Vol. 9, No. 1, 2021

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Computational implementation of nonuniform orthotropic directions in the femoral diaphysis based on cortical bone microstructure to build a constitutive model

Rachele Allena and Christophe Cluzel

Vol. 9 (2021), No. 1, 33–58
DOI: 10.2140/memocs.2021.9.33
Abstract

Cortical bone is a damageable elastic orthotropic material due to the orientation of its components at different scales. Thus, to consistently describe its mechanical behavior, it is necessary first to experimentally identify the anisotropy directions and second to be able to implement them in a numerical model. In our previous paper, we presented an original approach which enables one to get the numerical directions of orthotropy throughout a whole femur. In the present paper, we propose a significant improvement of such a computational approach in order to depict specific orientations in the femoral diaphysis. To do so, a correction of the main orientation of the Haversian canals has been applied based on experimental measurements. The influence of such a correction on the global distribution of the stresses has been quantified via two finite element applications which simulate pure torsion and flexion-compression. Our main objective is to provide the numerical tools to describe the orthotropic behavior of the cortical bone for any femur.

Keywords
orthotropic materials, cortical bone, Haversian canals, diffusion equations
Mathematical Subject Classification
Primary: 92-10
Milestones
Received: 22 June 2020
Revised: 17 November 2020
Accepted: 14 January 2021
Published: 17 March 2021

Communicated by Francesco dell'Isola
Authors
Rachele Allena
Institute de Biomécanique Humaine George Charpak
Arts et Métiers ParisTech
Paris
France
Christophe Cluzel
Laboratoire de Mécanique et Technologie
Ecole Normale Supérieure Paris-Saclay
Université Paris-Saclay
Gif-sur-Yvette
France
Département Science et Génie des Matériaux
Institut Universitaire de Technologie d’Evry Val d’Essonne
Evry
France