Identification of an elasticity-tensor random field at mesoscopic scale using experimental measurements at mesoscopic and macroscopic scales for complex hierarchical microstructures
Résumé
At a macro-scale, a mediumsuch as the cortical bone is often modeled as a homogeneous material for which the effective mechanical properties can be identified using experimental tests. At micro-scale, this material is not only non homogenous and random but it also cannot be described in terms of mechanical constituents. It is the reason why we consider a meso-scale for which the medium is modeled with apparent properties represented by an elasticity-tensor random field. A complete methodology is proposed for the experimental identification of the random field at meso-scale (1) using image field measurements at macro- and meso-scales, (2) introducing two associated boundary value problems for which the change of scale is performed in the context of stochastic homogenization and (3) using statistical inverse methods. A validation will be presented for cortical bone with experimental simulations which measure displacement (or strain) fields at the macro- and meso-scales for a given sample submitted to a given load.
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