Table 1. Constitutive models by biological structure.

Structure	Material formulation	Material constants	Additional information
Grey Matter, White Matter, Cerebellum, Brain Stem	viscoelastic	G∞ = 170 kPa, G0 = 530 kPa, β = 35 s−1, B = 2.19 GPa, ρ = 1080 kg/m3	G(t) = G∞+(G0−G∞)e −βt
Skull, Vertebrae	elastic	E = 6.50 GPa, ν = 0.22, ρ = 1700 kg/m3
Intervertebral Discs	elastic	E = 8.00E-03 GPa, ν = 0.35, ρ = 1140 kg/m3
Cerebrospinal Fluid, Ventricles	elastic fluid	B = 2.19 GPa, ρ = 1006 kg/m3	zero shear resistance
Scalp, Flesh	elastic	E = 1.67E-02 GPa, ν = 0.42, ρ = 1200 kg/m3
Scalp at impact site (non-linear)	user defined stress-strain relation [23]	E = variable, ν = 0, ρ = 1200 kg/m3
Impactor	elastic	E = 0.10 GPa, ν = 0.49, mlight = 10.0 g, mgolf = 44.4 g, mheavy = 14.0 kg

Table of material properties assigned to the segmented structures of the head model: grey matter, white matter, cerebellum and brain stem are assigned viscoelastic properties using the standard Flügge model [24]. The cerebrospinal fluid is represented by an inviscid fluid similar to water. The scalp is modelled as a non-linear solid, with a complete stress-strain curve as obtained from published impact tests [23]. The skull, mandible, cervical vertebrae and intervertebral discs are assigned linear elastic material properties.