Contribution of extrafibrillar matrix to the mechanical behavior of bone using a novel cohesive finite element model

Abstract

The mechanical behavior of bone is determined at all hierarchical levels, including lamellae (the basic building block of bone) that are comprised of mineralized collagen fibrils and extrafibrillar matrix. The mechanical behavior of mineralized collagen fibrils has been investigated intensively using both experimental and computational approaches. Yet, the contribution of the extrafibrillar matrix to bone mechanical properties is poorly documented. In this study, we intended to address this issue using a novel cohesive finite element (FE) model, in conjunction with the experimental observations reported in the literature. In the FE model, the extrafibrillar matrix was considered as a nanocomposite of hydroxyapatite (HA) crystals bounded through a thin organic interface modeled as a cohesive interfacial zone. The parameters required by the cohesive FE model were defined based on the experimental data reported in the literature. This hybrid nanocomposite model was tested in two loading modes (i.e. tension and compression) and under two hydration conditions (i.e. wet and dry). The simulation results indicated that (1) the failure modes of the extrafibrillar matrix predicted using the cohesive FE model were closely coincided with those experimentally observed in tension and compression tests; (2) the pre-yield deformation (i.e. internal strain) of HA crystals with respect to the applied strain was consistent with that obtained from the synchrotron X-ray scattering measurements irrespective of the loading modes and hydration status; and (3) the mechanical behavior of the extrafibrillar matrix was dictated by the properties of the organic interface between the HA crystals. Taken together, we postulate that the extrafibrillar matrix plays a major role in the pre-yield deformation and the failure mode of bone, thus, giving rise to important insights in the ultrastructural origins of bone fragility.

Computational modeling of interfacial behaviors in nanocomposite materials

“…5). Based on the previous convergence test of similar models (Lin et al, 2017; Lin et al, 2016), the mesh size in current work is around 150nm and the time step is Δ t = l× 10 −10 s. We have plotted the stress-strain curves after calculations, the stress-strain curves in the early post yield state agreed well with experimental measurements as shown in Fig. 7.…”

The Ultrastructure of Bone and Its Relevance to Mechanical Properties

“…The most cited model, proposing a staggered arrangement of crystals in a collagen fibril, is due to Jäger and Fratzl [70]. Fewer studies employed models in which minerals are also present on the outside of the collagen fibril (e.g., [40,54,[71][72][73][74][75]). …”

Age‐Related Deterioration of Bone Toughness Is Related to Diminishing Amount of Matrix Glycosaminoglycans (GAGs)

“…(20) However, bound water retained in the extrafibrillar matrix by NCPs (10% of the organic phase), which are highly hydrophilic too, may also significantly affect the mechanical behavior of bone. In fact, recent evidence shows that the effect of hydration on bulk mechanical properties of bone is also manifested in the mechanical response of the mineral phase, (32,66) suggesting that the hydration condition of extrafibrillar matrix is strongly associated with the bulk behavior of bone. (35) It is not surprising because the extrafibrillar matrix, which is primarily composed of mineral crystals, takes up at least 23% of bone volume (assuming mineralized collagen fibrils are closely packed).…”