Failure of trabecular bone: XFEM modelling of multiple crack growth

Abstract

Trabecular bone plays an important role in structural integrity of bone tissues. Its complex microstructure characterised by high porosity and intricate composition with multiple trabeculae is a challenge for analysis of fracture initiation and propagation in it. This work investigates mechanical behaviour and failure of representative volume elements (RVEs) of porous structure of trabecular bone using numerical simulations. The extended finite-element method (XFEM) is used together with an original algorithm for the growth of multiple cracks in individual trabeculae of the structure. The obtained results are presented in comparison with the model of degradation of elastic properties. The effect of morphology on accumulation of damage and crack growth - both on the scale of a RVE and in individual ligaments - was investigated using the developed approach for estimation of a relative crack-surface area. The results are presented for five RVEs, obtained with high-resolution computed tomography of human trabecular bone, subjected to applied tensile and compressive loads.