Nano-scale modeling of energy dissipation in a single lamella reveals the significant contribution of collagen-mineral sliding to intrinsic bone toughness

Abstract

Although collagen-mineral sliding is recognized as one of the intrinsic mechanisms that contribute to the bone toughness, its precise role in energy release at the nano-scale, as well as its relationship to other intrinsic toughness mechanisms, remains unclear. This lack of understanding stems from the challenges associated with quantifying the specific nature of contact at the mineral-collagen interface, and the energy dissipation capacity resulting from plastic deformation at this scale. To address this issue, we developed a three-dimensional model of mineralized collagen fibril using ABAQUS, incorporating hyperelastic isotropic collagen, elastic isotropic mineral, and a cohesive contact formulation to represent the collagen-mineral interface. Knowing the properties of collagen and mineral and using a parametric modeling approach, we estimated the properties of contact based on experimental measurements of the stress-strain behavior in a single bone lamella, considering the angle of the collagen fibril in relation to the loading axis. By comparing the experimental elastic modulus with the model predictions, we determined that the cohesive contact exhibited a maximum strength of 9 MPa and a fracture energy of 50 mJ/m2 within the bone. Further analysis indicated that fracture energy at the collagen-mineral interface is potentially closer to 5 mJ/m2. Using these findings, we concluded that the interfaces were responsible for 52% to 98% of the energy release in mineralized collagen fibrils, depending on collagen angle, both directly and indirectly by influencing stress and strain in adjacent collagen fibril. The results of this study demonstrated that plastic deformation at the collagen-mineral interface is the primary mechanism underlying bone toughness at the nano-scale. Importantly, we found that these conclusions held true regardless of the angle of the collagen fibril relative to the loading axis. The modeling framework presented in this study provides a valuable tool for investigating the elastic and post-yield behavior of bone across different mineral volume fractions at the nano-scale, and at the lamellar level.