Transient stability analysis of composite hydrogel structures based on a minimization-type variational formulation. (November 2021)

• Record Type: Journal Article
• Authors: Sriram, S.; Polukhov, E.; Keip, M.-A.
• Is Part Of: International journal of solids and structures. Volume 230/231(2021)
• Publication Date: 2021-11
• Subjects: Hydrogels -- Diffusion -- Chemo-mechanical coupling -- Variational minimization principle -- Transient structural instabilities; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2021.111080
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: We employ a canonical variational framework for the predictive characterization of structural instabilities that develop during the diffusion-driven transient swelling of hydrogels under geometrical constraints. 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 minimizers 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 equilibrium state has the lowest potential energy among all possible states within an infinitesimal neighborhood. 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 definiteness . This concept is then applied to determine the onset and nature of wrinkling instabilities occurring 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.