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

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Biomimetics -- Materials, Structures and Processes

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

Abstract

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).

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  1. Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien), Karlsplatz 13/202, 1040, Vienna, Austria

    Christian Hellmich

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  3. E202 Institut für Mechanik der, Werkstoffe und Strukturen, TU Wien, Karlsplatz 13, Wien, 1040, Austria

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Hellmich, C., Fritsch, A., Dormieux, L. (2011). Multiscale Homogenization Theory: An Analysis Tool for Revealing Mechanical Design Principles in Bone and Bone Replacement Materials. In: Gruber, P., Bruckner, D., Hellmich, C., Schmiedmayer, HB., Stachelberger, H., Gebeshuber, I. (eds) Biomimetics -- Materials, Structures and Processes. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11934-7_5

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