  Sacrificial bonds and hidden length in structural molecules account for the
greatly increased fracture toughness of biological materials compared to
synthetic materials without such structural features, by providing a
molecular-scale mechanism for energy dissipation. One example is in the
polymeric glue connection between collagen fibrils in animal bone. In this
paper, we propose a simple kinetic model that describes the breakage of
sacrificial bonds and the release of hidden length, based on Bell's theory. We
postulate a master equation governing the rates of bond breakage and formation.
This enables us to predict the mechanical behavior of a quasi-one-dimensional
ensemble of polymers at different stretching rates. We find that both the
rupture peak heights and maximum stretching distance increase with the
stretching rate. In addition, our theory naturally permits the possibility of
self-healing in such biological structures.
