Micromechanical modelling of transverse fracture behaviour of lamellar bone using a phase-field damage model: The role of non-collagenous proteins and mineralised collagen fibrils.

At the tissue-scale and above, there are now well-established structure-property relationships that provide good approximations of the biomechanical performance of bone through, for example, power-law relationships that relate tissue mineral density to elastic properties. However, below the tissue-level, the individual role of the constituents becomes prominent and these simple relationships tend to break down, with more detailed theoretical and computational models are required to describe the mechanical response. In this study, a two-dimensional micromechanics damage-based representative volume element (RVE) of lamellar bone was developed, which included a novel implementation of a phase-field damage model to describe the behaviour of non-collagenous proteins at mineral-mineral and mineral-fibril interface regions. It was found that, while the stiffness of the tissue was governed by the relative proportion of extra-fibrillar mineral and mineralised collagen fibrils, the strength and toughness of the tissue in transverse direction relied on the interactions occurring at mineral-mineral and mineral-fibril interfaces, highlighting the prominence of non-collagenous proteins in determine fracture-based processes at this scale. While fractures tended to initiate in mineral rich areas of the extra-fibrillar mineral matrix, it was found that the presence of mineralised collagen fibrils at low density did not provide a substantial contribution to crack propagation behaviour under transverse loading. However, at physiological volume fraction (VfMCF=50%), different scenarios could arise depending on the relative strength value of the interphase around the MCFs ( [Formula: see text] ) to the interphase between individual minerals ( [Formula: see text] ): (i) When [Formula: see text] , MCFs appear to facilitate crack propagation with MCF-mineral debonding being the dominant failure mode; (ii) once γ>1, the MCFs hinder the microcracks, leading to inhibition of crack propagation, which can be regarded as an energy dissipation mechanism. The effective fracture properties of the tissue also experience a sudden increase in fracture work density (J-integral) once the crack is arrested by MCFs or severely deflected. Collectively, the predicted behaviour of the model compared well to those reported through experimental and computational methods, highlighting its potential to provide further understanding into the mechanistic response of bone ultrastructure alterations related to the structural and compositional changes resulting from disease and aging.

Exploring the hierarchical structure of lamellar bone and its impact on fracture behaviour: A computational study using a phase field damage model.

Bone is a naturally occurring composite material composed of a stiff mineral phase and a compliant organic matrix of collagen and non-collagenous proteins (NCP). While diverse mineral morphologies such as platelets and grains have been documented, the precise role of individual constituents, and their morphology, remains poorly understood. To understand the role of constituent morphology on the fracture behaviour of lamellar bone, a damage based representative volume element (RVE) was developed, which considered various mineral morphologies and mineralised collagen fibril (MCF) configurations. This model framework incorporated a novel phase-field damage model to predict the onset and evolution of damage at mineral-mineral and mineral-MCF interfaces. It was found that platelet-based mineral morphologies had superior mechanical performance over their granular counterparts, owing to their higher load-bearing capacity, resulting from a higher aspect ratio. It was also found that MCFs had a remarkable capacity for energy dissipation under axial loading, with these fibrillar structures acting as barriers to crack propagation, thereby enhancing overall elongation and toughness. Interestingly, the presence of extrafibrillar platelet-based minerals also provided an additional toughening through a similar mechanism, whereby these structures also inhibited crack propagation. These findings demonstrate that the two primary constituent materials of lamellar bone play a key role in its toughening behaviour, with combined effect by both mineral and MCFs to inhibit crack propagation at this scale. These results have provided novel insight into the fracture behaviour of lamellar bone, enhancing our understanding of microstructure-property relationships at the sub-tissue level.

A multiscale finite element investigation on the role of intra- and extra-fibrillar mineralisation on the elastic properties of bone tissue.

Lamellar bone is one of the fundamental structural units of bone tissue and it consists of mineralised collagen fibrils (MCFs) embedded within an extra-fibrillar matrix comprised of hydroxyapatite minerals distributed throughout a matrix of non-collagenous proteins (NCPs). While both intra- and extra-fibrillar phases provide a critical contribution to tissue-level behaviour, the mechanical implications of their structural arrangement, and in particular the relative distribution of HA minerals between both phases, remains poorly understood. This study presents a multiscale finite element framework to investigate the role of intra- and extra-fibrillar mineralisation on the elastic properties of bone tissue by considering two levels of structural hierarchy. At the nanoscale, representative volume elements (RVEs) of both MCFs and the extra-fibrillar matrix were developed, and a homogenisation strategy was used to determine the effective elastic properties of each phase. At the sub-micron level, an RVE of lamellar bone that accounted for newly reported patterns of mineral platelets encircling collagen fibrils was used to predict the effective response of lamellar bone tissue, with material properties established from the previous length scale. The results demonstrated that the overall mineral content in the tissue is the biggest contributor to the effective elastic properties of lamellar bone. While this is perhaps unsurprising, importantly, it was demonstrated that the extra-fibrillar matrix (and mineral therein) is the phase that makes the primary contribution to the elastic response of the tissue. The two main reasons that the extra-fibrillar matrix dominated the load-bearing response are (i) the greater proportion of mineral content compared to the intra-fibrillar regions and (ii) the highly ordered arrangement of mineral platelets that are aligned to the longitudinal axis of MCFs. Both of these features resulted in extra-fibrillar mineral strain ratios that were consistently higher than intra-fibrillar mineral strain ratios under axial loading. As a result, the predicted elastic properties of MCFs were much lower than the extra-fibrillar matrix, indicating that intra-fibrillar mineralisation only provided a modest contribution to the stiffness of bone tissue. Collectively, the predicted results of the multiscale approach compared well to the range properties measured through various experimental testing methods, highlighting its potential to provide further insight into the role of sub-tissue features of tissue biomechanics.