**2.1 3D head model**

The head form was developed using Blender v. 2.79 3D computer graphics software toolset. Multiple digital pictures of a human head form were taken from different directions (top, front, rear, left, and right views) using a digital camera and imported into Blender to create the desired computer aided design (CAD) models, as shown in **Figure 1**.

As can be found in the open literature, the human head consists of a scalp, bone, and a series of three fibrous tissue layers namely Dura mater, Arachnoid, and Pia mater, known as the meninges [10], as shown in **Figure 2**. In this work, the head form was symmetrical to reduce the computation time. The brain and various skull parts were developed in SolidWorks by taking several cross-sections of the MRI sagittal, lateral, and transverse head images and corresponding dimensions [10]. Additional features such as neck bone and muscle were also incorporated in the model, as shown in **Figure 2**.

**143**

**2.2 Materials model**

*(b) detailed 3D head model.*

**Figure 2.**

**Figure 1.**

described by

*2.2.1 Materials model for head*

*Head Impact Injury Mitigation to Vehicle Occupants: An Investigation of Interior Padding…*

The mechanical properties of different sections of the head are the most critical and challenging parts to develop in order to construct a reliable finite element method (FEM) based head model. The material models chosen for the brain were isotropic and elastic linear viscoelastic with shear and bulk relaxation behaviors

*(a) Schematic diagram of the subarachnoid space (SAS) space, trabeculae, pia, and arachnoid. [10];* 

( ) ( ) /

τ

τ

=− − <sup>∑</sup> (1)

(2)

1 1 1 *<sup>k</sup> <sup>N</sup> <sup>P</sup> <sup>t</sup> k k Gt G g e*<sup>−</sup>

( ) ( ) *<sup>k</sup>*

1 1 1

*<sup>N</sup> <sup>P</sup> <sup>t</sup> k k Kt K k e*<sup>−</sup> = =− − <sup>∑</sup> /

=

0

0

*DOI: http://dx.doi.org/10.5772/intechopen.95250*

*3D head model: (a) Exterior section, (b) detailed modified interion section.*

*Head Impact Injury Mitigation to Vehicle Occupants: An Investigation of Interior Padding… DOI: http://dx.doi.org/10.5772/intechopen.95250*

#### **Figure 1.**

*Advancement and New Understanding in Brain Injury*

energy absorption and the resulting head injury varied.

ing strain and stress values.

**2. Numerical model**

models, as shown in **Figure 1**.

model, as shown in **Figure 2**.

**2.1 3D head model**

Recently, worldwide the number of people affected with war related TBI has

increased due to terrorism, civil and military conflicts [2, 3]. To minimize the severe illness and mortality resulting from blasts, vehicle crashes, and projectiles, several types of head protective equipment with different material options have been proposed since the end of the 19th century. Starting from the 1960s, multi-layers composite materials became a preferred option for personal armor applications, resulting in improved body armor with lightweight, good protection, flexibility, and improved comfort [4]. On the other hand, padding has been used for improving energy absorption in protective structures, packaging systems, sports equipment, handheld devices, as well as comfort and support systems. Particularly, the interior of motor vehicles has been identified as an area where severe head and neck/spinal injuries can occur in frontal, side, rear, roll over, or oblique impacts. Hence, there is a critical need to reduce occupant injuries, including potential head injury. Several researchers have investigated head impacts with the roof, pillars (A-Pillar, B-Pillar), and support structures [5–9]. For instance, Friedman and Nash [8] have proposed preventing head contact with the vehicle interior through interior padding and increased headroom to prevent serious injury during rollover crashes. Lim [9] investigated the energy absorption characteristic of foam and plastic paddings used for vehicle interior and the head injury performance. Results showed that depending on the type of materials and countermeasure space, the

However, despite evidence of correlations among impact energy, materials, and head acceleration, all of the above research did not present the influence of padding material and geometry variations on the skull-brain relative motion and the result-

In this study, simplified and complex head models with various geometries and materials including the skull, cerebrospinal fluid (CSF), muscle, and neck were considered to better understand and predict the behavior of each part and their effect on the brain response during the impact scenario. The effect of padding thickness was also considered to further analyze the interaction of the vehicle structure and the head. Particularly, the response of the head was evaluated based on the peak and rate of acceleration, strain, and stress at various locations in the brain.

