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Crack propagation in bone at the scale of mineralized collagen fibrils: Implications for bone toughness

Ahmed Elbanna (University of Illinois (UC)), wenyi Wang (), Charles Lieou (UC Santa Barbara), Jean Carlson (UC Santa Barbara)

Experimental Nanobiomechanics

Mon 4:20 - 5:40

Barus-Holley 163

Bone is a hierarchical composite of collagen and hydroxyapatite with mechanisms to resist fracture at different size scales. In this work, we investigate the dynamics of crack propagation in bone at the scale of mineralized collagen fibrils. The mineralized collagen fibril is modeled as a composite of tropocollagen molecules and hydroxyapatite plates governed by the stress strain response predicted from molecular dynamics simulations [e.g. Beuhler, 2007]. The fibrils are bound together by a polymer gel matrix consisting of polymers with sacrificial bonds and hidden length systems. The rate-and-displacement constitutive response of the polymeric glue is modeled within the framework of the worm-like chain model and the transition state theory. Cracks are introduced in the model by locally reducing the glue density or by locally overstressing the collagen fibrils or their interfaces. Our model predicts that bone, at theses scales, is quasi-brittle with size dependent strength. The size dependence does not conform with Griffith’s inverse square root prediction and it depends on the degree of the mineralization of the collagen fibrils as well as the glue density. The model also enables us to investigate many of the dynamic rupture properties of interest such as rupture propagation speed, particle velocity and fracture energy variation with rupture size. We discuss the implications of our results for understanding bone toughness at microscales and the characterization of bone quality.