Stress relaxation function of bone and bone collagen

Relaxation Young's and shear moduli of bovine bone and bone collagen were investigated. It was found that each relaxation process observed had two stages, which were referred to as process I and process II in order of time. Process II was described by a simple exponential decay while process I was not. The Kohlrausch-Williams-Watts (KWW) function, ψ(t) = exp[t/τ₁)^B] (0 < B < 1), was found to be suitable to describe process I. The normalized relaxation modulus, M_r(t), was expressed by the combination of the simple exponential type relaxation function and the KWW function

M_r=A₁exp[−(t/τ₁)^B]+A₂exp[(t/τ₁)](0<B1)

On the basis of this equation, the relaxation mechanism in bone and bone collagen was identified. According to the model proposed for the KWW relaxation function, the stress relaxation process in bone was considered to be governed by viscoelastic properties of matrix collagen fiber. The model for the KWW relaxation function requires the disordered glassy structure of collagen fiber, which is consistent with the results of the structural investigations.