The role of stress on chemical transformations in an elastic bar with nonconvex chemomechanical free energy<br/><br/><br/><br/>
Saturday, November 6, 2004 - 4:00pm - 4:30pm
Gianni Royer-Carfagni (Università di Parma)
The equilibrium of an elastic bar capable of undergoing chemomechanical transformations and in contact with a chemically aggressive environment is considered. In the proposed model, stable equilibrium states are identified with minimizers of a specific free energy functional, which depends upon the axial strain of the bar and the extent of reaction with an external agent, which is dispersed in a surrounding vapor or liquid solution with assigned chemical potential. In general, the corresponding minimization problem is nonconvex and, therefore, it predicts the coexistence of equilibrium phases. This work is related to the now classical problem of Ericksen for an elastic bar stretched in either a hard or a soft testing machine. However, here, the presence of an additional internal variable, which represents the extent of reaction, allows for phase transformations which are stress-induced and/or driven by changes in the chemical composition of the surrounding environment. We discuss a characterization of hard or soft environmental chemical boundary conditions. The model is germane to the description of several phenomena, such as the swelling of ionic gels under chemomechanical actions, or the formation of expanding crusts in stone monuments due to acid rain or an otherwise polluted atmosphere.