The increasing precision of shapes and displacements required by structures in both, aerospace and precision mechanics, as well as the desire of health monitoring of damaged components, lead to the concept of structures with actuatoric and sensoric capabilities. The basis for the adaptive structures are multi-functional materials. A very promising representative of these materials are electroactive polymers (EAP). In the first section of this paper we give a short overview on this group of materials. In the following we focus our interest on polyelectrolyte gels which is one key material of EAP. These gels - consisting of a polymer network with fixed ionizable groups and a liquid phase with mobile ions - are distinguished by enormous swelling capabilities under the influence of external physical or chemical stimuli. These properties make them very attractive for a new generation of "pseudomuscular" actuators. In the present work we investigate chemically and electrically stimulated polymer gels. At first we give a model based on the theory of "swelling of network structures" by Flory (1953). In the third section we present a coupled chemo-electro-mechanical multi-field formulation which is capable to describe the phenomena occulting in the different fields. Then, an overview over the space-time finite element discretization method is given. These unconditionally stable finite elements give the possibility to treat the phenomena in space and time equally. In the last section, chemical as well as electrical stimulation is considered. The numerical simulation is computed for all the fields involved. The numerical results of the electric potential show a promising correlation with experiments in which the Donnan potential has been registered in PAAm/PAA gels with a new microelectrode technique. For anionic gels, in both theory and experiment "hyperpolarisation", i.e. increased negativity, can be found on the anode-side of the gel and "depolarisation" on the cathode-side. These changes in the electric potential, which are supposed to affect swelling or deswelling of polyelectrolyte gels, lead to bending deformations of the gel.
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