Interrelation of creep and relaxation: A modeling approach for ligaments

Experimental data (Thornton et al., 1997) show that relaxation proceeds mor e rapidly (a greater slope on a log-log scale) than creep in ligament, a fa ct not explained by linear viscoelasticity. Ait interrelation between creep and relaxation is therefore developed for ligaments based on a single-inte gral nonlinear superposition model. This interrelation differs from the con volution I-elation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e., the stress-stra in curve is concave Icp as observed in ligament. We also show that it is in consistent to assume a Fung-type constitutive law (Fung, 1972) for both cre ep and relaxation. Using the published data of Thornton et al. (1997), the nonlinear interrelation developed herein predicts creep behavior from relax ation data well (R greater than or equal to 0.998). Although data are limit ed and the causal mechanisms associated with viscoelastic tissue behavior a re complex, continuum concepts demonstrated here appear capable of interrel ating creep and relaxation with fidelity.