Banding

I know the following: In linear FE analysis with linear constitutive law, say CST, there will not be any discontinuity across the adjacent (or neighboring) elements, for any of the fields---displacements, strains or stresses. But I do have certain questions that are not very well addressed in the introductory FEM texts:

(i) Assuming a displacement-based formulation, under what conditions would you expect discontinuities (or inter-element banding) to possibly appear in: (a) stresses? (b) strains? (c) displacements?