One of the most important and challenging problems of elastic rod-based models of polymers is to accurately take into account the self-intersections. Normally, such dynamics is treated with an introduction of a suitable short-range repulsive potential to the elastic string. Inevitably, such models lead to a sliding contact, because of the very nature of the potential interaction between two parts of the string. Such models, however, fail to take into account situations where the small scale structure of the polymer's "surface" is very rough, as is the case with e.g dendronized polymers. Such polymers are more likely to incur the rolling contact dynamics, or at the very least some combination of rolling and sliding contact. It is generally believed to be impossible to model rolling contact, even in the simplest cases, by introducing a contact potential.

We derive a consistent motion of two elastic strings in perfect rolling contact, a situation that can be easily visualized by putting two rubber strings in contact. We show that even the contact dynamics is essentially nonlinear, and even if the string's motion away from contact is assumed linear, the contact dynamics leads to strongly nonlinear motion, which we call "contact chaos". We also derive exact motion of contact when the string consists of discrete particles. We finish by presenting some exact solutions of the problem, as well as numerical simulations.