Hi Isabel, nice post. If you want to make it more physical, it's not easy, but there are definitely options for doing so. One typical starting place, you may already know, is the hanging chain (see this article on the St. Louis Arch).
Another odd but interesting possibility--more related to SW current issues than wear-ability--would be to treat the links as a statistical mechanical system of interlinked "Hard Tori", then calculate dynamics using conservation of momentum and energy. Perhaps in so doing you could find something like phonon modes, but I don't know for sure if they would exist without elasticity (what allows something really to "stretch").
I think the dynamics problem would really be too hard because individual links are usually in contact with more than one other link. It will be ambiguous how to update states, not to mention that chain mail should have a lot of frictional damping. That damping also has the added practical consequence of making the armor difficult to move around in.
Anyways, dynamics is a totally different issue from finding a static least-energy configuration, which is all you need if the chain mail is just going to sit in a museum somewhere and never go into battle. In that case the catenary problem already has all the essential physical principles. Larger problems can possibly be solved numerically by stochastic search procedure which looks like calculus of variations from an incremental perspective.
