Multiscale Homogenization Theory: An Analysis Tool for Revealing Mechanical Design Principles in Bone and Bone Replacement Materials

  • Christian Hellmich
  • Andreas Fritsch
  • Luc Dormieux
Part of the Biological and Medical Physics, Biomedical Engineering book series (BIOMEDICAL)


Biomimetics deals with the application of nature-made “design solutions” to the realm of engineering. In the quest to understand mechanical implications of structural hierarchies found in biological materials, multiscale mechanics may hold the key to understand “building plans” inherent to entire material classes, here bone and bone replacement materials. Analyzing a multitude of biophysical hierarchical and biomechanical experiments through homogenization theories for upscaling stiffness and strength properties reveals the following design principles: The elementary component “collagen” induces, right at the nanolevel, the mechanical anisotropy of bone materials, which is amplified by fibrillar collagen-based structures at the 100-nm scale, and by pores in the micrometer-to-millimeter regime. Hydroxyapatite minerals are poorly organized, and provide stiffness and strength in a quasi-brittle manner. Water layers between hydroxyapatite crystals govern the inelastic behavior of the nanocomposite, unless the “collagen reinforcement” breaks. Bone replacement materials should mimic these “microstructural mechanics” features as closely as possible if an imitation of the natural form of bone is desired (Gebeshuber et al., Adv Mater Res 74:265–268, 2009).


Representative Volume Element Bone Material Hydroxyapatite Crystal Observation Scale Haversian Canal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christian Hellmich
    • 1
  • Andreas Fritsch
  • Luc Dormieux
  1. 1.Institute for Mechanics of Materials and StructuresVienna University of Technology (TU Wien)ViennaAustria

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