SUMMARYThe 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.

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This paper deals with the identification of material parameters using a hybrid method of multi-objective optimization. This approach was used in a previous work to identify the Hill'48 criterion under the associative normality assumption and the Voce law hardening parameters of the Stainless Steel AISI 304. In this work, we apply the proposed method in order to identify the orthotropic criterion of Hill'48 under the non-associative normality assumption. The two models are compared and analysed using several experimental tests.

In this work, a bone damage resorption finite element model based on the disruption of the inhibitory signal transmitted between osteocytes cells in bone due to damage accumulation is developed and discussed. A strain-based stimulus function coupled to a damage-dependent spatial function is proposed to represent the connection between two osteocytes embedded in the bone tissue. The signal is transmitted to the bone surface to activate bone resorption. The proposed model is based on the idea that the osteocyte signal reduction is not related to the reduction of the stimulus sensed locally by osteocytes due to damage, but to the difficulties for the signal in travelling along a disrupted area due to microcracks that can destroy connections of the intercellular network between osteocytes and bone-lining cells. To check the potential of the proposed model to predict the damage resorption process, two bone resorption mechano-regulation rules corresponding to two mechanotransduction approaches have been implemented and tested: 1) Bone resorption based on a coupled strain-damage stimulus function without ruptured osteocyte connections (NROC); and 2) Bone resorption based on a strain stimulus function with ruptured osteocyte connections (ROC).The comparison between the results obtained by both models, shows that the proposed model based on ruptured osteocytes connections predicts realistic results in conformity with previously published findings concerning the fatigue damage repair in bone.

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This paper deals with the identification of material parameters for an elastoplastic behaviour model with isotropic hardening using several experimental tests at the same time. But, these tests are generally inhomogeneous and finite element simulations are necessary for their analysis. Therefore an inverse analysis is carried out and the identification problem is converted into a multi-objective optimization where prohibitive computing time is required. We propose in this work a hybrid approach where Artificial Neural Networks (ANN) are trained by finite element results. Then, the multi objective procedure calls the ANN function in place of the finite element code. The proposed approach is exemplified on the identification of non-associative Hill'48 criterion and Voce parameters model of the Stainless Steel AISI 304.

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