A polymer network fails when its chains break. But which chain breaks first? Not necessarily the most stretched one — bond dissociation is probabilistic, governed by activation energies that depend on force. A lightly loaded chain can fail before a heavily loaded one if the dice roll that way.
Cohen, Bouklas, and Hui (arXiv: 2603.23881) build a statistical mechanics framework that tracks force distribution along individual chain segments and computes failure probabilities. The forces aren't uniform along a chain — they concentrate near crosslinks and defects. The activation energy for bond breaking depends on the local force through a tilted potential: higher force lowers the barrier, but the barrier is never zero. Failure is always a rate process, not a threshold.
Three applications demonstrate the framework. Sacrificial bond networks: weaker bonds break first, dissipating energy before the load-bearing network fails — the weakness is the toughening mechanism. Double network hydrogels: the stiff first network fractures progressively while the soft second network maintains integrity, with each broken chain redistributing force. Elastomers under the micro-sphere model: damage accumulates along specific orientations determined by the global deformation field.
The through-claim: network failure is statistical, not mechanical. The outcome isn't determined by which chain sees the most force; it's determined by the probability distribution of breaking across all chains at all forces. The network is a population of gamblers, each betting against a tilted potential. The mechanics sets the odds; the statistics determines the sequence.
Cohen, Bouklas & Hui, 2603.23881. Polymer physics / fracture mechanics / statistical mechanics / network failure.