Micromechanical models of network materials presenting internal length scales: applications to trabecular bone under stable and evolutive conditions

Abstract : A methodology based on micromechanics has been developed to determine the effective behavior of network materials endowed with a discrete architecture at the microscopic level. It relies on the discrete homogenization method, which has been applied to textile monolayers and trabecular bones. The initially discrete topology of the considered network materials results after homogenization at the mesoscopic level in anisotropic micropolar effective continuum, which proves able to capture the observed internal scale effects. Such micromechanical methods are useful to remedy the difficulty to measure the effective mechanical properties at the intermediate mesoscopic level scale. The bending and torsion responses of vertebral trabecular bone beam specimens are formulated in both static and dynamic situations, based on the Cosserat theory. 3D models have been developed for describing the multiaxial yield and brittle fracture behavior of trabecular bone, including the analysis of size-dependent non-classical plastic yield. We have constructed by FE analyses a homogeneous, orthotropic couple-stress continuum model as a substitute of the 3D periodic heterogeneous cellular solid model of vertebral trabecular bone, based on the equivalent strain energy approach. Bone tissues are able to adapt their local density and load bearing capacities as well as their size and shape to mechanical stimuli. We have developed models for combined internal and external bone remodeling in the framework of the thermodynamics of irreversible processes, at both the cellular and macroscopic levels. We lastly combined anisotropic internal remodeling with fatigue continuum damage
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Ibrahim Goda. Micromechanical models of network materials presenting internal length scales: applications to trabecular bone under stable and evolutive conditions. Other [cond-mat.other]. Université de Lorraine, 2015. English. ⟨NNT : 2015LORR0055⟩. ⟨tel-01751647⟩

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