Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue.

The inelastic pressure dependent compressive behaviour of bovine trabecular bone is investigated through experimental and computational analysis. Two loading configurations are implemented, uniaxial and confined compression, providing two distinct loading paths in the von Mises-pressure stress plane. Experimental results reveal distinctive yielding followed by a constant nominal stress plateau for both uniaxial and confined compression. Computational simulation of the experimental tests using the Drucker-Prager and Mohr-Coulomb plasticity models fails to capture the confined compression behaviour of trabecular bone. The high pressure developed during confined compression does not result in plastic deformation using these formulations, and a near elastic response is computed. In contrast, the crushable foam plasticity models provide accurate simulation of the confined compression tests, with distinctive yield and plateau behaviour being predicted. The elliptical yield surfaces of the crushable foam formulations in the von Mises-pressure stress plane accurately characterise the plastic behaviour of trabecular bone. Results reveal that the hydrostatic yield stress is equal to the uniaxial yield stress for trabecular bone, demonstrating the importance of accurate characterisation and simulation of the pressure dependent plasticity. It is also demonstrated in this study that a commercially available trabecular bone analogue material, cellular rigid polyurethane foam, exhibits similar pressure dependent yield behaviour, despite having a lower stiffness and strength than trabecular bone. This study provides a novel insight into the pressure dependent yield behaviour of trabecular bone, demonstrating the inadequacy of uniaxial testing alone. For the first time, crushable foam plasticity formulations are implemented for trabecular bone. The enhanced understanding of the inelastic behaviour of trabecular bone established in this study will allow for more realistic simulation of orthopaedic device implantation and failure.