A second gradient continuum model accounting for some effects of micro-structure on reconstructed bone remodelling

Angela Madeo; D. George; T. Lekszycki; Mathieu Nierenberger; Yves Rémond

doi:10.1016/j.crme.2012.05.003

A second gradient continuum model accounting for some effects of micro-structure on reconstructed bone remodelling

Angela Madeo ^1,² ; D. George ³; T. Lekszycki ^4,^5,²; Mathieu Nierenberger ³; Yves Rémond ^3,²

¹ LGCIE, université de Lyon, INSA, 20, avenue Albert-Einstein, 69621 Villeurbanne cedex, France
² International Research Center M&MOCS, University of LʼAquila, Cisterna di Latina, Italy
³ IMFS, université de Strasbourg, CNRS, 2, rue Boussingault, 67000 Strasbourg, France
⁴ Department of Machinery Design and Biomedical Engineering, Warsaw University of Technology, 85 Narbutta Street, 02-524 Warsaw, Poland
⁵ Warsaw Medical University, 4 Lindleya Street, 02-005 Warsaw, Poland

Comptes Rendus. Mécanique, Volume 340 (2012) no. 8, pp. 575-589.

Abstract

We propose a second gradient, two-solids, continuum mixture model with variable masses to describe the effect of micro-structure on mechanically-driven remodelling of bones grafted with bio-resorbable materials. A one-dimensional numerical simulation is addressed showing the potentialities of the proposed generalized continuum model. In particular, we show that the used second gradient model allows for the description of some micro-structure-related size effects which are known to be important in hierarchically heterogeneous materials like reconstructed bones. Moreover, the influence of the introduced second gradient parameters on the final percentages of replacement of artificial bio-material with natural bone tissue is presented and discussed.

Received: 2012-02-11
Accepted: 2012-05-11
Published online: 2012-06-06

DOI: 10.1016/j.crme.2012.05.003

Keywords: Biomechanics, Second gradient continuum mixture model, Hierarchically heterogeneous materials, Micro-structure-related size effects, Natural bone tissue, Bio-resorbable material, Bone resorption and synthesis, Load-induced replacement of artificial material with natural bone tissue, Numerical simulations

Author's affiliations:

Angela Madeo ^{1, 2}; D. George ³; T. Lekszycki ^{4, 5, 2}; Mathieu Nierenberger ³; Yves Rémond ^{3, 2}

¹ LGCIE, université de Lyon, INSA, 20, avenue Albert-Einstein, 69621 Villeurbanne cedex, France
² International Research Center M&MOCS, University of LʼAquila, Cisterna di Latina, Italy
³ IMFS, université de Strasbourg, CNRS, 2, rue Boussingault, 67000 Strasbourg, France
⁴ Department of Machinery Design and Biomedical Engineering, Warsaw University of Technology, 85 Narbutta Street, 02-524 Warsaw, Poland
⁵ Warsaw Medical University, 4 Lindleya Street, 02-005 Warsaw, Poland

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     author = {Angela Madeo and D. George and T. Lekszycki and Mathieu Nierenberger and Yves R\'emond},
     title = {A second gradient continuum model accounting for some effects of micro-structure on reconstructed bone remodelling},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {575--589},
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     doi = {10.1016/j.crme.2012.05.003},
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Angela Madeo; D. George; T. Lekszycki; Mathieu Nierenberger; Yves Rémond. A second gradient continuum model accounting for some effects of micro-structure on reconstructed bone remodelling. Comptes Rendus. Mécanique, Volume 340 (2012) no. 8, pp. 575-589. doi : 10.1016/j.crme.2012.05.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.05.003/

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