Experimental 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 to 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. was conducted for each constitutive model to identify an accurate numerical solution for the experimental results under uniaxial compression. Following model calibration under uniaxial compression, parameter variation under confined compression was simulated in order to investigate the pressure dependent plastic behaviour of each material model. The computed response was compared to experimental confined compression data. The yield surface and flow potential of all four constitutive models considered in the study are governed by the von Mises equivalent stress ( q ) and the equivalent pressure stress ( p ) where And S is the stress deviator. pressure dependent yield behaviour of trabecular bone. We demonstrate that for DP and MC plasticity sufficient yielding is prevented at higher pressures in confined compression. In contrast, the crushable foam models better represent the inelastic behaviour of cellular PU and BTB, predicting a plateau region post yield for confined compression due to significant pressure dependent yielding. Results suggest that a ratio of uniaxial to hydrostatic yield stress K = 1 provides a good fit for BTB, with a slightly lower ratio being computed for cellular PU ( K = 0.7), indicating the importance of modelling pressure dependent yield for both materials ( K = 0 represents a standard von Mises type plasticity formulation). For the crushable foam models considered in the present study the computed plateau stress at high levels of deformation in the confined compression tests is lower than that observed experimentally. This suggests that a crushable foam plasticity model in which the ratio of uniaxial to pressure yield stress changes with plastic strain may provide further improvements in accuracy. The CFI and CFV plasticity models have previously been applied to cellular foams (Rizov et al., 2005; Flores-Johnson et al., 2008), however to our knowledge they have never been applied to trabecular bone.