Finite element modeling and validation of a soft array of spatially coupled dielectric elastomer transducers

Dielectric elastomer (DE) transducers are suitable candidates for the development of compliant mechatronic devices, such as wearable smart skins and soft robots. If many independently-controllable DEs are closely arranged in an array-like configuration, sharing a common elastomer membrane, novel types of cooperative and soft actuator/sensor systems can be obtained. The common elastic substrate, however, introduces strong electro-mechanical coupling effects among neighboring DEs, which highly influence the overall membrane system actuation and sensing characteristics. To effectively design soft cooperative systems based on DEs, these effects need to be systematically understood and modeled first. As a first step towards the development of soft cooperative DE systems, in this paper we present a finite element simulation approach for a 1-by-3 silicone array of DE units. After defining the system constitutive equations and the numerical assumptions, an extensive experimental campaign is conducted to calibrate and validate the model. The simulation results accurately predict the changes in force (actuation behavior) and capacitance (sensing behavior) of the different elements of the array, when their neighbors are subjected to different electro-mechanical loads. Quantitatively, the model reproduces the force and capacitance responses with an average fit higher than 93% and 92%, respectively. Finally, the validated model is used to perform parameter studies, aimed at highlighting how the array performance depends on a relevant set of design parameters, i.e. DE-DE spacing, DE-outer structure spacing, membrane pre-stretch, array scale, and electrode shape. The obtained results will provide important guidelines for the future design of cooperative actuator/sensor systems based on DE transducers.