Anatomical structure | Element type | Material parameters | References |
---|---|---|---|
Vertebral body | |||
- Cortical shell | 4-node shell | Linear elastic E = 11,300 MPa, ν = 0.2 | [25] |
- Cancellous bone | 8-node brick | Linear elastic E = 140 MPa, ν = 0.2 | [25] |
Vertebral posterior elements | 2-node beam | Quasi-rigid | |
Facet joints | 4-node shell | As for cortical bone, with exponential softened contact between adjacent facet surfaces | |
Intervertebral discs | |||
- Anulus fibrosus | 8-node brick | Hyperelastic, Mooney-Rivlin C10 = 0.7, C01 = 0.2 | |
- Collagen fibres | Tension-only, ABAQUS ‘rebar’ elements | Linear elastic E = 500 MPa, ν = 0.3 | [22] |
- Nucleus pulposus | 4-node, hydrostatic fluid | Incompressible | [26] |
Ribs | 4-node shell | Linear elastic E = 9,860 MPa, ν = 0.3 | [21] |
Costal cartilage | 4-node shell | Linear elastic E = 49 MPa, ν = 0.4 | [21] |
Sternum/Manubrium | 4-node shell | Linear elastic E = 9,860 MPa, ν = 0.3 | [21] |
Costo-vertebral joints | 2-node beam | Linear elastic Ecompr = 245 N/mm; Torsional stiffness, kt = 4167Nmm/rad; Bending stiffness, kb = 6706Nmm/rad (average antero-posterior and cranio-caudal flexion stiffness) | |
Ligaments | |||
- Ligamentum flava, supra-/inter-spinous, capsular, inter-transverse | 2-node, tension-only connector | Piecewise, non-linear elastic | |
- Anterior/posterior longitudinal ligament | 2-node spring | Piecewise, non-linear elastic | [27] |
- Inter-costal connections | 2-node, tension-only connector | Linear elastic, E = 25 MPa | [28] |
Implant | |||
- Screws | 8-node brick | Linear elastic, E = 108,000 MPa, ν = 0.3 | Titanium alloy |
- Rod | 8-node brick and 2-node rigid beam | Linear elastic, perfectly plastic E = 108,000 MPa, ν = 0.3 Yield Stress = 390 MPa | Titanium alloy |