Thank you very much for your great answer @DanielPiker!
Your explanation was easy to understand and the paper was an interesting read. It definitely helps me to understand what’s happening in this simulation. I modified the shape of the curve to prevent radial symmetry and voila no buckling.
Until now I have only folded such shapes by hand and was not quite sure what to expect from such a simulation. But I remembered seeing something similar on youtube and there was no problem breaking radial symmetry. I found this video again, it accompanied the paper Modeling Curved Folding with Freeform Deformations.
At minute 1:23 they simulate a similar folding pattern, but contrary to my memory they used a line that serves as a rope to break the radial symmetry of the disc.
They used evenly spaced quad meshes and are able to fold the mesh anywhere, the crease curve just have to intersect the quads. From what I understood they duplicate the intersected quads, split the mesh an stitch it back together somehow, the process is explained in a previous paper The Shape Space of Discrete Orthogonal Geodesic Nets
but they don’t simulate physics (at least I think so). Additionally their program is able to judge for itself whether to fold a crease as a mountain or valley fold.
The Discrete Geodesic Nets Editor used is also published on github but at the moment it’s an earlier version that can’t handle crease patterns yet but I plan on playing around with it. https://github.com/MichaelRabinovich/DOG-editor
I wonder how hard it would be to implement the functionality of their DOG Editor into rhino/gh for better modelling of curved folded surfaces or bend surfaces.
At least I’m thinking about implementing the use of an evenly spaced quad mesh + the intersection splitting at creases to generate the starting mesh. But I have a hard time to dertmine how I could define the hinges in kangaroo to fold the quads located between crease and edge or crease and crease that are not intersected.