Equilibrium of a solute in an elastic continuum -A statistical approach

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Department of Mechanical Engineering-Engineering Mechanics


A theory of stress-assisted diffusion has been previously derived using continuum mechanics by E. C. Aifantis [1]. This theory has subsequently served as the basis for a model of material degradation by Unger and Aifantis [2]. In this model, an equilibrium solution of Aifantis' stress-assisted diffusion equation was used to determine the distribution of a solute in an elastic continuum. However, as continuum mechanics gives no direct correlation between material coefficients and other physical characteristics such as temperature, these models relied solely on experimental data to determine the phenomenological coefficients of the theory. This process naturally limits the predictive capabilities of the model. In this paper we rederive the equilbrium distribution of a solute in an elastic stress field. We show that the use of a statistical approach can provide additional information about the various coefficients appearing in the equilibrium solution of the phenomenological theory. An equilibrium distribution for a dilute gas in an ideal gas thermostat is derived using statistical mechanics. It takes the form of the equilibrium solution of Aifantis' stress-assisted diffusion theory in terms of the hydrostatic stress and diffusion coefficients. However, as a result of the statistical approach, additional information is gained for the coefficients in terms of the temperature and number of atoms in the thermostat.

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© 1990 Springer-Verlag. Publisher’s version of record: https://doi.org/10.1007/BF01176990

Publication Title

Acta Mechanica