CONSTITUTIVE MODELING AND ALGORITHMIC IMPLEMENTATION OF A PLASTICITY-LIKE MODEL FOR TRABECULAR BONE STRUCTURES
A. Gupta, H.H. Bayraktar, J.C. Fox, T.M Keaveny and P. Papadopoulos Comp. Mech., 40, pp. 61-72, (2007)

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 formulations is the development of the plasticity-like mode in strain space for a yielding envelop expressed in terms of principal strains having assymetric yield behavior. An implicity return-mappong approach is adopted to obtain a symmetric algorithmic tanget moduls and a step-by-step procedure of algorithmic impementation 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 human femur structures are analyzed. The results show good agreement with experimental data.


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