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

TL;DR

This paper presents a kinetic model explaining how sacrificial bonds and hidden length in biomaterials like bone enhance toughness and strength through energy dissipation, with rate-dependent behavior and potential self-healing.

Contribution

It introduces a simple kinetic model based on Bell's theory to describe bond breakage and hidden length release, predicting mechanical behavior at different stretching rates.

Findings

Rupture peak heights increase with stretching rate

Maximum stretching distance increases with stretching rate

Model suggests possibility of self-healing in biological structures

Abstract

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.