The Deformation–Diffusion Coupling in Thin Elastomeric Gels

Abstract

Elastomeric gel is a three-dimensional network of cross-linked polymer which are able to swell in an environment containing solvent molecules. When a gel undergoes external load or stimuli such as solvent concentration and temperature, the gel evolves over time in which solvent diffusion is coupled to the elastic deformation of the network. We first present a mixture formulation of elastomeric gels and derive the linearized deformation–diffusion coupling model based on the incremental motion and the Onsager’s variational principle. Then, we derive the Föppl–von Kármán equations for gel sheets by making dimensional reduction of the deformation–diffusion coupling model.