Multiaxial deformations of ionic polymer metal composites

Abstract

Ionic polymer metal composites (IPMCs) are a promising class of soft active materials. Their high compliance, low actuation voltage, and ability to operate in wet environments have motivated two decades of intensive research on IPMC actuators. While we have witnessed several breakthroughs in the technology of IPMCs, from additive manufacturing to IPMC-based robots, our understanding of the physical underpinnings of their actuation remains elusive. There is a paucity of continuum physically-based models to investigate IPMC actuation, where the literature relies on structural models that postulate admissible mechanical deformations from classical beam or plate theories. In this sense, we know little about multiaxial deformations elicited by counterions’ diffusion and electromigration through the ionomer. Here, we demonstrate that macroscopic actuation of IPMCs is accompanied by localized mechanical deformations in the vicinity of the electrodes, caused by osmotic pressure and Maxwell stress. Toward this aim, we put forward a comprehensive nonlinear finite element analysis, conducted in Abaqus™ through a newly developed user element that allows for testing hypotheses on the inner workings of IPMC actuation and exploring complex configurations. Alongside with computational advances, we establish an exact solution for the two-dimensional Saint-Venant problem of plane-strain actuation of an IPMC, based on linear elasticity and nonlinear electrochemistry. Verified against finite element results, the exact solution offers a mathematically-tractable treatment of localized phenomena in the vicinity of the electrodes. Our results unveil a rich dependence of through-the-thickness deformation on the electric double layers that are formed in the vicinity of the electrodes. Due to the asymmetry of the boundary layers in the vicinity of the cathode and the anode, the ionomer deforms asymmetrically with respect to its mid-axis that also experiences an axial stretch. The Poisson ratio of the ionomer is found to have a critical role in shaping the response of the IPMC, from the onset of actuation to its back-relaxation. This study constitutes a first modeling step toward illuminating complex, multiaxial deformations of IPMCs, whose understanding is critical toward the design and manufacturing of high performance IPMC actuators.