Layered Water in Crystal Interfaces as Source for Bone Viscoelasticity: Arguments from a Multiscale Approach

Lukas Eberhardsteiner, Christian Hellmich, and Stefan Scheiner


Bone, Viscoelasticity, database management system


Extracellular bone material can be characterized as a nanocomposite where, in a liquid environment, nanometer-sized hydroxyapatite crystals precipitate within as well as between long fibre-like collagen fibrils (with diameters in the hundred nanometer range). Accordingly, these crystals are referred to as ``interfibrillar mineral'' and ``extrafibrillar mineral'', respectively. During mineralization, crystals grow both into the fibril, as well as into the extrafibrillar space, with the majority of crystals lying in the extrafibrillar space. Thus, the extrafibrillar mineral plays a pivotal role for bone elasticity, as identified by the micromechanics community. Furthermore, the surfaces of single crystals within the extrafibrillar crystal agglomerates are covered with very thin water layers which have been identified as weak interfaces governing rate-independent gliding effects once an elastic threshold is exceeded. Extending this idea, the present paper is devoted to viscous gliding along these interfaces, manifesting itself, on the macroscopic scale, in the well-known, experimentally evidenced phenomenon of bone viscoelasticity. In this paper, a multiscale homogenization scheme is developed accounting for bone viscoelasticity, with mineral-cluster-specific creep parameters being identified from three-point bending tests on hydrated bone samples. The model is further validated by statistically and physically independent experiments on partially dried samples. We expect this model to be relevant when it comes to prediction of time-dependent phenomena, e.g. in the context of bone remodeling.

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