From knots to weaved baskets: Unravelling the mechanics of a clasp between two contacting filaments through numerical experiments

Tight elastic knots and weaved structures tend to exhibit intricate modes of deformation with nontrivial regions of contact that call for a fully three-dimensional description. Given this complexity, there is a striking lack of predictive models for knotted or weaved structures, the design of which tends to rely mostly on accumulated experience and empirical craftsmanship. Here, we study the elementary, yet rich and informative, canonical case of ‘a clasp’ formed by two elastic rods in crossing contact. We first start with the case of rods that have an originally circular cross-section. We tackle this problem by performing finite element simulations of this clasp configuration and contrast our results with experimental data obtained using X-ray tomography of the corresponding physical structures. We compare our results to a well-established description for ideal claps of geometrically rigid strings (that exclude elasticity), finding that the latter acts as an underlying ‘backbone’ for the full elastic solution. Finally, we extend our framework to a clasp formed by strips of non-circular cross-sections, which is the building block in basket weaving.