Coupled Multi-field Formulation in Space and Time for the Simulation of Intelligent Hydrogels

Hydrogels are hydrophilic polymer networks. Immersed in water-based solutions they show an enormous swelling due to the inflow of water into the network. In the case of charged hydrogels the polymer network additionally contains bound charges which influence the diffusion of dissolved charges in ionic solutions. The swelling of the hydrogels can be influenced by various external stimuli such as temperature, pH value, concentration of dissolved ions in the solution, or applied electric fields. By varying these parameters the state of the hydrogels can be selectively affected. This accounts for the designation `intelligent hydrogels'. Applications of this type of material can be either as sensors e.g., for pH value or ion concentrations in solutions (Gerlach et al., 2005), or as actuators e.g., as artificial muscles or chemo-electric energy converters (Shiga and Kurauchi, 1990; Gülch et al., 2001). In either case the coupling of chemical, electrical, and mechanical field variables is exploited. In order to simulate the complicated behavior of hydrogels, a mathematical description of the coupled three-field problem is necessary. In the present work, an approach to a fully coupled three-field description using the finite element method is made. The formulation of the problem is based on the works of Wallmersperger et al. (2001, 2004b), who have sequentially solved the three-field problem by first calculating the coupled chemo-electric system and then using the results as input for a mechanical analysis. As an advancement of this modeling approach, a specialized finite element containing degrees of freedom for chemical concentrations, electric potential, and mechanical displacements is developed. It enables a fully coupled simultaneous solution of the three-field problem and makes it possible to describe the hydrogel behavior in sensor as well as in actuator-applications. The implementation is conducted as a user-defined element in the commercial software package ABAQUS. For the numerical solution the Newton-Raphson method in conjunction with the backward Euler time integration scheme is applied. Results for the electrical stimulation, proving the applicability of the developed numerical model, are obtained.