Topology optimization of bone using cubic material design and evolutionary methods based on internal remodeling

Ibrahim Goda , Jean-Francois Ganghoffer , Sławomir Adam Czarnecki , Radosław Tomasz Czubacki , Paweł Wawruch


In the present paper, the influence of the loading conditions on the trabecular architecture of a femur is investigated by using the cubic material design and an evolutionary approach based on internal remodeling. The response of bone to mechanical loading stimuli leads to alterations of the internal architecture of bone, traduced by a modification of its effective density and mechanical properties. The cubic material design approach deals with the minimum compliance problem of femur bone made of a non-homogeneous elastic material with cubic symmetry. The optimal cubic material characteristics are in fact reflected by the properties of the underlying microstructure. Internal remodeling is here also considered and thus belongs to the class of evolutionary topology optimization methods. The effective continuum mechanical properties of the trabecular bone are derived from an initially discrete planar hexagonal structure representative of femur bone microstructure, relying on the discrete homogenization approach. This leads to scaling laws of the effective elastic properties of bone versus density at an intermediate mesoscopic scale. The performed simulations of the optimal trabecular bone architecture illustrate the respective advantages and limitations of the employed methods. The simulation results indicate that the proposed approaches could reasonably mimic the major geometrical and material features of the natural bone.
Author Ibrahim Goda
Ibrahim Goda,,
, Jean-Francois Ganghoffer
Jean-Francois Ganghoffer,,
, Sławomir Adam Czarnecki (FCE / ICE)
Sławomir Adam Czarnecki,,
- The Institute of Civil Engineering
, Radosław Tomasz Czubacki (FCE / ICE)
Radosław Tomasz Czubacki,,
- The Institute of Civil Engineering
, Paweł Wawruch (FCE)
Paweł Wawruch,,
- Faculty of Civil Engineering
Journal seriesMechanics Research Communications, ISSN 0093-6413, (A 25 pkt)
Issue year2019
Publication size in sheets0.5
Keywords in EnglishTopology optimization, Cubic material design, Bone remodeling, Discrete homogenization, FE simulations
ASJC Classification2210 Mechanical Engineering; 2211 Mechanics of Materials; 3104 Condensed Matter Physics; 2500 General Materials Science; 2205 Civil and Structural Engineering
Languageen angielski
1-s2.0-S0093641317302872-main.pdf 1.22 MB
Score (nominal)30
ScoreMinisterial score = 25.0, 14-12-2018, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 14-12-2018, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.056; WoS Impact Factor: 2017 = 1.64 (2) - 2017=1.942 (5)
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