  Electroactive polymers such as dielectric elastomers (DEs) have attracted
significant attention in recent years. Computational techniques to solve the
coupled electromechanical system of equations for this class of materials have
universally centered around fully coupled monolithic formulations, which while
generating good accuracy requires significant computational expense. However,
this has significantly hindered the ability to solve large scale, fully
three-dimensional problems involving complex deformations and electromechanical
instabilities of DEs. In this work, we provide theoretical basis for the
effectiveness and accuracy of staggered explicit-implicit finite element
formulations for this class of electromechanically coupled materials, and
elicit the simplicity of the resulting staggered formulation. We demonstrate
the stability and accuracy of the staggered approach by solving complex
electromechanically coupled problems involving electroactive polymers, where we
focus on problems involving electromechanical instabilities such as creasing,
wrinkling, and bursting drops. In all examples, essentially identical results
to the fully monolithic solution are obtained, showing the accuracy of the
staggered approach at a significantly reduced computational cost.
