Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fosdick, R.: On the thermostatic behavior of coexistent phases and critical point analysis in elastic solids. Lecture notes
Aregba-Driollet, D., Diele, F., Natalini, R.: A mathematical model for the SO\(_2\) aggression to calcium carbonate stones: Numerical approximation and asymptotic analysis. SIAM J. Appl. Math. 64, 1636–1667 (2004)
Tanaka, T.: Collapse of gels at critical endpoint. Phys. Rev. Lett. 40(12), 820–823 (1978)
Flory, P.J., Rehner, J.: Statistical mechanics of cross-linked polymer networks – II swelling. J. Chem. Phys. 11(11), 521–526 (1943)
Katchalsky, A., Michaeli, I.: Polyelectrolyte gels in salt solutions. J. Polym. Sci. 15, 69–86 (1955)
Baek, S., Srinivasa, A.R.: Modeling the pH-sensitive behavior of an ionic gel in the presence of diffusion. Int. J. Non-linear Mech. 39, 1301–1318 (2004)
Rajagopal, K.R., Tao, L.: Mechanics of Mixtures. World Scientific, Singapore (1996)
Treolar, L.R.G.: The physics of Rubber Elasticity. Oxford University Press, London (1958)
Rajagopal, K.R., Roubívček, T.: On the effect of dissipation in shape-memory alloys. Nonlinear Anal. 4, 581–597 (2003)
Bhattacharya, K.: Comparison of geometrically nonlinear and linear theories of martensitic transformation. Cont. Mech. Thermodyn. 5, 205–242 (1993)
Ericksen, J.: Equilibrium of bars. J. Elast. 5, 191–201 (1975)
Ericksen, J.: Introduction to the Thermodynamics of Solids. Chapman & Hall, London (1991)
Gibbs, J.W.: On the equilibrium of heterogeneous substances. Trans. Conn. Acad. III, 108–248 (1875–1978)
Dunn, J.E., Fosdick, R.: The morphology and stability of material phases. Arch. Rat. Mech. Anal. 74, 1–99 (1980)
Fosdick, R., Royer-Carfagni, G.: The static state of a two-phase solid mixture in a stressed elastic bar. Int. J. Solids Struct. 33, 2267–2281 (1996)
Fosdick, R., Royer-Carfagni, G.: Alloy separation of a binary mixture in a stressed elastic sphere. J. Elast. 42, 49–77 (1996)
Bugini, R., Laurenzi-Tabasso, M., Realini, M.: Rate of formation of black crusts on marble. A case study. J. Cult. Herit. 1, 111–116 (2000)
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to J. L. Ericksen for his contributions to mechanics.
Rights and permissions
About this article
Cite this article
Buonsanti, M., Fosdick, R. & Royer-Carfagni, G. Chemomechanical Equilibrium of Bars. J Elasticity 84, 167–188 (2006). https://doi.org/10.1007/s10659-006-9062-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10659-006-9062-4