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Poro-Micromechanics of Bone: Impact Loading and Wave Propagation

Published online by Cambridge University Press:  01 February 2011

Christian Hellmich  and
Franz-Josef Ulm
Christian Hellmich
Affiliation:
Vienna University of Technology (TU Wien), Institute for Mechanics of Materials and Structures, A-1040 Vienna, Austria
Franz-Josef Ulm
Affiliation:
Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, Cambridge, MA 02139, USA
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Abstract

Based on ‘universal’ mechanical building blocks inherent to all different bones, this paper shows the integration of two classically separated fields of bone biomechanics, namely bone micromechanics[1] on the one hand, and bone poromechanics[2] on the other. Indeed, despite the complex hierarchical organization of bone, it was recently possible to identify such elementary components at the micro and nanolevel of the material for the explanation of the diversity of macroscopic (poro-)elastic properties of different bones. The mechanical properties (i.e. elasticity) of these elementary components are (within limits of experimental scatter) 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.

Continuum micromechanics has turned out as well-suited theoretical tool to derive tissue-dependent elastic properties at different length scales from upscaling the elasticity of ‘universal’ building blocks from the nanometer scale. Once respective micromechanics models are developed and validated, poro-micromechanics allows for the quantification of poroelastic properties such as the Biot and Skempton coefficients, as functions of the volume fractions of mineral, collagen, and the micropore space (Haversian and Volkmann canals, and the inter-trabecular space). Skempton coefficients, related to undrained conditions, allow for quantification of the marrow pressure rise due to impact loading, as can be shown by model predictions of non-destructive impact experiments. Moreover, the aforementioned poroelastic properties enter the governing equations for wave propagation in anisotropic porous media. They allow for the prediction of undrained, fast and slow waves, as is verified by comparison of model results with experimental findings.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 844: Symposium Y – Mechanical Properties of Bio-Inspired and Biological Materials , 2004 , Y8.6
Copyright
Copyright © Materials Research Society 2005

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