Skip to main content

Table 1 The material properties of the anterior cruciate ligament found by fitting the constitutive model (Eq. 24 ) to tensile experimental data

From: Visco-hyperelastic constitutive modeling of soft tissues based on short and long-term internal variables

Elastic properties Short-term viscous properties Long-term viscous properties
a 2 = 2.213 × 106 Pa a 3 = 3.879 (dimensionless) a 4 = 0.3653 × 106 Pa.s, a 5 = 0.652 (dimensionless) τ i  = 3.77, 148.24, 10987.98 s
w i  = 0.154, 0.161, 0.682 s−1
(i = 1, 2, 3)
  1. The elastic properties, a 2 and a 3 , were found from the near equilibrium loading (1.2%/s); and the short-term viscous properties, a 4 and a 5 , were determined using the ramp loading under 25%/s strain-rate (Figure 1). Finally, the long term viscous parameters, τ i and w i , were determined from the stress relaxation data (Figure 2). The compressive property of the ligament, a 1, was neglected in the fit. All parameters were enforced to be positive to satisfy the second law of thermodynamics. Additionally, the constraint of Σw i  = 1 was also applied (Eq. 7) during the optimization.