Gaseous diffusion in a stressed-thermoelastic solid. Part I: The thermomechanical formulation

A phenomenological theory is proposed for the diffusion of a dilute solution of a gas in a thermoelastic solid. It is assumed that the thermomechanical behavior of the solid is unaffected by the presence of the gas. On the other hand the presence of the solid is recognized by the gas by letting certain thermomechanical variables of the solid to enter into the constitutive equations of the gas. The constitutive functionals of the gas are restricted by the principles of continuum physics. These principles are currently referred to as equipresence, material objectivity, entropy production inequality, as well as the balance equations of mass, linear and angular momentum and internal energy. By this approach, axiomatic statements on the existence of equations of state are avoided and the classical results of linear irreversible thermodynamics are obtained by further specialization of the proposed theory.