Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach

Abstract

Extracellular bone material can be characterised as a nanocomposite where, in a liquid environment, nanometre-sized hydroxyapatite crystals precipitate within as well as between long fibre-like collagen fibrils (with diameters in the 100 nm range), as evidenced from neutron diffraction and transmission electron microscopy. Accordingly, these crystals are referred to as ‘interfibrillar mineral’ and ‘extrafibrillar mineral’, respectively. From a topological viewpoint, it is probable that the mineralisations start on the surfaces of the collagen fibrils (‘mineral-encrusted fibrils’), from where the crystals grow both into the fibril and into the extrafibrillar space. Since the mineral concentration depends on the pore spaces within the fibrils and between the fibrils (there is more space between them), the majority of the crystals (but clearly not all of them) typically lie in the extrafibrillar space. There, larger crystal agglomerations or clusters, spanning tens to hundreds of nanometers, develop in the course of mineralisation, and the micromechanics community has identified the pivotal role, which this extrafibrillar mineral plays for tissue elasticity. In such extrafibrillar crystal agglomerates, single crystals are stuck together, their surfaces being covered with very thin water layers. Recently, the latter have caught our interest regarding strength properties (Fritsch et al. 2009 J Theor Biol. 260(2): 230–252) – we have identified these water layers as weak interfaces in the extrafibrillar mineral of bone. Rate-independent gliding effects of crystals along the aforementioned interfaces, once an elastic threshold is surpassed, can be related to overall elastoplastic material behaviour of the hierarchical material ‘bone’. Extending this idea, the present paper is devoted to viscous gliding along these interfaces, expressing itself, at the macroscale, in the well-known experimentally evidenced phenomenon of bone viscoelasticity. In this context, a multiscale homogenisation scheme is extended to viscoelasticity, mineral-cluster-specific creep parameters are identified from three-point bending tests on hydrated bone samples, and the model is 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 remodelling.

The Ultrastructure of Bone and Its Relevance to Mechanical Properties

“…Further theoretical and experimental studies can be done to address these idealizations for the studied model. This computational study of bone at the nanoscale complements other modeling studies which incorporated elastoplasticity [81], creep [82] and poroelasticity [55] and more complex 3D geometries of collagen structures within the collagen fibril [83][84][85][86], cross-linking between collagen fibrils [67], and formulated molecular dynamics models [87]. Extensions of such constitutive models and theoretical frameworks to the lamellar model presented in this paper would further advance understanding of the proposed model and the mechanical behavior of bone at the nanoscale and higher scales.…”

Influence of interfacial interactions on deformation mechanism and interface viscosity in α-chitin–calcite interfaces

“…calcite) (Fig. 2) pointed that the shear deformation between the soft matrix and inorganic crystals is the main stress transfer mechanism of such loaded biomaterials, and recent studies proposed that the layered water in crystal interfaces could be the source for biomaterial viscoelasticity [30,31]. Therefore, the magnitude of viscosity reported in this study is a potentially important value to be used with analytical models to determine the biomaterial viscoelastic properties.…”

“…This ''glue'' interface promotes energy dissipation during deformation of the material and this mechanism works better when more positive ions, such as Ca 2+ , are involved [72]. These viscous hydrated interfaces can act as the source of the macroscopic phenomenon of biomaterial viscoelasticity, [30,31]. Presence of the interface with higher viscosity is the main contributor of the toughening mechanisms to prevent catastrophic failure.…”

“…The framework developed in this work to understand interface deformation mechanics using SMD is based on a combination of frameworks reported by Katti and coworkers [23][24][25], Lindal and Edholm [26], and Frankland and Harik [27]. Similar molecular mechanics framework has been incorporated with the continuum micromechanics to top-down access to interface viscosity of bone material systems in the earlier studies [30][31][32][33]. NEMD simulations to evaluate interface strength are based on the pressure profile calculation method, [26].…”

Multiscale approach including microfibril scale to assess elastic constants of cortical bone based on neural network computation and homogenization method

“…At the ultrastructure level of bone, water exists in the form of bound water in the collagen network (including the collagenmineral interface) and tightly bound water in the mineral phase [58]. Consequently, water may play an important role in bone behavior involving creep, fatigue and fracture [59][60][61][62].…”