Interest in examining the viscoelastic response of calcified tissues arises due to a variety of reasons. First, the presence of such response implies energy dissipation in the loading of bone, which may have functional importance. Second, the implication of mismatched mechanical impedance between implant and bone in the loosening of prostheses suggests that knowledge of this response in bone will be useful in prosthesis design. Third, knowledge of bone's viscoelastic behavior will lead to better understanding of the form-function relationships and deformation mechanisms in bone. Although early experiments clearly showed the existence of viscoelastic behavior in bone, the linearity of the response has generally been assumed rather than demonstrated. In an effort to compare the results of various experiments done on bone, the resulting viscoelastic functions were transformed into a common representation using the theory of linear viscoelasticity. The lack of agreement among the results as well as the failure*of results of individual experiments to satisfy internal consistency tests led to the conclusion that cortical bone in compression appears to be non-linearly viscoelastic.

Therefore, the dynamic moduli for frequencies between 2×10^-3 and 100 Hz and the relaxation modulus between 1 and 10⁵ 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 axial load. At body temperature the dynamic loss tangent increased from .009 at 100 Hz to .013 at 1 Hz to .025 below 0.1 Hz. The total change in shear modulus over eight decades of time-scale was 15 to 35%, most of this change occurring at long times in relaxation. Bovine bone, although stiffer, exhibited viscoelastic behavior similar to human bone.

Nonlinear response, in the form of the shear modulus increasing with strain level, became apparant for strains above 10^-4. The observation that this effect is less pronounced in dynamic tests than in relaxation, was shown to be consistent with both single and multiple integral nonlinear theories. 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 a superposed axial stress.

Biaxial experiments were also performed since bones in the body are subjected to stresses which are more complex than uniaxial tension or shear. An axial tensile stress 2500 psi 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 3200 psi.

The temperature dependence of the viscoelastic response was thermorheologically complex. This implies that bone experiments must be done at body temperature to be relevant to the in vivo situation and suggests multiple mechanisms for the response, several of which were examined theoretically.

The contributions of homogenous and inhomogenous thermoelastic coupling to mechanical loss in bone was calculated using Zener's theory. These contributions are small but measurable. An expression for the loss due to piezoelectric coupling was derived;​ this loss is too small to be measurable. Motion of fluids in Haversian canals gives rise to a loss peaking near 3 Hz. In compression this loss can exceed several percent for large specimens. Analysis of previous work suggests strongly that boundary motion (cement lines and lamellae) is responsible for the longterm relaxations observed in the present study.