Average of the elastic properties of bio-heterogeneous structures
David Guinovart Sanjuan1; Reinaldo Rodriguez Ramos1; Raul Guinovart Diaz1; Julian Bravo Castillero1; Aura Conci2; Andrei Martínez-Finkelshtein3; Frederic Lebon4; Serge Dumont5
1 Facultad de Matemática y Computación, Universidad de La Habana; 2 Instituto de Computação/UFF, Av. Gal. Milton Tavares de Souza, s/nº , Niterói, CEP: 24210-346 Rio de; 3 University of Almería and Instituto Carlos I de Física Teórica y Computacional, Granada University,; 4 Laboratoire de Mécanique et d'Acoustique, Université Aix-Marseille, CNRS, Centrale Marseille, 31 Che; 5 Laboratoire Amiénois de Mathématiques Fondamentale et Appliquées, UPJV, CNRS UMR 7352, 33, rue Saint
doi:10.20906/CPS/COB-2015-0156
Resumo
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. In order to study the physical and material properties of the bio-composites, the two scale of AHM is used to solve the heterogeneous elastic problem. As examples of the application of the AHM, two different bio structures are studied: aorta and cornea. The aorta is a layered bio-composite. In this case a three layered model is developed with thickness of intima, media and adventitia layers varying at a ratio of 1:6:3. The aorta is studied as a curvilinear laminated shell bio-composite and the effective elastic tensors for the aorta are determinate using the AHM and Finite Element Method (FEM). On the other hand, the cornea is laminate shell composite also, 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 was introduced to study the geometry of this media. A function that describes the variation of the thickness was used to generate the model of the cornea. The effective elastic tensor was calculated considering two models, one where the thickness is constants along the cornea and other considering thickness variation. These two models 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 both models constant and variable thickness.
Palavras-chave: Laminated composites; Mechanical properties; Asymptotic Homogenization Method; Numerical Analysis; Bio-composites; Analytical modeling; Computational modelling