  The complexity and heterogeneity of bone tissue require a multiscale
modelling to understand its mechanical behaviour and its remodelling
mechanisms. In this paper, a novel multiscale hierarchical approach including
microfibril scale based on hybrid neural network computation and homogenisation
equations was developed to link nanoscopic and macroscopic scales to estimate
the elastic properties of human cortical bone. The multiscale model is divided
into three main phases: (i) in step 0, the elastic constants of collagen-water
and mineral-water composites are calculated by averaging the upper and lower
Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril
are computed using a trained neural network simulation. Finite element (FE)
calculation is performed at nanoscopic levels to provide a database to train an
in-house neural network program; (iii) in steps 2 to 10 from fibril to
continuum cortical bone tissue, homogenisation equations are used to perform
the computation at the higher scales. The neural network outputs (elastic
properties of the microfibril) are used as inputs for the homogenisation
computation to determine the properties of mineralised collagen fibril. The
mechanical and geometrical properties of bone constituents (mineral, collagen
and cross-links) as well as the porosity were taken in consideration. This
paper aims to predict analytically the effective elastic constants of cortical
bone by modelling its elastic response at these different scales, ranging from
the nanostructural to mesostructural levels. Our findings of the lowest scale's
output were well integrated with the other higher levels and serve as inputs
for the next higher scale modelling. Good agreement was obtained between our
predicted results and literature data.
