Diffusion-driven swelling-induced instabilities of hydrogels

Under a variety of external stimuli, hydrogels can undergo coupled solid deformation and fluid diffusion and exhibit large volume changes. The numerical analysis of this process can be complicated by numerical instabilities when using mixed formulations due to the violation of the inf-sup condition. In addition, the large deformations produce complex instability patterns causing singularities in the underlying set of equations. For these reasons, the experimentally observed complex patterns remain elusive and poorly understood. Furthermore, a stability criterion suitable to detect critical conditions and predict post-instability patterns is lacking for hydrogel simulations. Here we investigate the stability criterion for coupled problems with a saddle point nature and propose a generic framework to study diffusion-driven swelling-induced instabilities of hydrogels. Adopting a numerically stable subdivision-based mixed isogeometric analysis, we show that the proposed framework for stability analysis accurately captures instability points during the transient swelling of hydrogels. The influence of geometrical and material parameters on the critical conditions are also presented in stability diagrams for two useful problems involving the buckling of hydrogel rods and the wrinkling on the surface of hydrogel bilayers. The results show that the short-time response of hydrogels immersed in water are highly unstable. We believe that this generic scheme provides a theoretical and computational foundation to study the morphogenesis in nature, and it also paves the way to create functional materials and design novel hydrogel devices through stability diagrams. (C) 2018 Elsevier Ltd. All rights reserved.