Relationships of Viscosity With Contact Hardness and Modulus of Bone Matrix Measured by Nanoindentation

Creep is an active form of time-dependent viscoelastic deformation that occurs in bone tissue during daily life. Recent findings indicate bone mineralization, which is involved in determining the elastic and plastic properties of bone matrix, can also contribute in controlling its viscoelastic property. Nanoindentation viscosity was used as a direct measure for the capacity of a material to resist viscous-like flow under loading. The objectives of this study were to examine (1) whether the nanoindentation viscosity obtained using the traditional viscoelastic Voigt model can describe creep response of bone matrix and (2) how the nanoindentation viscosity is related to contact hardness and elastic modulus. The Voigt model accurately described the creep behavior of bone matrix $(r2>0.96,p<0.001)$⁠. The nanoindentation viscosity had strong relationships with nanoindentation contact hardness $(r2=0.94,p<0.001)$ and modulus $(r2=0.83,p<0.001)$ independent of tissue ages of osteonal bone matrix. The strong positive relationships of nanoindentation viscosity with contact hardness and modulus can be interpreted as increases in the mineral portion of bone matrix may limit the interfibril motion of collagen while enhancing the mechanical stability of bone. We suggest that previous nanoindentation results can be reanalyzed to characterize the viscoelastic creep using the Voigt model.