Preview of the Conclusions |
Regrettably, I think this problem has no elegant solution; stress fields such as Finley described, using a small number of intelligible terms, are perhaps not found in ideally isotropic materials; even this problem, selected to be the simplest possible that admits diffusion in two dimensions, perhaps suffers from intractable awkwardness. However, the second approach, emphasizing the material’s isotropy, brings some points of interest to the fore. I will therefore run through them, and hope that someone using Finley’s insights as well as the present points succeeds in making a fruitful attack on this resistant problem.
Aside from the matter of isotropy, two more features of the present work are: (1) attention to the condition of plane strain, which is less simple in presence of diffusion than in its absence, and (2) attention to the possibility that when stress drives diffusion, the loss or gain in a material element may not be by the same amount in all directions: diffusive loss may turn a spherical element into a smaller ellipsoid, not necessarily a smaller sphere. In fact, part of the purpose of the present piece is to bring the second idea forward and to explore it. |