## 2 Simulation Methodology
### Segmental Properties of Human Body in Finite Element Environment  
Defining accurate Young's modulus (YM) for the human muscle and bone structure is a great challenge for modelling a realistic human body, as human muscle and bone properties are non-linear in nature, especially the muscles and skin, which exhibit hyper-elastic and viscoelastic properties. Mechanical indentation and tensile measurement processes on soft biological tissues [30] found the YM values for the tendons, muscles, and tissues to be in-between 3 kPa and 8 kPa. A comparative study on the mechanical properties of human bones with respect to gender and age [31] found the maximum YM value of human bone as 20.04 GPa. Another investigation on the finite element modelling of  
Figure 1: (**a**) Displacement of a point on ellipsoidal section and (**b**) the axial directions considered for this analysis. Figure 2: (**a**) Practical human male sitting on a car seat, and (**b**) established CAD (Computer Aided Design) model of human. human bones [32] considered the YM as 15 GPa. For this research work, YM values for the human bones and muscles were considered as 20.04 GPa and 8 kPa, respectively. The integrated structure of human muscles and bones can be represented either by composite, fibre, or silicon substances. Considering composite had distinct advantages over other materials, as the stresses and stiffness parameters inside the composites can be calculated in an accurate way. Advanced human nutrition database [33] defines the percentage of bone inside a male human body as 15%, whereas the percentage of organ, fat, and muscles is 85%. On the basis of these percentage data, YM values for each of the human segments in all three directions were evaluated using the following relationships:  
\[E_{i-Axial}=E_{Muscle}\times f_{Muscle}+E_{Bone}\times(1-f_{Muscle}) \tag{2}\]  
\[E_{i-Transverse}=\frac{E_{Muscle}\times E_{Bone}}{E_{Muscle}\times(1-f_{Muscle })+E_{Bone}\times f_{Muscle}} \tag{3}\]  
\(E_{i-Axial}\) = axial YM of ith segment;  
\(E_{i-Transverse}\) = transverse YM of ith segment. Combining the YM values and ellipsoidal segment parameters, the stiffness values for all the human portions in all three directions were calculated using the relationship between force, stress, strain, and cross-sectional area:  
\[K_{ij-Directional}=\pi\frac{E_{ij-Directional}\theta_{per-ij-Directional}b_{per- ij-Directional}}{C_{ij-Directional}} \tag{4}\]  
\(K_{ij-Directional}\) = stiffness of jth segment in ith direction;  
\(E_{ij-Directional}\) = YM of jth segment in ith direction;  
\(a_{per-ij-Directional}\) = half axis (transverse axis-1) length of the of jth segment perpendicular to ith direction;  
\(b_{per-ij-Directional}\) = half axis (transverse axis-2) length of the of jth segment perpendicular to ith direction;  
\(C_{ij-Directional}\) = half axis length of the of jth segment in ith direction. Soft human tissues are fully incompressible in nature, and the Poisson's ratio is generally considered in the range of 0.45 and 0.49. While measuring the YM value of human soft tissue [34], the value of [PERSON]'s ratio was considered as 0.49, and the finite element model of human tissue considered [35] [PERSON]'s ratio as 0.49995. Human bones are rigid in nature and most of the past studies on human bio-dynamics assumed the bone to be a fully rigid body. From the practical point of view, the human soft tissue and muscles are more sensitive to being deformed faster than the rigid bones. [PERSON]'s ratio was considered as 0.49 for the human segments in this project. Damping coefficient varies from one portion to another inside human body.