Topological features of average stresses and strains induced by dislocation pileups

Abstract

When averaged over half-spaces, the elastic stress and strin fields generated by a number of dislocation pileups are shown to take a peculiar topological feature of the form y/|y| i.e., they undergo an abrupt change when passing through the pileup plane. The average fields appear to be equivalent to the dislocation fields of the most general form (Somigliana dislocations). In terms of the average fields, a description of strain boundaries in crystals, specifically of torsion boundaries, proves to be most convenient. In this kind of description the torsion boundary, for example, is a surface where the average rotation field experiences a topological jump.