A Nonlinear Constitutive Model for Stress Relaxation in Ligaments and Tendons

Frances M. Davis · Raffaella De Vita
Virginia Tech


Abstract. A novel constitutive model that describes stress relaxation in transversely isotropic soft collagenous tissues such as ligaments and tendons is presented. The model is formulated within the nonlinear integral representation framework proposed by Pipkin and Rogers [1]. It represents a departure from existing models in biomechanics since it describes not only the strain dependent stress relaxation behavior of collagenous tissues but also their finite strains and transverse isotropy. Axial stress-stretch data and stress relaxation data at different axial stretches are also collected on rat tail tendon fascicles in order to evaluate the constitutive model. Toward this end, the rat tail tendon fascicle is assumed to be incompressible and undergo an isochoric axisymmetric deformation. A comparison with the experimental data proves that, unlike the quasi-linear viscoelastic model [2], the constitutive law can capture the observed nonlinearities in the stress relaxation response of rat tail tendon fascicles.

  1. Pipkin, A. C., and Rogers, T. G., 1968. “A non-linear integral representation for viscoelastic behavior” Journal of the Mechanics and Physics of Solids , 16(1), pp.59–72.
  2. Fung, Y. C., 1993. Biomechanics, Mechanical Properites of Living Tissues , 2nd ed. Springer- Verlag, New York.

Keywords: nonlinear viscoelasticity, stress relaxation, transversely isotropic material, finite strain, quasilinear viscoelasticity (QLV), collagenous tissue, rat tail tendon.