Shuqiao Xie

Evaluating the macroscopic yield behaviour of trabecular bone using a nonlinear homogenisation approach

Computational homogenisation approaches using high resolution images and finite element (FE) modelling have been extensively employed to evaluate the anisotropic elastic properties of trabecular bone. The aim of this study was to extend its application to characterise the macroscopic yield behaviour of trabecular bone. Twenty trabecular bone samples were scanned using a micro-computed tomography device, converted to voxelised FE meshes and subjected to 160 load cases each (to define a homogenised multiaxial yield surface which represents several possible strain combinations). Simulations were carried out using a parallel code developed in-house. The nonlinear algorithms included both geometrical and material nonlinearities. The study found that for tension-tension and compression-compression regimes in normal strain space, the yield strains have an isotropic behaviour. However, in the tension-compression quadrants, pure shear and combined normal-shear planes, the macroscopic strain norms at yield have a relatively large variation. Also, our treatment of clockwise and counter-clockwise shears as separate loading cases showed that the differences in these two directions cannot be ignored. A quadric yield surface, used to evaluate the goodness of fit, showed that an isotropic criterion adequately represents yield in strain space though errors with orthotropic and anisotropic criteria are slightly smaller. Consequently, although the isotropic yield surface presents itself as the most suitable assumption, it may not work well for all load cases. This work provides a comprehensive assessment of material symmetries of trabecular bone at the macroscale and describes in detail its macroscopic yield and its underlying microscopic mechanics.

Nonlinear viscoelastic characterization of bovine trabecular bone

The time-independent elastic properties of trabecular bone have been extensively investigated, and several stiffness–density relations have been proposed. Although it is recognized that trabecular bone exhibits time-dependent mechanical behaviour, a property of viscoelastic materials, the characterization of this behaviour has received limited attention. The objective of the present study was to investigate the time-dependent behaviour of bovine trabecular bone through a series of compressive creep–recovery experiments and to identify its nonlinear constitutive viscoelastic material parameters. Uniaxial compressive creep and recovery experiments at multiple loads were performed on cylindrical bovine trabecular bone samples (

Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone

n = 19

Characterisation of time-dependent mechanical behaviour of trabecular bone samples

n=19). Creep response was found to be significant and always comprised of recoverable and irrecoverable strains, even at low stress/strain levels. This response was also found to vary nonlinearly with applied stress. A systematic methodology was developed to separate recoverable (nonlinear viscoelastic) and irrecoverable (permanent) strains from the total experimental strain response. We found that Schapery’s nonlinear viscoelastic constitutive model describes the viscoelastic response of the trabecular bone, and parameters associated with this model were estimated from the multiple load creep–recovery (MLCR) experiments. Nonlinear viscoelastic recovery compliance was found to have a decreasing and then increasing trend with increasing stress level, indicating possible stiffening and softening behaviour of trabecular bone due to creep. The obtained parameters from MLCR tests, expressed as second-order polynomial functions of stress, showed a similar trend for all the samples, and also demonstrate stiffening–softening behaviour with increasing stress.

Time-dependent behaviour of bone accentuates loosening in the fixation of fractures using bone-screw systems

Trabecular bone is a cellular composite material comprising primarily of mineral and organic phases with their content ratio known to change with age. Therefore, the contribution of bone constituents on bone’s mechanical behaviour, in tension and compression, at varying load levels and with changing porosity (which increases with age) is of great interest, but remains unknown. We investigated the mechanical response of demineralised bone by subjecting a set of bone samples to fully reversed cyclic tension–compression loads with varying magnitudes. We show that the tension to compression response of the organic phase of trabecular bone is asymmetric; it stiffens in tension and undergoes stiffness reduction in compression. Our results indicate that demineralised trabecular bone struts experience inelastic buckling under compression which causes irreversible damage, while irreversible strains due to microcracking are less visible in tension. We also identified that the values of this asymmetric mechanical response is associated to the original bone volume ratio (BV/TV).