Constitutive model development and micro-structural topology optimisation for nafion hydrogel membranes with ionic clustering.

The deployment of electroactive ionic polymer hydrogel-metal composites in artificial muscle and BioMEMS applications has recently been intensively investigated. In order to analyse their electromechanical responses to externally applied electrical fields, it is critical to develop a constitutive model linking the macro-mechanical moduli with the micro-mechanical characteristics, and to determine the geometric size and shape of the micro-structural cluster and investigate the effect of cluster morphology on the effective electro-elastic moduli of the polymer hydrogels. As a typical ionic polymer-based hydrogel, the Nafion membrane is studied in this work. Based on the Biot poroelasticity theory, a multi-scale constitutive model which includes both macro and micro characteristics is developed using an asymptotic homogenisation method. The effect of water-volume fraction on the effective elastic moduli of the hydrogel membrane is examined for different equivalent weights. Numerical investigations show that the simulated effective constitutive moduli agree well with experimental data. The presently developed constitutive model is thus validated. In order to determine the micro-structural shape of the polymer skeleton subject to fluid pressure, a representative volume element (RVE) is designed by topology optimisation of the periodic microstructures of the Nafion hydrogels, through the minimisation of the electro-elastic interaction energy between the polymer-based fluorocarbon matrix and the surrounding fluid. This optimal RVE correctly predicts the geometric shapes of the clusters.