamic system, with static electric and mechanical load where quasi-static equilibrium states can be achieved. To describe the inhomogeneous deformation and to correctly account for the hyperelastic behavior of the material over the whole deformation range an asymmetric model is built based on the Arruda-Boyce material model. The results of the numerical simulation are fitted to the experimental data to obtain significant material parameters in order to predict the optimal operation regime of the dielectric elastomer generator. The experimental results accompanied by the theoretical analysis may be used as a benchmark for the applicability of dielectric elastomer generators and pave ways for understanding the dielectric elastomer behavior under inhomogeneous deformation.