A detailed solution framework for the out-of-plane displacement of circular dielectric elastomer actuators

The out-of-plane displacement (OPD) of a circular dielectric elastomer actuator (DEA) membrane has been explored in recent years for a variety of important applications. Circular DEAs consist of an elastomer membrane that is prestretched to a rigid frame and coated with compliant electrodes. Such a simple configuration has found many interesting applications such as in pumps, pulse tracking, hopping search and rescue robots, dielectric elastomer generators for renewable energy harvesting, linear actuators, and many others. Here, we present an easy-to-implement solution framework of the OPD for circular DEAs via a detailed numerical solution using the shooting method (SM) on a system of differential algebraic equations (DAE). The material model incorporated follows the robust Gent hyperelastic representation, and a comparison (of the OPD of a single-cone DEA) against a neo-Hookean based solution is included. The SM-based numerical solution to the resulting boundary value DAE problem is applied to a practical range of values based on the reported literature. Analysis of the results and comparison against other studies are provided. The current work provides a go-to framework for implementation in further research and development that can be useful to a broader audience including nonexperts in the field of soft robotics.