Abstract
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 (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.
Highlights
Trabecular bone is an open porous composite cellular solid material from an engineering perspective
Trabecular bone is anisotropic and principal trabecular orientations vary with anatomical site; it is recognized that its anisotropic character becomes pronounced with age (Singh et al 1970)
The study of time-dependent behaviour is of interest in a number of contexts: loosening of orthopaedic implants, non-traumatic fractures due to prolonged load over time, viscoelastic compatibility of synthetic bone substitutes and energy absorption during dynamic loads (Norman et al 2006; Pollintine et al 2009; Phillips et al 2006; Linde et al 1989)
Summary
Trabecular bone is an open porous composite cellular solid material from an engineering perspective. The apparent level mechanical properties of this cellular material depend on its heterogeneous microstructure, which varies with age, disease, gender and anatomical site being considered (Keaveny et al 2001). Trabecular bone is anisotropic and principal trabecular orientations vary with anatomical site; it is recognized that its anisotropic character becomes pronounced with age (Singh et al 1970). The density of this cellular solid has been related to its time-independent elastic stiffness in a number of studies (Currey 1986; Morgan et al 2003), and these relations are frequently used in computational models of bone and bone-implant systems (Goffin et al 2013). The study of time-dependent behaviour is of interest in a number of contexts: loosening of orthopaedic implants, non-traumatic fractures due to prolonged load over time, viscoelastic compatibility of synthetic bone substitutes and energy absorption during dynamic loads (Norman et al 2006; Pollintine et al 2009; Phillips et al 2006; Linde et al 1989)
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