Modeling the Stimulus-Responsive Behaviors of Fiber-Reinforced Soft Materials

Hydrogels can change their size upon swelling. The swelling ratio is the same for all directions in the stress-free state. Dielectric elastomers can reduce their thickness and expand the area upon an electric field. Similarly, the expansion ratio in the plane is also the same for different directions. This isotropic shape change effect limits the function of these soft materials in certain circumstances. To address this issue, recent works have shown that the incorporation of fibers into the polymer matrix can induce an anisotropic response upon external stimulus. In this work, we develop multi-field coupling models for both fiber-reinforced hydrogels and dielectric elastomers. For the former, the change in free energy is caused by the stretching of polymer chains and fibers and the mixing of solvents and polymer networks. The Fickian-type law is adopted for the solvent diffusion. The free energy density for the latter consists of a mechanical part, considering the deformation of both polymer matrix and fibers, and an electric polarization component. Gauss’s law is adopted to obtain the distribution of the electric field. The multi-field models are then implemented for finite element analysis. We consider the stimulus-responsiveness of bilayer strips with an active layer and a passive layer. Without fibers, the strips bend upon the external stimulus. In contrast, the shape changes to helix shapes, which can be further tuned by changing the distribution of fibers. The work provides an efficient design tool for self-folding structures based on stimulus-responsive polymers.