Failure behaviour of human trabecular bone

Abstract

A trabecular bone tissue with its complex microstructural morphology can demonstrate a complex and random pattern of fracture. This paper analyses the effect of material’s mechanical behaviour on failure modelling of human trabecular bone. For this purpose, a 3D unit cell of trabecular tissue was obtained from scans of human distal tibia performed with high-resolution peripheral quantitative computed tomography (HR-pQCT). In simulations, two types of fracture of trabeculae were considered - brittle and ductile, with respective elastic and elastoplastic formulations. Two types of loading – tension and compression – were applied to the unit cell in order to assess its stress state and locations of the failure onset. Positions of damaged areas in case of brittle-fracture approach differed for tension and compression, while the same damage regions were observed for the ductile criterion in both loading conditions. It was found that the first modelling approach resulted in about two times higher effective strength of trabecular bone as compared to that for the second approach: 11.49 MPa and 4.94 MPa, respectively. The calculated values of effective strength for brittle and ductile material models are in good agreement with the magnitudes of tensile and compressive strength of trabecular bone reported in the literature. Effective parameters of the trabecular bone tissue – ultimate compressive and tensile strength as well as yield stress – are considerably lower than those of individual trabeculae: some 8% of the respective magnitudes for trabeculae.