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A nonlocal constitutive model for trabecular bone softening in compression

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Abstract

Using the three-dimensional morphological data provided by computed tomography, finite element (FE) models can be generated and used to compute the stiffness and strength of whole bones. Three-dimensional constitutive laws capturing the main features of bone mechanical behavior can be developed and implemented into FE software to enable simulations on complex bone structures. For this purpose, a constitutive law is proposed, which captures the compressive behavior of trabecular bone as a porous material with accumulation of irreversible strain and loss of stiffness beyond its yield point and softening beyond its ultimate point. To account for these features, a constitutive law based on damage coupled with hardening anisotropic elastoplasticity is formulated using density and fabric-based tensors. To prevent mesh dependence of the solution, a nonlocal averaging technique is adopted. The law has been implemented into a FE software and some simple simulations are first presented to illustrate its behavior. Finally, examples dealing with compression of vertebral bodies clearly show the impact of softening on the localization of the inelastic process.

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Authors and Affiliations

  1. Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29, Prague, Czech Republic

    Mathieu Charlebois & Milan Jirásek

  2. Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology, Gusshausstrasse 27-29, 1040, Vienna, Austria

    Philippe K. Zysset

Authors
  1. Mathieu Charlebois
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  2. Milan Jirásek
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  3. Philippe K. Zysset
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Correspondence to Mathieu Charlebois.

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Charlebois, M., Jirásek, M. & Zysset, P.K. A nonlocal constitutive model for trabecular bone softening in compression. Biomech Model Mechanobiol 9, 597–611 (2010). https://doi.org/10.1007/s10237-010-0200-3

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  • DOI: https://doi.org/10.1007/s10237-010-0200-3

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