Annals of Biomedical Engineering

, Volume 40, Issue 12, pp 2541–2550 | Cite as

A Nonlinear Constitutive Model for Stress Relaxation in Ligaments and Tendons

  • Frances M. Davis
  • Raffaella De Vita


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 (J. Mech. Phys. Solids. 16:59–72, 1968). 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 collected on rat tail tendon fascicles in order to compute the model parameters. Toward this end, the rat tail tendon fascicles are assumed to be incompressible and undergo an isochoric axisymmetric deformation. A comparison with the experimental data proves that, unlike the quasi-linear viscoelastic model (Fung, Biomechanics: Mechanics of Living Tissues. Springer, New York, 1993) the constitutive law can capture the observed nonlinearities in the stress relaxation response of rat tail tendon fascicles.


Nonlinear viscoelasticity Stress relaxation Transversely isotropic material Finite strain Quasilinear viscoelasticity (QLV) Collagenous tissue Rat tail tendon 



Funding was provided by NSF Grant No. 1150397. Ms. Frances M. Davis was supported by the Ford Foundation Pre-Doctoral Fellowship and National Science Foundation Graduate Research Fellowship Program.

Conflict of Interest

The authors have no conflicts of interest with regard to this manuscript and the data presented therein.


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Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  1. 1.Mechanics of Soft Biological Systems Laboratory, Department of Engineering Science and MechanicsVirginia TechBlacksburgUSA

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