Abstract

In the present work, a numerical framework to simulate the bending and actuation behavior of stimuli-responsive polymer gels is presented. Specifically, polyelectrolyte gels (or hydrogels) and magnetic gels (or ferrogels) of permanent network structures, i.e., chemical gels, are investigated. The former is usually regarded as electroactive gels in the literature, while the latter falls into the category of magnetoactive gels. The response of a polymer gel to environmental changes is usually realized in the form of conformational changes. Swelling of a polymer gel due to the pH variation of the system, bending of a polyelectrolyte gel because of an externally applied electric field, and elongation of a magnetic gel sphere in a magnetic field are examples of such conformational changes. The modeling approach is based on the multicomponent, multiphase nature of hydrogels and ferrogels. The constituents of hydrogels and ferrogels, therefore, need to be identified. The theory of mixtures is adopted for derivation and presentation of the respective field equations along with the theory of electromagnetism. Using the procedure introduced, a coupled chemo-electro-mechanical formulation for hydrogels and a magneto-mechanical formulation for ferrogels are achieved. Both formulations are numerically treated in 2D using the finite element method. Using the developed numerical procedure, the actuation mechanism of the polymer gels under study can be simulated. For hydrogels, the aim is to simulate the local bending deformation under the electrical stimulation for the application as hydrogel grippers. A system consisting of both an anionic gel and a cationic gel, immersed in NaCl solution bath, is considered. By the application of an electric field between two electrodes on the top and bottom of the solution bath, gels bend towards or away from each other, mimicking the closing and opening of a hydrogel gripper. Deformation (elongation or contraction) of ferrogels under an applied magnetic field is also simulated using the finite element method. By the finite element simulation, elongation of a ferrogel is observed parallel to the applied magnetic field and contraction of a ferrogel is seen perpendicular to the applied magnetic field. With the modeling approach of the present work, the resulting mechanical deformation of a ferrogel, in an applied magnetic field, can be determined.