Average of the elastic properties of bio-heterogeneous structures
Résumé
Sometimes the analysis of the stress state, crack initiation and some others phenomenon in heterogeneous media is complicated. In order to facilitate the ulterior study of such problems, we apply the asymptotic homogenization method (AHM) to a general laminated shell composite and an equivalent homogeneous elastic problem with effective properties is obtained. The physical and material properties of the bio-composites are studied using the two scale of AHM. The heterogeneous elastic problem is solved. As examples of the application of the AHM the cornea is considered as a laminated shell bio-composite. The cornea is composed with three cell layers: the outer epithelial cells, stromal cells and endothelial cells. Between these layers are extracellular structures called Bowman’s and Descemet’s membranes. The cornea has a variable thickness. The polar coordinates system is introduced to study the geometry of this media. A function that describes the variation of the thickness is used to generate the model of the cornea. The effective elastic tensor is calculated by AHM and FEM considering two models, one where the thickness is constants along the cornea and other considering thickness variation. These two models by AHM and FEM are compared and the influence of the variation of the thickness in the effective properties of the cornea is shown. The effective stress is determinate solving the homogenized problem for constant and variable thickness.
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY - Paternité
Licence : CC BY - Paternité