Table 2 Details of the element types and material parameters (with references) included in the FE models

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

[24, 26]

- 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 E_compr = 245 N/mm; Torsional stiffness, k_t = 4167Nmm/rad; Bending stiffness, k_b = 6706Nmm/rad (average antero-posterior and cranio-caudal flexion stiffness)

[19, 23]

Ligaments

- Ligamentum flava, supra-/inter-spinous, capsular, inter-transverse

2-node, tension-only connector

Piecewise, non-linear elastic

[20, 27, 30]

- 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