Thermomechanical modeling for gaseous diffusion in elastic stress fields

A mechanical theory is formulated for the diffusion of a gas, behaving as an elastic fluid, through an isotropic elastic solid. It is assumed that each point of the mixture is occupied simultaneously by both constituents in given proportions. The mechanical properties of each component are specified by means of constitutive equations for the stresses. Diffusion effects are accounted for by means of a body force acting on each constituent which depends upon the composition, the elasticity of the solid, and the relative motion of the substances in the mixture. Coupled diffusion equations for both constituents are derived. Uncoupling of the equations is attempted within a linearized theory by adopting particular motions for the mixture. The result is compared with the classical diffusion equations derived by intuitive modifications to the empirical Fick's law.