Table 1.

Material properties of model components

Name	Element Type	Material Model	Material property	Reference
Cancellous bone	C3D4	Isoelastic	E = 100 MPa μ = 0.3	[30]
Cortical bone	C3D4	Isoelastic	E = 8000 MPa μ = 0.3	[30]
Cartilaginous end-plate	C3D8	Isoelastic	E = 23.8 MPa μ = 0.3	[31]
Cartilage of zygapophysial joint	C3D8	Isoelastic	E = 23.8 MPa μ = 0.3	[31]
Nucleus	C3D8H	Hyperelastic	C10 = 0.12, C01 = 0.09	[31]
Annulus ground substance	C3D8H	Hyperelastic	C10 = 0.133, C01 = 0.0333, D = 0.6	[27, 32]
Annulus fiber	Spring A	Nonlinear spring	Stress–strain curve	[31, 33, 34]
ligaments	Spring A	Nonlinear spring	Force–defection curve	[35, 36]

Material properties assumed for initial model and ATc-PECD model. E: Young modulus; μ: Poission’s ratio