Hierarchical Biomaterials Mechanics of Bone and Bone Substitutes
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Hierarchical biomaterials mechanics of bone and bone substitutes Christian Hellmich1, Andreas Fritsch1, and Luc Dormieux2 1 Vienna University of Technology (TU Wien), Karlsplatz 13, A-1040 Wien, Austria 2 Ecole des Ponts ParisTech, 6-8 av. Blaise Pascal, 77455 Marne-la-Vallee, France 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 nano-composite, unless the ‘collagen reinforcement’ breaks. Bone replacement materials should mimic these ‘microstructural mechanics’-features as closely as possible. INTRODUCTION Biomimetics deals with the application of nature-made ‘design solutions’ to the realm of engineering. In this context, large efforts have aimed at imitating biological materials with interesting mechanical properties. However, biological materials are hierarchically organized and very complex, and frequently, the way they work is not easily comprehensible. Hence, successful biomimetics solutions require a deep understanding of ‘universal’ functioning principles of biological materials. It now appears that multiscale mechanics may hold the key to such an understanding of ‘building plans’ inherent to entire material classes. For relating the vision of hierarchical organization of materials to effective mechanical properties, we rely on continuum micromechanics, which is a well-established tool for structureproperty investigations. Based on various physical-chemical and mechanical experiments, our focus is the development of multiscale mechanical models, which mathematically and computationally quantify how the basic building blocks of biological materials (such as hydroxyapatite minerals, collagen, and water in all bones found throughout the vertebrate kingdom) govern the materials’ mechanical properties at different length scales, from a few nanometers up to the macroscopic level. Thereby, multiscale homogenization theory allows us, at each scale, to identify material representations which are as simple as possible, but as complex as necessary for reliable computational predictions of key material properties, such as poroelasticity, creep, and strength. This can
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