An experimentally informed statistical elasto-plastic mineralised collagen fibre model at the micrometre and nanometre lengthscale

Abstract

Bone is an intriguingly complex material. It combines high strength, toughness and lightweight via an elaborate hierarchical structure. This structure results from a biologically driven self-assembly and self-organisation, and leads to different deformation mechanisms along the length scales. Characterising multiscale bone mechanics is fundamental to better understand these mechanisms including changes due to bone-related diseases. It also guides us in the design of new bio-inspired materials. A key-gap in understanding bone’s behaviour exists for its fundamental mechanical unit, the mineralised collagen fibre, a composite of organic collagen molecules and inorganic mineral nanocrystals. Here, we report an experimentally informed statistical elasto-plastic model to explain the fibre behaviour including the nanoscale interplay and load transfer with its main mechanical components. We utilise data from synchrotron nanoscale imaging, and combined micropillar compression and synchrotron X-ray scattering to develop the model. We see that a 10-15% micro- and nanomechanical heterogeneity in mechanical properties is essential to promote the ductile microscale behaviour preventing an abrupt overall failure even when individual fibrils have failed. We see that mineral particles take up 45% of strain compared to collagen molecules while interfibrillar shearing seems to enable the ductile post-yield behaviour. Our results suggest that a change in mineralisation and fibril-to-matrix interaction leads to different mechanical properties among mineralised tissues. Our model operates at crystalline-, molecular- and continuum-levels and sheds light on the micro- and nanoscale deformation of fibril-matrix reinforced composites.

The intriguing role of collagen on the rheology of cancer cell spheroids

“…Biological tissues containing nanofibres may be modeled as elasto-plastic materials, with only a few heterogeneities enough to generate such plastic effects (Groetsch et al (2021)). On the other hand, with a large collagen content and a small amount of cells (around 10%), the behavior becomes viscoelastic (Iordan et al (2010)), but the interactions between cells and the ECM are essential, since cells can remodel the collagen network and change tissue properties.…”

The elasto-plastic nano- and microscale compressive behaviour of rehydrated mineralised collagen fibres

“…Recently, we reported results on the micro-and nanometre lengthscale compressive behaviour of single mineralised collagen fibres [21,56]. Micropillar compression [25,57] and synchrotron radiation Xray scattering and diffraction techniques (SAXS/XRD) [42,[58][59][60][61][62][63][64][65] were used to extract the mechanical behaviour of a mineralised collagen fibre and the interplay with its mechanical components under dry conditions.…”

“…Micropillar compression [25,57] and synchrotron radiation Xray scattering and diffraction techniques (SAXS/XRD) [42,[58][59][60][61][62][63][64][65] were used to extract the mechanical behaviour of a mineralised collagen fibre and the interplay with its mechanical components under dry conditions. Combined with ultrastructural data, those findings were used to develop a statistical elastoplastic model that explains the micro-and nanoscale fibre behaviour [21]. The extension towards a setup with rehydrated samples now lets us deduce the fibre mechanical properties close to their hydration state in a combined experimental and computational approach.…”

“…We also have to consider the swelling and deformation of an excised array of fibrils. In contrast to microindentation tests, testing a free micropillar of an array of uniaxially arranged fibrils 13 [21,56] lacks the support of surrounding fibres. Since our dry testing results [56] compare well with nanoindentation [88], considering this different set of boundary conditions suggests that we observe lubrication and swelling but that this is not blocked by surrounding tissue, thus losing a reinforcing and stabilising element.…”

“…As a result, a higher amount of energy is dissipated extrafibrillar in the fibril-matrix interactions. The increased mobility might lead to a rigid body movement of the mineralised collagen fibrils within the matrix which in turn results in smaller 15 axial fibril strains since fibrils rather move past each other than being deformed along their longitudinal direction in their uniaxial arrangement [21,56], which affects the measured SAXS signal.…”