Using Non-linear Homogenization to Improve the Performance of Macroscopic Damage Models of Trabecular Bone - Levrero-Florencio, Francesc; Pankaj, Pankaj (Frontiers in Physiology, 2018)
Realistic macro-level finite element simulations of the mechanical behaviour of trabecular bone, a cellular anisotropic material, require a suitable constitutive model; a model that incorporates the mechanical response of bone for complex loading scenarios and includes post-elastic phenomena, such as plasticity (permanent deformations) and damage (permanent stiffness reduction), which bone is likely to experience. Some such models have been developed by conducting homogenisation-based multiscale finite element simulations on bone micro-structure. While homogenisation has been fairly successful in the elastic regime and to some extent in modelling the macroscopic plastic response, it has remained a challenge with respect to modelling damage. This study uses a homogenisation scheme to upscale the damage behaviour from the tissue level (microscale) to the organ level (macroscale) and assesses the suitability of different damage constitutive laws. Ten cubic specimens were each subjected to 21 strain-controlled load cases for a small range of macroscopic post-elastic strains. Isotropic and anisotropic criteria were considered, density and fabric relationships were used in the formulation of the damage law, and a combined isotropic/anisotropic law with tension/compression asymmetry was formulated, based on the homogenised results, as a possible alternative to the currently used single scalar damage criterion. This computational study enhances the current knowledge on the macroscopic damage behaviour of trabecular bone. By developing relationships of damage progression with bone's micro-architectural indices (density and fabric) the study also provides an aid for the creation of more precise macroscale continuum models, which are likely to improve clinical predictions.