The head form was developed using Blender v. 2.79 3D computer graphics software toolset. Multiple digital pictures of a human head form were taken from different directions (top, front, rear, left, and right views) using a digital camera and imported into Blender to create the desired computer aided design (CAD)

As can be found in the open literature, the human head consists of a scalp, bone, and a series of three fibrous tissue layers namely Dura mater, Arachnoid, and Pia mater, known as the meninges [10], as shown in **Figure 2**. In this work, the head form was symmetrical to reduce the computation time. The brain and various skull parts were developed in SolidWorks by taking several cross-sections of the MRI sagittal, lateral, and transverse head images and corresponding dimensions [10]. Additional features such as neck bone and muscle were also incorporated in the

**142**

*3D head model: (a) Exterior section, (b) detailed modified interion section.*

**Figure 2.**

*(a) Schematic diagram of the subarachnoid space (SAS) space, trabeculae, pia, and arachnoid. [10]; (b) detailed 3D head model.*

#### **2.2 Materials model**

#### *2.2.1 Materials model for head*

The mechanical properties of different sections of the head are the most critical and challenging parts to develop in order to construct a reliable finite element method (FEM) based head model. The material models chosen for the brain were isotropic and elastic linear viscoelastic with shear and bulk relaxation behaviors described by

$$\mathbf{G}\left(t\right) = \mathbf{G}\_0 \left[\mathbf{1} - \sum\_{k=1}^{N} \underline{\mathbf{g}}\_k^P \left(\mathbf{1} - e^{-t/\varepsilon\_k}\right)\right] \tag{1}$$

$$K(t) = K\_o \left[ \mathbf{1} - \sum\_{k=1}^{N} \underline{k\_k}^p \left( \mathbf{1} - e^{-t/\tau\_k} \right) \right] \tag{2}$$

The characteristic parameters of the Prony law used in Abaqus, *<sup>k</sup> g* and , *kk* are the weight factors, defined as.

$$\mathbf{g}\_k = \frac{\mathbf{G}\_k}{\mathbf{G}\_0}, \mathbf{k}\_k = \frac{\mathbf{K}\_k}{\mathbf{K}\_0} \tag{3}$$

Where *Gk* and *Kk* are the bulk moduli associated with the relaxation time *<sup>k</sup>* τ , and *G*<sup>0</sup> and *K*0 represent the instantaneous glassy shear and bulk modulus, respectively,

where N, , *<sup>P</sup> <sup>i</sup> g* and τ , *<sup>G</sup> <sup>i</sup> i = 1, 2, …, N* are material constants. Substitution in the small-strain expression for the shear stress yields

$$\pi(t) = G\_o \left( \mathcal{V} - \sum\_{i=1}^{N} \mathcal{V}\_i \right) \tag{4}$$

$$\text{Where } \mathcal{V}\_i = \frac{\underline{\mathbf{g}}\_i^{\mathcal{P}}}{\underline{\tau}\_i^G} \Big|\_{0}^{t} e^{-s/\tau\_i^G} \mathcal{V}(t-s) \, ds.$$

Different authors [10–14] have proposed the short-time shear modulus G0 from G0 = 528 kPa to G0 = 10 kPa and the long-time (infinite) shear modulus *G*∞ from *G*<sup>∞</sup> =168 kPa to *G*<sup>∞</sup> =2 kPa. In this work, values of 0 τ , , *G G*<sup>∞</sup> , *K*, chosen for the FEM model are shown in **Table 1**.

