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A couple of papers on the modeling of swelling gels

The first paper presents an original formulation of a three-dimensional non-linear model coupling elasticity and solvent migration which can be employed to describe swelling phenomena in neutral gels. A swollen state is chosen as the reference configuration and the swelling constraint, which relates the amount of solvent entering the body and the induced change in volume, usually written in the dry state, is re-formulated to agree with the choice of a reference configuration which is not dry. Moreover, the formulation discussed in the paper allows for a description of the surface spreading and absorption of the solvent on the boundary of the gel, that may be important in some applications, in a consistent theoretical framework which considers the boundary as a physical surface (i.e. a surface equipped with its own balance equations). Then, a discussion regarding the representation form of the mobility tensor, including the case of anisotropic diffusion, is presented. The finite element model is also introduced and applied to the study of an experiment regarding bending deformations in a gel bar. 

The second paper concerns a plane stress-diffusion and 1D linear models aimed at specifically describing swelling-induced bending deformations in a gel bar. The linearization procedure around a pre-swollen equilibrium state is carried out in a thermodynamically-consistent framework, starting from the 3D non-linear theory coupling solvent migration and elasticity, and leads to the formulation of the 3D poroelastic (linear) theory for gels, from which the reduced models are derived. The models are applied to an experiment on the bending of a gel bar. 

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