Viscoelastic properties of wet cortical bone—I. Torsional and biaxial studies

The dynamic moduli for frequencies between 2 × 10 −3 and 100 Hz and the relaxation modulus between 1 and 10 5 sec have been measured in torsion for human and bovine cortical bone kept wet in Ringer's solution, as a function of temperature, strain-level and a superposed axial load. At body temperature, the dynamic loss tangent increased from 0.009 at 100 Hz, to 0.013 at 1 Hz, to 0.025 below 0.1 Hz. The total change in shear modulus over 8 decades of time-scale was 15–35%, most of this change occurring at long times in relaxation. Bovine bone, although stiffer, exhibited viscoelastic behavior similar to that of human bone. Nonlinear viscoelastic response, in the form of the isochronous shear modulus increasing with strain level, became apparent for strains above 10 −4, and was observed to be less pronounced in dynamic tests than in relaxation. Recovery at long times occurred more slowly than relaxation, but always approached completion asymptotically. This effect, small in human bone and negligible in bovine bone, is accentuated by the superposition of an axial stress on the torsion sample. Biaxial experiments were performed, since bones in the body are subjected to stresses which are more complex than uniaxial tension or shear. An axial tensile stress of 17.2 MN/m 2 increased the high frequency loss tangent of human bone by ⋍20% and changed the shear modulus by ⋍1.5%; for bovine bone, the shear modulus was changed by 0.6% by an axial stress of 22.1 MN/m 2. The temperature dependence of the viscoelastic response was found to be thermorheologically complex. This implies that bone experiments must be done at body temperature to be relevant to the in vivo situation, and that time-temperature superposition is of questionable validity for bone.