Transient stability analysis of composite hydrogel structures based on a minimization-type variational formulation

We employ a canonical variational framework for the predictive characterization of structural instabilities that develop during diffusion-driven transient swelling hydrogels under geometrical constraints. The formulation finite elasticity coupled with Fickian diffusion has two-field minimization structure, wherein deformation map and fluid-volume flux are obtained as minimizers time-discrete potential involving internal external energetic contributions. To analyze stability certain equilibrium state gel satisfying principle, we apply local criterion on incremental potential, which is based idea stable lowest energy among all possible states within an infinitesimal neighborhood. Using this in finite-element context, it understood bifurcation-type activated when global stiffness matrix loses its positive definiteness . This concept then applied to determine onset nature wrinkling occurring pair representative film-substrate hydrogel systems. In particular, dependencies critical buckling load mode shape system geometry material parameters.