The UK-based team that shared an Ig Nobel Physics Prize in 2012 for exploring the physics of why ponytails (the hair style) are shaped like pony tails, has now looked into a different question from everyday life: Why clothes don’t fall apart. They published a study about it:
“Why Clothes Don’t Fall Apart: Tension Transmission in Staple Yarns,” Patrick B. Warren, Robin C. Ball, and Raymond E. Goldstein, Physical Review Letters, vol. 120, 2018, 158001. The authors report:
In his celebrated Dialogues Concerning Two New Sciences, Galileo identified a fascinating puzzle in the mechanics of ropes…. From a modern perspective, we would say that the mechanical integrity of ropes derives from frictional contacts between fibers, and Galileo’s rope problem is but one exemplar of a host of related frictional phenomena in fiber assemblies, of which perhaps the canonical case is the ‘staple’ yarn.
The problem of how staple yarns transmit tension is addressed within abstract models in which the Amontons–Coulomb friction laws yield a linear programing (LP) problem for the tensions in the fiber elements. We find there is a percolation transition such that above the percolation threshold the transmitted tension is in principle unbounded. We determine that the mean slack in the LP constraints is a suitable order parameter to characterize this supercritical state. We argue the mechanism is generic, and in practical terms, it corresponds to a switch from a ductile to a brittle failure mode accompanied by a significant increase in mechanical strength.
(Thanks to Joan Codina for bringing this to our attention.)