Modeling the actuation of curved ionic polymer metal composites

An ionic polymer metal composites (IPMC) is a soft actuator that consists of an ionomer membrane, neutralized by mobile counterions and plated by metal electrodes. Despite their early promise in robotics, medical devices, and microsystem technologies, widespread application of IPMC actuators is far from being reached. Recent advancements in additive manufacturing technologies have the potential to expand the reach of IPMCs by affording the realization of complex, design-specific geometries that were impossible to attain with standard manufacturing techniques. For this potential to be attained, it is critical to establish physically-based models that could inform 3D printing, beyond the flat, thin, non-tapered geometries that have been the object of investigation for almost three decades. Here, we bridge this gap by presenting an analytical framework to study actuation of a double-clamped IPMC arch under an applied voltage. We adopt a thermodynamically the consistent continuum model to describe the coupled electrochemo-mechanical phenomena taking place within the IPMC. We establish an analytical solution for the electrochemistry using the method of matched asymptotic expansions, which is, in turn, utilized to compute osmotic pressure and Maxwell stress. The mechanical response of the IPMC arch is modeled as a plane strain problem with an induced state of eigenstress, which is solved with the use of a smooth Airy function. The accuracy of our analytical solution is validated through finite element simulations. Through a parametric analysis, we investigate the effect of curvature on the deformation and the reaction forces exerted by the clamps. The proposed analytical framework offers new insight into the response of curved IPMCs, in which progress on 3D printing should be grounded.