In this work, the mechanical properties of the bone were considered as isotropic and elastic with the Young's modulus, E = 15GPa, the Poisson's ratio υ = 0.21, and the materials' density 3 1800 , *kg m* ρ = [11]. The CSF had an average thickness of 2 mm and was considered as an elastic, incompressible medium with Young's modulus, E1 = E2 = 15 kPa, Poisson's ratio, v = 0.499, and shear modulus, G12 = 0.01 kPa [15]. The material properties for the neck bone, inner and outer tables, dipole, and neck muscles used in this work are summarized in **Table 2**.

The mechanical properties of the steel were found from the experimental tests performed in our lab, E = 210 GPa, υ <sup>=</sup> 0.3 , and 3 <sup>7890</sup> *kg m* ρ = , yield strength, *S MPa <sup>y</sup>* = 330 , and ultimate strength *S MPa ut* = 523 . Also, the characteristic of polypropylene foam, which was utilized as an energy absorber for the vehicle structural padding, was taken from the previous work [19]. The material model


**145**

**Figure 3.** *FEM head models.*

*Head Impact Injury Mitigation to Vehicle Occupants: An Investigation of Interior Padding…*

**[GPa]**

Neck bone [16] 1 1300 0.24 Inner Tables [17] 12.2 2120 0.22 Outer Tables [17] 12.2 2120 0.22 Dipole [18] 1.3 900 0.22 Neck muscles [10] 0.01 1010 0.38

**Density [kg/m3 ]** **Poisson's ratio**

used for the foam was isotropic, elastoplastic, crushable foam with hardening and

In this work, the numerical model was carried out using ABAQUS® version 2017–1. In the FEM model, three main parts were involved in the impact scenario: a steel pole, padding made of polypropylene foam, and the head, as shown in **Figure 3**. Three FEM head models were considered to evaluate the effect of modeling assumptions on the response of the head skull and the brain during an impact scenario, as shown in **Figure 3**: a) the simplified form, Skull-Brain (SB), b) Skull-CSF-Brain (SCB), and c) Composite Skull-CSF-Brain (SCCB). For the head models, 8-node solid elements with a size of 5 mm were used. For the steel pole and the padding, 4-node shell and hexahedral solid elements were used, respectively. To reduce computational resources, the head model was reduced to a symmetrical model, as shown in **Figure 3**. Depending on the padding thickness and the head skull models,

the entire model consisted of a various number of elements and nodes.

The contact between the head and the pole was defined with penalty contact (for tangential behavior) and hard contact for normal behavior. The "hard contact" option allows automatic adjustment for the stiffness generated by the "penalty contact" algorithm to minimize penetration without detrimentally affecting the time increment. The coefficient of friction between the pole and the head was

= 0.3 . The padding was constrained with the steel pole using the

*DOI: http://dx.doi.org/10.5772/intechopen.95250*

**Parts Young's modulus,**

rate dependency.

**Table 2.**

assumed to be

µ

**2.3 Modeling and meshing**

*Material properties for the head model.*

#### **Table 1.**

*The mechanical properties of brain tissue for a linear viscoelastic material model.*


*Head Impact Injury Mitigation to Vehicle Occupants: An Investigation of Interior Padding… DOI: http://dx.doi.org/10.5772/intechopen.95250*

#### **Table 2.**

*Advancement and New Understanding in Brain Injury*

the weight factors, defined as.

*<sup>i</sup> g* and

model are shown in **Table 1**.

the materials' density 3 1800 , *kg*

performed in our lab, E = 210 GPa,

τ

ρ

muscles used in this work are summarized in **Table 2**.

