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Sacrificial bonds and hidden length in biomaterials -- a kinetic, constitutive description of strength and toughness in bone

Charles Lieou (UC Santa Barbara), Ahmed Elbanna (Univ. of Illinois at Urbana-Champaign), Jean Carlson (UC Santa Barbara)

Joint Session: Mechanics of cell sheets, multicellular assemblies and tissues and Mechanics and Physics of Biological Cells

Mon 2:40 - 4:00

Barus-Holley 141

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.