Early stage stress relaxation in compact bone

The early stage of stress relaxation, up to 10 s after strain application, in compact bone was investigated in order to find the limit of the applicab ility of the empirical equation (Sasaki et al., 1993. Journal of Biomechani cs 26, 1369-1376), E(t) = E-0{A(1) exp[-(t/tau(1))(beta)] + A(2) exp(-t/tau(2))}, A(1) + A(2) = 1, 0 < beta less than or equal to 1, where E, is the relaxation modulus value at t = 0, A(1) and A(2) are portio ns of the first term (the KWW relaxation) and the second term (the Debye re laxation), respectively, and tau(1) and tau(2) are relaxation times of resp ective relaxation processes. The relaxation modulus was generally well fitt ed to the empirical equation, although magnification revealed that in the s hort-time response region there was an inconsistency between the empirical equation and the measured data. The residual deviation increases with the d ecrease in time of the initial datum point which was used for the regressio n analysis. This tendency was concluded to be due to material properties. T hese results indicate the existence of a new relaxation in the short time r esponse region (t < 2-3 s) of the stress relaxation process that cannot be described by the empirical equation. (C) 1999 Elsevier Science Ltd. All rig hts reserved.