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doi:10.3850/978-981-08-7619-7_P022
Probabilistic Model of Human Cortical Bones with Uncertain Mechanical Properties for Modeling Random Experimental Measurements in Ultrasonic Range
C. Desceliers1,a, C. Soize1,b, S. Naili2, Q. Grimal3,c and M. Talmant3,d
1Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR8208 CNRS, 5 Bd Descartes, 77454 Marne la Vallée, France.
achristophe.desceliers@univ-paris-est.fr
bchristian.soize@univ-paris-est.fr
2Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR8208 CNRS, 61 avenue du Général de Gaulle, 94010 Crṫeil Cedex, France.
naili@univ-paris12.fr
3Université Paris 6, Laboratoire d'Imagerie Parametrique, UMR7623 CNRS, 15 rue de l'école de médecine, 75006 Paris, France.
cquentin.grimal@upmc.fr
dTalmant@lip.bhdc.jussieu.fr
ABSTRACT
The biomechanical materials are among the most complex mechanical systems. Most often, their micro-structure are complex and random. This is the case for the human cortical bones which are considered in this paper. For such a system, the microstructure can be altered near its interface with the marrow (osteoporosis). A gradient of porosity is then observed in the thickness direction but, in this case, none usual theory of porous materials can be applied. For this reason, we present a simplified model with gradient for the elasticity tensor. The predictability of this model is improved by taking into account uncertainties. The elasticity tensor is then modeled by a random field. This random model is well adapted for the modeling of the random experimental measurements in ultrasonic range for the human cortical bone.
Keywords: Probabilistic model, Uncertainties, Ultrasonic range, Cortical bones, Porous media.
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