Microelasticity of Bone

  • Christian Hellmich
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 480)


Despite the complex hierarchical organization and the astonishing variety of bones, it was recently possible to identify a few elementary mechanical components at the micro and nanolevel of the material: hydroxyapatite crystals, collagen molecules, and water. The mechanical properties (i.e. elasticity) of these elementary components are (up to experimental scattering) the same for all bones; they are’ universal’, i.e., independent of tissue-type, species, and anatomical location. The mechanical interaction between these elementary components (mechanical morphology) and the dosages of these components in different tissues determine the macroscopic material properties. Whereas the mechanical interaction is limited to certain patterns, it is mainly the tremendous number of different dosages of the elementary components by which nature produces the admirable diversity of different bones.

This contribution covers the description and validation of a microelastic model for bone, based on a four-step homogenization scheme. At a length scale of several hundred nanometers, oriented, highly organized collagen molecules, the minority of the hydroxyapatite crystals present in bone tissues, and water build up (mineralized) fibrils. At the same length scale, but in the extraflbrillar space, the majority of (largely disordered) hydroxyapatite crystals build up a mineral foam (polycrystal), with water filling the inter-crystalline (nano)space. At a length scale of several micrometers, the fibrils and the extrafibrillar space build up solid bone matrix or ultrastructure. Finally, at a length scale of several milimeters, macroscopic bone material (cortical or trabecular bone) comprises solid bone matrix and the microporous space (Haversian and Volkmann canals, as well as the intertrabecular space).

Model validation rests on statistically and physically independent experiments: The ultrastructural or macroscopic (=microstructural) stiffness values predicted by the micromechanical model on the basis of tissue-independent phase stiffness properties of hydroxyapatite, collagen, and water (experimental set I) for tissue-specific composition data (experimental set Ha) are compared to corresponding experimentally determined tissue-specific stiffness values (experimental set IIb). Experinental set I comprises ultrasonic and Brillouin light scattering tests; experimental set Ha comprises dehydration-demineralization tests, neutron diffraction tests, mass density tests based on Archimedes’ principle, and microradiography; experimental set IIb comprises ultrasonic tests at different frequency ranges, and quasi-static tests.

Having in mind that the aforementioned dosages are dependent on complex biochemical control cycles (defining the metabolism of the organism), the purely mechanical theory can be linked to biology, biochemistry, and, on the applied side, to clinical practice.


Trabecular Bone Representative Volume Element Ultrasonic Test Collagen Volume Fraction Mineralized Collagen Fibril 


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© CISM, Udine 2005

Authors and Affiliations

  • Christian Hellmich
    • 1
  1. 1.Institute for Mechanics of Materials and StructuresVienna University of Technology (TU Wien)Wien (Vienna)

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