HAL Id: hal-01509003
https://hal.archives-ouvertes.fr/hal-01509003 Submitted on 15 Apr 2017
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SINUPROS: un modèle et un logiciel nano-maco pour
les propriétés mécaniques de l’os cortical humain
Mihaela Racila, Jean-Marie Crolet
To cite this version:
Mihaela Racila, Jean-Marie Crolet. SINUPROS: un modèle et un logiciel nano-maco pour les pro-priétés mécaniques de l’os cortical humain. 8e Colloque national en calcul des structures, CSMA, May 2007, Giens, France. �hal-01509003�
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Laboratoire de Mathématiques, UMR CNRS 6326 ** Institut Supérieur des Ingénieurs de Franche-Comté
Université de Franche-Comté, 16 Route de Gray, 25000 Besançon, France mracila@yahoo.com, jmcrolet@univ-fcomte.fr
***
Département de Mathématiques Appliquées
Université de Craiova, 13 Rue A. I. Cuza, 200585 Craiova, Roumanie
RÉSUMÉ. Sinupros est un modèle de l’os cortical humain qui prend en compte les aspects
architecturaux, multi physiques et multi-échelles de ce milieu. Tous les paramètres introduits dans chacun des cinq niveaux sont décrits, une loi de comportement permettant de prendre en compte l’effet de la minéralisation est suggérée et la théorie de l’homogénéisation est mise en œuvre pour déterminer les propriétés physiques de cette structure à chacun des niveaux concernés. Les schémas numériques évoqués sont implémentés dans un code écrit en Matlab, lequel permet aisément de simuler l’effet de chacun des paramètres. La première analyse des résultats de ce modèle qui est menée porte sur la composition minérale de ce milieu et les composantes élastiques longitudinales et transverses obtenues au niveau macroscopique.
ABSTRACT. Sinupros is a model of the human cortical bone that takes into account the
architectural, multiphysics and multi scale aspects of this medium. All the introduced parameters in each of the five levels are described, a behavior law allowing the modelisation of the mineralization effect is suggested and the homogenization theory is used in order to determine the physical properties at each level of this structure. The numerical algorithms are implemented in a software based on Matlab which allows easily simulating the effect of each parameter. The first analysis of the results which is pursued deals with the mineral composition of this medium and with the longitudinal and transverse elastic properties obtained at the macroscopic scale.
MOTS-CLÉS: Os cortical humain, Homogénéisation, Piézoélectricité, Minéralisation osseuse,
Multi-échelle, Lois de comportement évolutives.
KEYWORDS: Human cortical bone, Homogenization, Piezoelectricity, Bony mineralization,
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