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

[摘要] We employ a canonical variational framework for the predictive characterization of structural instabili-ties that develop during the diffusion-driven transient swelling of hydrogels under geometrical con-straints. The variational formulation of finite elasticity coupled with Fickian diffusion has a two-field minimization structure, wherein the deformation map and the fluid-volume flux are obtained as minimiz-ers of a time-discrete potential involving internal and external energetic contributions. To analyze the structural stability of a certain equilibrium state of the gel satisfying the minimization principle, we apply the local stability criterion on the incremental potential, which is based on the idea that a stable equilib-rium state has the lowest potential energy among all possible states within an infinitesimal neighbor-hood. Using this criterion in a finite-element context, it is understood that bifurcation-type structural instabilities are activated when the coupled global finite-element stiffness matrix loses its positive defi-niteness. This concept is then applied to determine the onset and nature of wrinkling instabilities occur-ring in a pair of representative film-substrate hydrogel systems. In particular, we analyze the dependencies of the critical buckling load and mode shape on the system geometry and material parameters. (c) 2021 Elsevier Ltd. All rights reserved.

[发布日期] 2021-11-01

[关键词] Hydrogels;Diffusion;Chemo-mechanical coupling;Variational minimization principle;Transient structural instabilities