A Three Dimensional Constitutive Model for the Stress Relaxation of Articular Ligaments

Frances M. Davis · Raffaella De Vita
Virginia Tech


Abstract. A new nonlinear constitutive model for the three-dimensional stress relaxation of articular ligaments is proposed. The model accounts for finite strains, anisotropy, and strain-dependent stress relaxation behavior exhibited by these ligaments. The model parameters are identified using published uniaxial stress–stretch and stress relaxation data on human medial collateral ligaments (MCLs) subjected to tensile tests in the fiber and transverse to the fiber directions (Quapp and Weiss in J Biomech Eng Trans ASME 120:757–763, 1998; Bonifasi-Lista et al. in J Orthop Res 23(1):67–76, 2005). The constitutive equation is then used to predict the nonlinear elastic and stress relaxation response of ligaments subjected to shear deformations in the fiber direction and transverse to the fiber direction, and an equibiaxial extension. A direct comparison with stress relaxation data collected by subjecting human MCLs to shear deformation in the fiber direction is presented in order to demonstrate the predictive capabilities of the model.

Keywords: nonlinear viscoelasticity, stress relaxation, transversely isotropic material, finite strain, simple shear, biaxial stretch, collagenous tissue, medial collateral ligament (MCL).