A comparison of material characterizations in frequently used constitutive models of ligaments

Longitudinal tensile and simple shear stress-strain curves of human medial collateral ligaments (MCL) were fitted by six frequently used constitutive relations of ligaments using two different fitting methods for determining which was the best fitting method and the most preferable constitutive model for describing the ligament properties. According to the results of fitting goodness, two typical constitutive models were further analyzed by FEM to investigate the effect of the variation in MCL constitutive models under some physiological loads (i.e., 4.5 Nm external tibial and 10 Nm valgus tibial torques). It was found that different fitting methods induced great variations in describing the simple shear behavior whereas no obvious difference in the longitudinal tensile behavior. The most accurate description of both the longitudinal tensile and simple shear behaviors was obtained from the constitutive model with ground substance defined by an exponential function when the parameters were fitted by the two test data, respectively. Although the distributions of maximal principal stress were almost the same, the variation in MCL constitutive models affected the highest value of the stress greatly when MCL was under the complex physiological loads.