Recently, a new carnival called The Giant's Shoulders has been started and the first edition of the same is out at A blog around the clock. A post of mine on the elastic stresses due to inclusions and inhomogeneities made it to the carnival. I am cross-posting the piece here since it might also be of interest to the readers of iMechanica (though I did post a short note earlier here which forms the core of this long post too).

Eshelby and the inclusion/inhomogeneity problems

Any materials scientist interested in mechanical behaviour would be aware of the contributions of J.D. Eshelby. With 56 papers, Eshelby revolutionised our understanding of the theory of materials. The problem that I wish to discuss in this page is the elastic stress and strain fields due to an ellipsoidal inclusion/inhomogeneity - a problem that was solved by Eshelby using an elegant thought experiment.

In two papers published in the Proceedings of Royal Society (A) in 1957 and 1959 (Volume 241, p. 376 and Volume 252, p. 561) Eshelby solved the following problem ("with the help of a simple set of imaginary cutting, straining and welding operations"): In his own words,