Finite element modeling of hydrogel swelling under arbitrary confinements

Hydrogels are polymer networks that have an incredible capacity to absorb water while remaining intact. This makes them amenable to a variety of different practical applications. Due to the inevitable involvement of shape change, continuum modeling of hydrogels is often restricted to simple geometries. Incorporating constraints presents further challenges. In this work, we present a finite element model of hydrogel swelling in the presence of arbitrary impenetrable confinements, written in Morpho, an open-source programmable environment for shape optimization. We demonstrate the versatility of our approach by investigating a variety of different confinements and analyze the swelling ratios as well as the internal stress-strain variations resulting from them.