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 applicability of the empirical equation (Sasaki et al., 1993. Journal of Biomechanics 26, 1369–1376), E(t)=E0{A1 exp[−(t/τ1)β]+A2exp(−t/τ2)}, A1+A2=1, 0<β 1,where E0 is the relaxation modulus value at t=0, A1 and A2 are portions of the first term (the KWW relaxation) and the second term(the Debye relaxation), respectively, and τ1 and τ2 are relaxation times of respective relaxation processes. The relaxation modulus was generally well fitted to the empirical equation, although magnification revealed that in the short-time response region there was an inconsistency between the empirical equation and the measured data. The residual deviation increases with the decrease in time of the initial datum point which was used for the regression analysis. This tendency was concluded to be due to material properties. These results indicate the existence of a new relaxation in the short time response region (t<2–3 s) of the stress relaxation process that cannot be described by the empirical equation.