Modelling of ionic polymer–metal composites by a multi-field finite element method

Ionic polymer–metal composites (IPMCs), a new type of smart material, offer the attractive features of high sensitivity and light weight for developing novel designs in the fields of dynamic sensors, robotic actuators and artificial muscles. The non-linear water molecule diffusion resistance force exists in the process of sodium ion migration, which may cause a significant effect on the dynamic electro-mechanical properties of this kind of material. In this paper, Tadokoro's model constructed by taking the electrostatic force, the viscous resistance force, the sodium ion diffusion force, and the water molecule diffusion resistance force into account was applied for simulation of electro-mechanical properties of IMPC. By coupling these forces and based on the principle of internal force equilibrium and the laws of motion, a multi-field finite element method (MFFEM) was derived using the dynamic electro-mechanical model, and a numerical solving scheme was proposed. Using the MFFEM, the electro-active behaviours of an IPMC beam have been simulated and discussed. The simulation results show that the water molecule diffusion resistance force has various effects on an IPMC beam, such as the water concentration, charge density of sodium ions and internal equilibrium forces. Furthermore, MFFEM has also been applied to study the migration speed of the hydrated sodium ions, electric-field intensity and bending displacement distribution across the thickness direction of the IPMC beam. Compared with the experimental findings reported by other investigators, it has been demonstrated that the proposed method provided a more realistic and scientific way to predict the electro-mechanical behaviours of IPMC by introduction of the non-linear force component in the model. Hence, the accuracy of prediction may also be improved and more information may be provided for developing new IPMC devices.