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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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