This is a crossed post.
Slip-line field theory* is a technique (essentially a change of variables, but with a great deal of physics) to solve problems in elasticity theory, in particular plasticity in two dimensions. There's abundant material in the Engineering and applied math literature, but almost all of it focuses on solutions on unbounded domains (which have more direct applications to optimization problems) like the upper half plane and the exterior of a disk. Considering bounded domains (like a disk) is significantly more difficult (the equations governing slip line fields are hyperbolic, so the Cauchy problem is not well defined. One has to consider Goursat conditions or some others) and there's almost no material about this kinds of problems, then
Are there examples of slip-line fields constructed on interiors of closed domains ?
*Integral lines of slip-line fields are also called Hencky (or Hencky-Prandtl) nets in some Engineering contexts.