Table 2.
Material parameters and their values for the inhomogeneous models of cartilage, i.e., depth-dependent transversely isotropic poroelastic and fibril-reinforced poroelastic models.
| Model | Parameters | Superficial zone | Middle zone | Deep zone | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
|
| ||||||||||
| Sim. 1 | Sim 2.1 | Sim. 2.2 | Sim. 1 | Sim 2.1 | Sim 2.2 | Sim. 1 | Sim. 2.1 | Sim. 2.2 | ||
|
| ||||||||||
| Depth-dependent transversel y isotropic poroelastic | Ep (MPa) | 5.80 | 20.00 | 24.00 | 4.00 | 14.14 | 16.97 | 2.00 | 7.07 | 8.49 |
| Et (MPa) | 0.46 | 0.46 | 0.46 | 0.46 | 0.46 | 0.46 | 0.46 | 0.46 | 0.46 | |
| νp (−) | 0.87 | 0.42 | 0.42 | 0.87 | 0.42 | 0.42 | 0.87 | 0.42 | 0.42 | |
| νtp (−) | 0.030 | 0.07 | 0.06 | 0.05 | 0.08 | 0.08 | 0.20 | 0.12 | 0.12 | |
| Gt (MPa) | 2.50 | 10.00 | 12.00 | 2.00 | 7.07 | 8.45 | 1.00 | 3.53 | 4.24 | |
| (Danso et al., 2014; Elliott et al., 2002; Mow et al., 2005; Vaziri et al., 2008; Wilson et al., 2004) | k (10−15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| m4/Ns) | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | |
| e0 (−) | ||||||||||
|
| ||||||||||
| Depth-dependent fibril-reinforced poroelastic | Ef (MPa) | 5.80 | - | - | 5.80 | - | - | 5.80 | - | - |
| Em (MPa) | 0.46 | - | - | 0.46 | - | - | 0.46 | - | - | |
| νm (−) | 0.42 | - | - | 0.42 | - | - | 0.42 | - | - | |
| k (10−15 | 1.00 | - | - | 1.00 | - | - | 1.00 | - | - | |
| m4/Ns) | 4.00 | - | - | 4.00 | - | - | 4.00 | - | - | |
| (Danso et al., 2014; Halonen et al., 2014; Mow et al., 2005; Wilson et al., 2003; Wilson et al., 2004) | e0 (−) | |||||||||
Parameters in Simulation (Sim.) 1 for the transversely isotropic poroelastic model are based on the literature. Parameters for depth-dependent transversely isotropic poroelastic model: Ep- the in-plane Young’s modulus, Et- out-of-plane Young’s modulus, νp- in-plane Poisson’s ratio, νtp- the Poisson’s ratio determining strain resulting from the stress which is normal to the plane of isotropy, Gt - out-of-plane shear modulus, k- permeability and e0- void ratio; and fibril-reinforced poroelasticEf - the fibril network modulus, Em- non-fibrillar matrix modulus, νm- Poission’s ratio of the non-fibrillar matrix, k- permeability and e0- void ratio. For the transversely isotropic poroelastic cartilage Simulation (Sim.) 2.1 and Simulation (Sim.) 2.2, the longitudinal Poisson’s ratio (νtp) was adjusted so that the material stability conditions were fulfilled (ABAQUS Documentation, 2013).