On structural theories for ionic polymer metal composites: balancing between accuracy and simplicity

Ionic polymer metal composites (IPMCs) are soft electroactive materials that are finding increasing use as actuators in several engineering domains, where there is a need of large compliance and low activation voltage. Similar to traditional sandwich structures, an IPMC comprises a hydrated ionomer core that is sandwiched by two stiffer electrodes. The application of a voltage across the electrodes drives charge migration within the ionomer, which, in turn, contributes to the development of an eigenstress, associated with osmotic pressure and Maxwell stress. Critical to IPMC actuation is the variation of the eigenstress through the thickness of the ionomer, which is responsible for strain localization at the ionomer-electrode interfaces. Despite considerable progress in the development of reliable continuum theories and finite element tools, accurate structural theories that could beget physical insight into the inner workings of IPMC actuation are lacking. Here, we seek to bridge this gap by contributing a principled methodology to structural modeling of IPMC actuation. Our approach begins with the study of the IPMC electrochemistry through the method of matched asymptotic expansions, which yields a semi-analytical expression for the eigenstress as a function of the applied voltage. Hence, we establish a total potential energy that accounts for the strain energy of the ionomer, the strain energy of the electrodes, and the work performed by the eigenstress. By projecting the IPMC kinematics on select beam-like representation and imposing the stationarity of the total potential energy, we formulate rigorous structural theories for IPMC actuation. Not only do we examine classical low-order and higher-order beam theories, but we also propose enriched theories that account for strain localization near the electrodes. The accuracy of these theories is assessed through comparison with finite element simulations on a plane-strain problem of non-uniform bending. Our results indicate that an enriched Euler-Bernoulli beam theory, with three independent field variables, is successful in capturing the main features of IPMC actuation at a limited computational cost.