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Constitutive Modeling and Algorithmic Implementation of a Plasticity-like Model for Trabecular Bone Structures

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Abstract

Trabecular bone is a highly porous orthotropic cellular solid material present inside human bones such as the femur (hip bone) and vertebra (spine). In this study, an infinitesimal plasticity-like model with isotropic/kinematic hardening is developed to describe yielding of trabecular bone at the continuum level. One of the unique features of this formulation is the development of the plasticity-like model in strain space for a yield envelope expressed in terms of principal strains having asymmetric yield behavior. An implicit return-mapping approach is adopted to obtain a symmetric algorithmic tangent modulus and a step-by-step procedure of algorithmic implementation is derived. To investigate the performance of this approach in a full-scale finite element simulation, the model is implemented in a non-linear finite element analysis program and several test problems including the simulation of loading of the human femur structures are analyzed. The results show good agreement with the experimental data.

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Authors and Affiliations

  1. Orthopaedic Biomechanics Laboratory, University of California, 94720, Berkeley, CA, USA

    Atul Gupta, Harun H. Bayraktar, Julia C. Fox & Tony M. Keaveny

  2. ABAQUS West, Inc., 94538, Fremont, CA, USA

    Atul Gupta

  3. ABAQUS, Inc., 02909, Providence, RI, USA

    Harun H. Bayraktar

  4. Piziali & Associates, 94070, San Carlos, CA, USA

    Julia C. Fox

  5. Department of Mechanical Engineering, University of California, 94720, Berkeley, CA, USA

    Tony M. Keaveny & Panayiotis Papadopoulos

  6. Department of Bioengineering, University of California, 94720, Berkeley, CA, USA

    Tony M. Keaveny

  7. Computational Solid Mechanics Laboratory, University of California, 94720, Berkeley, CA, USA

    Harun H. Bayraktar & Panayiotis Papadopoulos

Authors
  1. Atul Gupta
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  2. Harun H. Bayraktar
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  3. Julia C. Fox
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  4. Tony M. Keaveny
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  5. Panayiotis Papadopoulos
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Corresponding author

Correspondence to Panayiotis Papadopoulos.

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Gupta, A., Bayraktar, H.H., Fox, J.C. et al. Constitutive Modeling and Algorithmic Implementation of a Plasticity-like Model for Trabecular Bone Structures. Comput Mech 40, 61–72 (2007). https://doi.org/10.1007/s00466-006-0082-5

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  • DOI: https://doi.org/10.1007/s00466-006-0082-5

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