Generalized solution for predicting relaxation from creep in soft tissue: Application to ligament

Creep and relaxation are two viscoelastic phenomena that are easily interrelated for a linearly viscoelastic material, but interrelationships are complex for nonlinearly viscoelastic materials. We use a single-integral nonlinear superposition principle to relate creep and relaxation, where the kernel is assumed to be a nonseparable product of strain and time. Herein, we develop time dependence as general power laws with up to four terms for creep compliance and relaxation modulus. Higher-order formulations give better results for ligament in terms of curve fitting and prediction of relaxation from creep. This is illustrated by a comparison between a two- and a three-term formulation on the experimental data of rabbit medial collateral ligaments. Also, an interrelation between several aspects of creep and relaxation is presented for arbitrarily high order, and the nature of high-order interrelation is discussed. The generality of the method makes it suitable to phenomenologically model many complex materials, to predict complex behaviors and to therefore reduce the amount of testing for robust material characterization.