Isometric (unstretchable) limit accounts for singularities
These singularities occur in general spatial dimensions
Two types:
vertices caused by conflict between confinement and bending constraints
ridges: caused by mutual constraints of two vertices. 
They occur
When a thin manifold with an internal distance is confined
Elastic sheets
Fluid sheets: viscosity resists rapid changes in internal distances
More general metric manifolds?
How do these singularities show up in real materials?
How big are they?, what shape? how much energy?