Application of nonlinear viscoelastic models to describe ligament behavior

Recent experiments in rat medial collateral ligament revealed that the rate of stress relaxation is strain dependent and the rate of creep is stress dependent. This nonlinear behavior requires a more general description than the separable quasilinear viscoelasticity theory commonly used in tissue biomechanics. The purpose of this study was to determine whether the nonlinear theory of Schapery or the modified superposition method could adequately model the strain-dependent stress-relaxation behavior of ligaments. It is shown herein that both theories describe available nonlinear experimental ligament data well and hence can account for both elastic and viscous nonlinearities. However, modified superposition allows for a more direct interpretation of the relationship between model parameters and physical behavior, such as elastic and viscous nonlinearities, than does Schapery's theory. Hence, the modified superposition model is suggested to describe ligament data demonstrating both elastic nonlinearity and strain-dependent relaxation rate behavior. The behavior of the modified superposition model under a sinusoidal strain history is also examined. The model predicts that both elastic and viscous behaviors are dependent on strain amplitude and frequency.