Polymeric gels consist in a cross-linked polymer chains network which contains a large quantity of solvent molecules. The main property of gels is their ability to absorb solvent molecules without being dissolved, and to shrink when they release fluid. This swelling/deswelling phenomenon involves large volume changes of the gel, when the solvent diffuses into the large strain elastic solid.
In recent literature, constitutive equations, in which the gel is considered as a single continuum body, have been derived to describe such a coupled deformation/diffusion problem. However, these works are based on the simple mono-dimensional models of both Flory and Treloar devoted to rubber swelling. The aim of the present work is the derivation of a new constitutive equation based on an original definition of the elastic strain energy. The differences with the classical theory are highlighted on two simple examples.