Obstructed swelling and fracture of hydrogels

Obstacles influence growth and expansion in a wide range of biological and non-biological processes, but isolating and understanding their impact can be difficult in complex systems. We study obstructed expansion in a simple system accessible with experiments, simulations, and theory---a crosslinked polymer network called a hydrogel swelling around fixed cylindrical pillars. In experiments, we observe that some obstacle geometries permit hydrogels to swell around the obstacles and remain intact, while other configurations force hydrogels to fracture as they expand. In order to predict which obstacle geometries are likely to prevent or promote fracture, we use finite element simulations to study the stresses that build up during swelling. Applying lessons from indentation theory, poroelasticity, and nonlinear continuum mechanics, we develop a theoretical framework for understanding how the maximum principal compressive and tensile stresses vary as a function of obstacle geometry in the long-time limit.