Application of a Nonlinear Viscoelastic Model to the Relaxation Behavior to the Ligaments

Frances M. Davis · Raffaella De Vita
Virginia Tech


Abstract. The most successful model developed to describe viscoelasticity in soft tissues is the quasi-linear viscoelastic (QLV) model [1]. In the QLV model, the relaxation function is assumed to be a separable function of time and strain. This assumption requires that the rate of relaxation is constant for all levels of strain. Recent experimental evidence [2] demonstrated that the rate of relaxation is a non-linear function of strain, especially at small physiological strains. Therefore, a more robust model, which considers these strain-dependent nonlinearities, is necessary to characterize the relaxation behavior in soft tissues. A new transversely isotropic non-linear viscoelastic model for relaxation in ligaments is presented. In this model, a non-separable tensorial relaxation function that depends on the strain invariants and time is adopted. To the authors’ knowledge, the model represents the first fully non-linear, finite strain, anisotropic viscoelastic model applied to ligaments.

  1. Fung, Y.C. 1993. Biomechanics: Mechanical Properties of Living Tissues.
  2. Hingorani, R.V., et al., 2004. Ann Biomed Eng, 32 (2), pp. 306--312.