Modelling bone tissue mechanics with a viscoelastic-viscoplastic-damage framework
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Bone tissue has a hierarchical structure and exhibits mechanical properties that vary with biological and anatomical factors, making its mechanical behaviour difficult to capture with a single mathematical formulation [1]. Understanding and predicting bone mechanical behaviour is essential in both clinical and aerospace contexts, where exposure to ionizing radiation and microgravity can compromise bone integrity and increase the risk of late-onset fractures [2]. This work aims to develop a constitutive formulation to describe bone mechanical behaviour, accounting for differences between cortical and trabecular tissue. In this study, a coupled viscoelastic-viscoplastic-damage model [3] has been formulated by incorporating orthotropic elasticity and a subsequent plastic phase, each coupled to viscous behaviour. The isotropic hardening function governs the softening phase by gradually decreasing once a threshold of accumulated plastic strain is reached [4]. The constitutive model was implemented in a finite element framework and, together with micro CT-derived femur geometries, employed to realistically simulate and numerically reconstruct the bone’s biomechanical response. CT was also used to identify the orthotropic axes by linking voxel positions to the principal material directions. Finally, data taken from an experimental campaign on murine model have been used to perform the model calibration. Model versatility in interpreting cortical and trabecular tissue behaviour was demonstrated by comparing experimental data with numerical results. Furthermore, the model is able to reproduce the mechanical response of bone under both tension and compression. The proposed procedure enables an advanced and computationally efficient representation of bone mechanical behaviour, supporting predictive analyses across different application fields.
