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Table 2 The material properties of articular cartilage (Eq. 28 ) found using data obtained from both confined compression and multistep tension and relaxation tests

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
b 1 = 0.425 × 105 Pa b 4 = 190 × 106 Pa.s τ i  = 141.00, 3.55, 14303.43 s
b 2 = 0.5 × 105 Pa w i  = 0.346, 0.0709, 0.582 s−1
b 3 = 14.2 × 106 Pa (i = 1, 2, 3)
  1. The confined compressive test was used to evaluate the stiffness of the non-fibrillar matrix, b 1 (Figure 3). The tensile test consisted of 5 steps, and 2% tensile strain was applied at 0.15%/s in each step, followed by stress relaxation. The equilibrium data at each step were used to find the elastic stiffness of the fibers, b 2 and b 3 (Figure 4). The short-term, b 4, and the long-term viscous parameters, τ i and w i , were determined by fitting the model to the entire ramp loading and stress relaxation data (Figure 5). All parameters were enforced to be positive. Additionally, the constraint of Σw i  = 1 was also applied (Eq. 7) during the optimization.