Chemomechanical equilibrium of bars

The chemomechanical equilibrium of an elastic bar in contact with a chemically aggressive environment is considered. In the proposed model, we neglect dissipative phenomena associated with entropy production and we surmise that equilibrium states are minimizers of the free energy of the system. The free energy depends upon the axial strain in the bar and the degree of reaction of its constituent material with an external agent which is dispersed in a surrounding vapor or liquid solution. The chemical potential of the external agent is assigned. In general, the corresponding minimization problem is nonconvex and it predicts the coexistence of equilibrium phases, induced by mechanical loading and/or environmental chemical composition. The model is germane to the description of several phenomena, such as the swelling of ionic gels in a solvent of varying pH, or the formation of expanding crusts in stone monuments due to acid rain or an otherwise polluted atmosphere.