Musculoskeletal diseases such as osteoporosis, osteoarthritis and bone cancer pose a significant social and economic challenge in ageing societies worldwide. In digital healthcare, computational models could be a cornerstone in mitigating these challenges by facilitating, for example, personalised bone strength analyses or manufacturing of bespoke implants. Such models, however, critically depend on understanding the complex characteristics of bone as a material. Currently, there is limited knowledge on the elasto-plastic behaviour of bone’s fundamental mechanical building block, the mineralised collagen fibre. Especially the load transfer between mineralised collagen fibrils and mineral particles, its main mechanical components, is unclear. Therefore, we aimed at (i) simultaneously quantifying the fibre, fibril and mineral deformation using a micro- and nanomechanical testing protocol, (ii) formulating a statistical constitutive model to explain the fibre behaviour and the load transfer between its constituents as well as (iii) using (i) and (ii) to test under quasi-physiologic conditions.

Laser manufacturing and focused ion beam milling were used to extract micrometre sized samples from individual mineralised collagen fibres of mineralised turkey leg tendon, a model system for bone. These micropillars were tested in an experimental set-up that combined micropillar compression and X-ray scattering or diffraction under dry and rehydrated conditions. An elasto-plastic statistical constitutive model was developed in which two shear lag models simulate the stress transfer between fibre, fibril and mineral. Ultrastructural features were included based on nanoscale imaging data.

Experimental data show small fibril and mineral strains compared to the fibre strain. This was related to localised strains and heterogeneous fibril deformations due to a gradual nonlinear fibril recruitment. By incorporating this recruitment, the model can explain the elasto-plastic fibre behaviour as seen in dry and rehydrated experiments including the load transfer between fibre, fibrils and mineral particles with an accuracy of 95% for dry and 89% for rehydrated conditions. The model provides distributions for the micro- and nanomechanical responses and, thus, directly simulates strain ratios determined experimentally by in-situ mechanical testing and X-ray scattering/diffraction measurements. Experiment and model allowed it to identify the micro- and nanomechanical behaviour of the fibril array. Rehydration decreased fibre stiffness by 60%, yield and compressive strength by 75%, and fibril stiffness by 25%.

The new insights into the micro- and nanoscale elasto-plastic behaviour of bone’s fundamental mechanical building block help to understand bone’s hierarchical material mechanics. Results may be used to inform computational models for nonlinear bone strength analyses as well as the design of tissue engineered bio-inspired implants.