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

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.Comment: 2

Fracture strength assessment and aging signs detection in human cortical bone using an X-FEM multiple scale approach.

International audienceWe present a multiple scale approach for modeling multiple crack growth in human cortical bone under tension. The Haversian microstructure, a four phase composite, is discretized by a classical finite element method fed with the morphological and mechanical characteristics, experimentally measured, to mimic human bone heterogeneity at the micro scale. The fracture strength of human bone, exhibiting aging signs, is investigated through tensional percolation simulations in statistical microstructures. The cracks are initiated at the micro scale at locations where a critical elastic-damage strain-driven criterion is met. The cracks, modeled by the eXtended Finite Element Method, are then grown until complete failure when a critical stress intensity factor criterion is attained. The model provides the fracture strength and the global response at the material scale and the stress–strain fields at the microscopic level. The model creates a constitutive law at the material scale and emphasizes the influence of the microstructure on bone failure and fracture risk assessment. These results are validated against experiments

Physical Imaging of Bone Sequential Light Microscopy Observations

National audienceSee http://hal.archives-ouvertes.fr/docs/00/59/27/03/ANNEX/r_OOW53O9P.pd

Physical Imaging of fracturing Human Cortical Bone

International audienceIn the present study, we present a procedure associating either the eXtended Finite Element Method (XFEM) or the standard Finite Element Method (FEM) to a Digital Imaging Correlation technique (DIC) called microextensometry (CorrelmanuV) in order to investigate the local fracture toughness of micro cracks in human Haversian cortical bone at the scale of the osteons. The micro cracks are tested in tension and in compression