Can stress tensor be defined on feature edges?

Question

Assume a rod is being extruded out of a cylinder by pushing the cylinder into a hole (See Figure below).
Do the feature edges (or corners in 2D) cause the traction (the surface force) to be discontinuous?
Can we define the stress tensor at the corners?

Answer 1

The stress does not make sense at absolutely sharp corners. In reality, the corners will have some radii on which actual stress/strain will depend.