When averaged over half-spaces, the elastic stress and strain fields which arose from dislocation pile-ups were shown to exhibit peculiar topological features of the form, y/|y|. That is, they changed abruptly upon passing through the pile-up plane. The average fields appeared to be equivalent to those of Somigliana dislocations, and provided a description of the strain boundaries in crystals. This included the torsion boundary, which represented a surface where the average rotation field experienced a topological jump.

Dislocation Pile-Ups, Topological Features of Stresses and Strains. S.D.Borisova, I.I.Naumov: Theoretical and Applied Fracture Mechanics, 2001, 35[3], 237-42