From tension to compression: Asymmetric mechanical behaviour of trabecular bone's organic phase

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)

Characterisation of time-dependent mechanical behaviour of trabecular bone and its constituents

Trabecular bone is a porous composite material which consists of a mineral phase (mainly hydroxyapatite), organic phase (mostly type I collagen) and water assembled into a complex, hierarchical structure. In biomechanical modelling, its mechanical response to loads is generally assumed to be instantaneous, i.e. it is treated as a time-independent material. It is, however, recognised that the response of trabecular bone to loads is time-dependent. Study of this time-dependent behaviour is important in several contexts such as: to understand energy dissipation ability of bone; to understand the age-related non-traumatic fractures; to predict implant loosening due to cyclic loading; to understand progressive vertebral deformity; and for pre-clinical evaluation of total joint replacement. To investigate time-dependent behaviour, bovine trabecular bone samples were subjected to compressive loading, creep, unloading and recovery at multiple load levels (corresponding to apparent strain of 2,000-25,000 με). The results show that: the time-dependent behaviour of trabecular bone comprises of both recoverable and irrecoverable strains; the strain response is nonlinearly related to applied load levels; and the response is associated with bone volume fraction. It was found that bone with low porosity demonstrates elastic stiffening followed by elastic softening, while elastic softening is demonstrated by porous bone at relatively low loads. Linear, nonlinear viscoelastic and nonlinear viscoelastic-viscoplastic constitutive models were developed to predict trabecular bone’s time-dependent behaviour. Nonlinear viscoelastic constitutive model was found to predict the recovery behaviour well, while nonlinear viscoelastic-viscoplastic model predicts the full creep-recovery behaviour reasonably well. Depending on the requirements all these models can be used to incorporate time-dependent behaviour in finite element models. To evaluate the contribution of the key constituents of trabecular bone and its microstructure, tests were conducted on demineralised and deproteinised samples. Reversed cyclic loading experiments (tension to compression) were conducted on demineralised trabecular bone samples. It was found that demineralised bone exhibits asymmetric mechanical response - elastic stiffening in tension and softening in compression. This tension to compression transition was found to be smooth. Tensile multiple-load-creep-unload-recovery experiments on demineralised trabecular samples show irrecoverable strain (or residual strain) even at the low stress levels. Demineralised trabecular bone samples demonstrate elastic stiffening with increasing load levels in tension, and their time-dependent behaviour is nonlinear with respect to applied loads . Nonlinear viscoelastic constitutive model was developed which can predict its recovery behaviour well. Experiments on deproteinised samples showed that their modulus and strength are reasonably well related to bone volume fraction. The study considers an application of time-dependent behaviour of trabecular bone. Time-dependent properties are assigned to trabecular bone in a bone-screw system, in which the screw is subjected to cyclic loading. It is found that separation between bone and the screw at the interface can increase with increasing number of cycles which can accentuate loosening. The relative larger deformation occurs when this system to be loaded at the higher loading frequency. The deformation at the bone-screw interface is related to trabecular bone’s bone volume fraction; screws in a more porous bone are at a higher risk of loosening

Hydro-structural stability investigation of a 100 MW Francis turbine based on experimental tests and numerical simulations

Abstract This work focuses on a 100 MW Francis turbine prototype, part of one of the four horizontal ternary groups of Grimsel 2 PSPP, in Switzerland. Due to the massive integration of new renewable energy, the number of daily starts/stops of the machines has increased. Consequently, cracks on the runner blades of the Francis turbines have been noticed, without a clear explanation regarding the phenomenon responsible for their onset. To identify the main stress-full operating condition causing these cracks, the full turbine hill chart has been covered during the in situ measurement campaign including start-up, speed no-load, deep part load, best efficiency, full load and shut-down operating conditions. Then hydro-structural stability diagnosis diagrams of the prototype have been established for the whole operating range of the turbine. In addition, CFD numerical simulations for different operating conditions, along with FEM structural and modal analysis of the runner, have been carried out. The onboard measurements evidenced the highest mechanical stresses on the runner blades at speed no-load operating condition. This conclusion is supported by CFD and FEM analysis, which put in evidence the possible excitation of one of the runner’s eigen frequency by the fluctuations of the pressure field.</jats:p