Viscoelastic properties of bone as a function of water content

Stress relaxation of bovine femur was investigated as a function of water content, phi. As found for bone and bone collagen [Sasaki et al. (1993) J. Biomech. 26, 1369-1376], all the relaxation curves measured were described by a linear combination of a Kohlrausch-Williams-Watts (KWW) function and a simple exponential decay (Debye) function: G(t)/Gi = A1 exp[- (t/tau 1)beta] + A2 exp(= t/tau 2), A1 + A2 = 1, 0 < or = beta < or = 1, where Gi is an initial value of the relaxation shear modulus G(t), A1 and A2 are portions of KWW and Debye relaxations, respectively, and tau 1 and tau 2 are relaxation times of respective relaxations. Shear modulus values in the relaxation described by the KWW function (KWW relaxation) depend remarkably on phi while those in Debye relaxation are almost constant for increasing phi. phi dependencies of A1, tau 1 and beta are explained by assuming that the elementary process for the KWW relaxation would be a rearranging process of local disorders in the collagen molecular array. The relaxation rate for the Debye relaxation (= 1/tau 2) decreases linearly with phi. This linear relation between tau 2-1 and phi was well described on the basis of the concept of non-elasticity of a solid by the nuclearion of microcracks at the area of stress concentration.