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Modeling orthotropic elasticity, localized plasticity and fracture in trabecular bone

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Abstract

This work develops a model for the mechanical response of trabecular bone including plasticity, damage and fracture. It features a resultant lamellar orientation that captures trabecular strut anisotropic elasticity, and introduces asymmetric J2 plasticity with isotropic hardening to capture evolving strut tensile and compressive dissipative properties. A continuum compatibility based damage and fracture criterion is also proposed to model fracture surface generation. We investigated fracture of a trabecular bone network under a compressive load, for which failure modes of both tension and compression were identified at the strut level. The predicted trabecular network response was found to fall within the range of experimental results reported in literature. We also investigated the response of idealized struts under compression, tension and bending using our model. Individual struts were found to exhibit micro-buckling under compression and micro-necking under tension. These instabilities are however masked by the multiplicity and complexity of strut orientations at the trabecular network level.

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Acknowledgments

D.T. O’Connor would like acknowledge the National Physical Sciences Consortium (NPSC) and Argonne National Laboratory for their partial support. K.I. Elkhodary gratefully acknowledges the financial and technical support received from AUC for this research. J. Qian and Y. Zhang were supported in part by NSF CAREER Award OCI-1149591.

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Authors and Affiliations

  1. Exponent Failure Analysis Associates, 2595 Canyon Boulevard, Suite 440, Boulder, CO, 80302, USA

    D. T. O’Connor

  2. Department of Mechanical Engineering, The American University in Cairo, New Cairo, 11835, Egypt

    K. I. Elkhodary & Y. Fouad

  3. Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA

    M. S. Greene & W. K. Liu

  4. Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

    J. Qian & Y. Zhang

  5. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    F. A. Sabet & I. Jasiuk

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  1. D. T. O’Connor
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  2. K. I. Elkhodary
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  3. Y. Fouad
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  4. M. S. Greene
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  6. J. Qian
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  7. Y. Zhang
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  8. W. K. Liu
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Correspondence to K. I. Elkhodary.

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O’Connor, D.T., Elkhodary, K.I., Fouad, Y. et al. Modeling orthotropic elasticity, localized plasticity and fracture in trabecular bone. Comput Mech 58, 423–439 (2016). https://doi.org/10.1007/s00466-016-1301-3

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