  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.
