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

摘要

The complexity and heterogeneity of bone tissue require a multiscalemodelling to understand its mechanical behaviour and its remodellingmechanisms. In this paper, a novel multiscale hierarchical approach includingmicrofibril scale based on hybrid neural network computation and homogenisationequations was developed to link nanoscopic and macroscopic scales to estimatethe elastic properties of human cortical bone. The multiscale model is dividedinto three main phases: (i) in step 0, the elastic constants of collagen-waterand mineral-water composites are calculated by averaging the upper and lowerHill bounds; (ii) in step 1, the elastic properties of the collagen microfibrilare computed using a trained neural network simulation. Finite element (FE)calculation is performed at nanoscopic levels to provide a database to train anin-house neural network program; (iii) in steps 2 to 10 from fibril tocontinuum cortical bone tissue, homogenisation equations are used to performthe computation at the higher scales. The neural network outputs (elasticproperties of the microfibril) are used as inputs for the homogenisationcomputation to determine the properties of mineralised collagen fibril. Themechanical and geometrical properties of bone constituents (mineral, collagenand cross-links) as well as the porosity were taken in consideration. Thispaper aims to predict analytically the effective elastic constants of corticalbone by modelling its elastic response at these different scales, ranging fromthe nanostructural to mesostructural levels. Our findings of the lowest scale'soutput were well integrated with the other higher levels and serve as inputsfor the next higher scale modelling. Good agreement was obtained between ourpredicted results and literature data.