Shear modulus, <sup>0</sup> *G* , **at** *t* = 0 328*kPa* Shear modulus, *G* , <sup>∞</sup> at *t* = ∞ 168*kPa* Bulk modulus, K 307*kPa*

1040 kg/m3

) <sup>1</sup>

*The mechanical properties of brain tissue for a linear viscoelastic material model.*

τ, *<sup>G</sup>*

small-strain expression for the shear stress yields

respectively, where N, , *<sup>P</sup>*

The characteristic parameters of the Prony law used in Abaqus, *<sup>k</sup> g* and , *kk* are

*k k*

Where *Gk* and *Kk* are the bulk moduli associated with the relaxation time *<sup>k</sup>*

( ) *<sup>N</sup>*

Where ( ) / 0

*i G i*

τ

γ

and elastic with the Young's modulus, E = 15GPa, the Poisson's ratio

υ

*m*

*G*<sup>∞</sup> =168 kPa to *G*<sup>∞</sup> =2 kPa. In this work, values of 0

 γγ

*t G*

τ

and *G*<sup>0</sup> and *K*0 represent the instantaneous glassy shear and bulk modulus,

0 0 , *k k*

*G K g k G K* = = (3)

(4)

, , *G G*<sup>∞</sup> , *K*, chosen for the FEM

υ

= 0.21, and

*<sup>i</sup> i = 1, 2, …, N* are material constants. Substitution in the

*i i*

= = − <sup>0</sup> ∑1

> *G i <sup>P</sup> <sup>t</sup> <sup>i</sup> <sup>s</sup>*

<sup>−</sup> <sup>=</sup> <sup>−</sup> ∫

Different authors [10–14] have proposed the short-time shear modulus G0 from G0 = 528 kPa to G0 = 10 kPa and the long-time (infinite) shear modulus *G*∞ from

In this work, the mechanical properties of the bone were considered as isotropic

and was considered as an elastic, incompressible medium with Young's modulus, E1 = E2 = 15 kPa, Poisson's ratio, v = 0.499, and shear modulus, G12 = 0.01 kPa [15]. The material properties for the neck bone, inner and outer tables, dipole, and neck

*S MPa <sup>y</sup>* = 330 , and ultimate strength *S MPa ut* = 523 . Also, the characteristic of polypropylene foam, which was utilized as an energy absorber for the vehicle structural padding, was taken from the previous work [19]. The material model

τ

= 0.02 sec, 2

τ= 10−4 sec

The mechanical properties of the steel were found from the experimental tests

<sup>=</sup> 0.3 , and 3 <sup>7890</sup> *kg*

ρ

*<sup>g</sup> e t s ds* τ

 γ

τ

= [11]. The CSF had an average thickness of 2 mm

*m*

= , yield strength,

τ,

**144**

**Table 1.**

Density, ρ

Relaxation time, (

*Material properties for the head model.*

used for the foam was isotropic, elastoplastic, crushable foam with hardening and rate dependency.

#### **2.3 Modeling and meshing**

In this work, the numerical model was carried out using ABAQUS® version 2017–1. In the FEM model, three main parts were involved in the impact scenario: a steel pole, padding made of polypropylene foam, and the head, as shown in **Figure 3**. Three FEM head models were considered to evaluate the effect of modeling assumptions on the response of the head skull and the brain during an impact scenario, as shown in **Figure 3**: a) the simplified form, Skull-Brain (SB), b) Skull-CSF-Brain (SCB), and c) Composite Skull-CSF-Brain (SCCB). For the head models, 8-node solid elements with a size of 5 mm were used. For the steel pole and the padding, 4-node shell and hexahedral solid elements were used, respectively. To reduce computational resources, the head model was reduced to a symmetrical model, as shown in **Figure 3**. Depending on the padding thickness and the head skull models, the entire model consisted of a various number of elements and nodes.

The contact between the head and the pole was defined with penalty contact (for tangential behavior) and hard contact for normal behavior. The "hard contact" option allows automatic adjustment for the stiffness generated by the "penalty contact" algorithm to minimize penetration without detrimentally affecting the time increment. The coefficient of friction between the pole and the head was assumed to be µ= 0.3 . The padding was constrained with the steel pole using the

**Figure 3.** *FEM head models.*

"Tie option" interaction available in ABAQUS®. Similarly, at the interface between the skull and the CSF, the CSF and the brain, as well as the skull and the scalp, a tie option was also implemented. In this work the pole was constrained with a fixed boundary condition at the two ends. The initial condition was imposed on the head with a predefined velocity of 4 km/hr. towards the pole.
