ASSUMPTIONS:
- no deformation is separate, all deformations touch with at least another points deformation, i.e., no deformation is by itself.
- point force preferred, but small dense balls okay too.
- The point forces are all identical (or balls have the same weight and size.)
- While the deformations touch, no balls touch.
- infinite elastic medium
- isotropic material
- linear elasticity
- homogeneous material
- static loading
- no pre-stress or pre-strain
- flat surface before deformation
- 2D analysis
- neglecting body forces
Below is a picture that represents the phenomenon, except that the ball on the right is by itself, that I got from Blender Stack Exchange 
And below are the best I could do to demonstrate examples of two curves. Essentially the shape of the threads while ignoring weaving.
Curve 1:
Curve 2:
