On structural models for ionic polymer metal composites

Ionic polymer metal composites (IPMCs) are a class of soft electroactive polymers. IPMCs comprise a soft ionic polymer core, on which two stiff metal electrodes are plated. These active materials exhibit large bend- ing upon the application of a small driving voltage across their electrodes, in air or in aqueous environments. In a recent work, we presented compelling theoretical and numerical evidence suggesting that ionic polymer membranes exhibit complex multiaxial deformations neglected by reduced-order structural models. Where most beam theories (including Euler-Bernoulli, Timoshenko, and most higher-order shear deformation models) would suggest vanishing through-the-thickness deformation, we discover the onset of localized deformation that rever- berates into axial stretching. Building upon this effort, here we investigate the role of the electrodes and shear on multiaxial deformations of IPMCs. We establish a novel structural theory for IPMCs, based on the Euler- Bernoulli kinematics enriched with the through-the-thickness deformation in the ionic polymer, computed from a Saint-Venant-like problem for uniform bending. While considering boundary conditions that elicit non-uniform bending, we compare the results of this model against classical Euler-Bernoulli beam theory without enrichment and finite element simulations, encapsulating the nonlinear response of the material. We demonstrate that our theory can predict the macroscopic displacement of the IPMC, along with the localized deformation in the ionic polymer at the interface with the electrodes, which are not captured by the classical Euler-Bernoulli beam theory. This work paves the way to the development of more sophisticated structural theories for IPMCs and analogous active materials, affording an accurate description of deformations at a limited computational cost.