## 2 Methodology
### New Helmet and Its Optimization
For instance, stress and strains are compared against proposed injury thresholds, and conclusions about possible brain injuries are inferred. By using YEAHM as a tool to optimize the thickness of the liner made of AC, the objective is to find a configuration capable of not reproducing injuries, or with an injury risk as low as possible and lower than EPS. After determining the best solution for AC, the same helmet was tested with EPS to establish a further and direct comparison. This is important to verify if a helmet composed of AC liners is an alternative to the ones made of EPS. Once finding the optimum thickness that results in a better performance from the sustainable solution in comparison with the synthetic one, some new liners were modelled by keeping the thickness and removing sections of material, reducing the overall weight of the helmet. The same procedure described above was repeated and the results compared. YEAHM, the Finite Element Head Model  
The human brain can be simply described as a soft highly metabolically active tissue, floating in cerebrospinal fluid (CSF) within the rigid cranium [66]. YEAHM consists of skull, CSF and brain as shown in Figure 7. The brain model is constituted by the following sections: frontal, parietal, temporal, and occipital lobes, both hemispheres, cerebrum, cerebellum, corpus callosum, thalamus, midbrain, and brain stem. CSF volume represents all the intracranial structures between skull and brain. The CSF is described using solid elements with a low shear modulus, as in other publications [67]. The global CSF model is a combination of the CFS and the meninges. For instance, the inner surface of the CSF model acts as the pia mater, surrounding the brain and dipping down into sulci and fissures and thus, acquiring the brain shape. YEAHM's skull has a variable thickness ranging from 4 to 9 mm. In addition to the ventricles and the skull with a variable thickness, the latter was also modelled with its real irregularities at the base. All parts were modelled as solid. Due to the complex geometry of skull, brain and CSF, these were meshed with 10-noded-tetrahedral elements. The YEAHM is constituted by a total of 991617 ten-node tetrahedrons. More details about the mesh are presented in Table 2.  
Figure 7: YEAHM consists of skull (blue), CSF (red) and brain (green). To model the brain's nonlinear elasticity and the time-dependent behavior, the one-term Ogden hyperelastic model and a Prony-series are combined, forming a hyper-viscoelastic material model. Coupled visco-hyperelastic constitutive models were used to describe the nonlinear mechanical behavior of brain tissue [68]. Table 3 presents the values used for brain matter, where \(\mu_{0}\) is the initial shear modulus, \(\tau_{k}\) are the characteristic relaxation times and \(g_{k}\) are the relaxation coefficients. CSF was modelled as a solid with a very low shear modulus and as a hyperelastic material, using the Mooney-Rivlin strain energy potential. Table 4 gives the values used to model the CSF. The CSF density used is the same as water since the two are similar. Skull bone was modelled as an isotropic linear-elastic material. Table 5 gives the values used to model the bone, where \(\rho\), \(E\) and \(v\) are the density, Young's modulus and Poisson's ratio, respectively. In YEAHM, it is possible for the brain to move relatively to the skull, which is a biofidelic interaction. The relative motion between the skull and brain is simulated by the sliding interface between the skull and CSF and between the CSF and brain. Finite sliding formulation and kinematic contact method were used with a friction coefficient for tangential behavior of 0.2 as used in [PERSON] and [PERSON] [69]. YEAHM was validated against experimental data from impact tests on cadavers performed by [PERSON] et al. [70], comparing the intracranial pressure at frontal, parietal, occipital, and posterior fossa regions. YEAHM was also validated in terms of brain intracranial motion by simulating the impact performed by [PERSON] et al. [71].