Crack Propagation in Bone on the Scale of Mineralized Collagen Fibrils : Role of Polymers with Sacrificial Bonds and Hidden Length

TL;DR

This study models how sacrificial bonds and hidden length in polymers at the nanoscale enhance fracture toughness in mineralized collagen fibrils, providing insights for biomimetic material design and bone fracture modeling.

Contribution

It introduces a simplified 1D model to quantify the impact of SBHL systems on bone fibril toughness, linking nanoscale features to macroscopic fracture behavior.

Findings

Interface toughness increases with polymer density and sacrificial bonds.

Bond strength and hidden loop length influence fracture resistance.

Model explains variations in mechanical behavior due to physiological changes.

Abstract

Sacrificial bonds and hidden length (SBHL) in structural molecules provide a mechanism for energy dissipation at the nanoscale. It is hypothesized that their presence leads to greater fracture toughness than what is observed in materials without such features. Here, we investigate this hypothesis using a simplified model of a mineralized collagen fibril sliding on a polymeric interface with SBHL systems. A 1D coarse-grained nonlinear spring-mass system is used to model the fibril. Rate-and-displacement constitutive equations are used to describe the mechanical properties of the polymeric system. The model quantifies how the interface toughness increases as a function of polymer density and number of sacrificial bonds. Other characteristics of the SBHL system, such as the length of hidden loops and the strength of the bonds, are found to influence the results. The model also gives insight into the variations in the mechanical behavior in response to physiological changes, such as the degree of mineralization of the collagen fibril and polymer density in the interfibrillar matrix. The model results provide constraints relevant for bio-mimetic material design and multiscale modeling of fracture in human bone.