## 2 Human-Seat Coupling Modelling
### The Mechanical Model Based on Energy Method  
In physics, the law of conservation of energy states that the total energy of an isolated system remains constant and it is said to be conserved over time [28]. Therefore, the energy input to the human-seat coupling system can be divided into four parts after collision. The first part of the energy is absorbed through deformation and fracture of the seat structures. The second part of the energy is converted into the kinetic energy of the seat. The third part of the energy is dissipated through the work of the impact on the occupants. The fourth part is the kinetic energy of the system after the collision. Similarly, the energy absorbed by the deformation and fracture of the seat structures can also be divided into two parts. One part is the energy absorbed by the deformation of the key energy-absorbing structure, and the other part is the energy absorbed by the deformation of other structures of the seat.  
\[E_{in}=W+W^{e}=K_{0}-W_{human}-W_{other}-E \tag{1}\]  
\[E=\frac{1}{2}\int_{V}\rho\ddot{\mathbf{u}}\mathrm{d}v \tag{2}\]  
In Equation (1), \(E_{in}\) is the energy absorbed by the key energy-absorbing structure of the seat. \(W\) is the energy absorbed by the elastic deformation of the key energy-absorbing structure of the seat. \(W^{e}\) is the energy absorbed through the plastic deformation of the key energy-absorbing structure. \(K_{0}\) is the total energy input to the system. Since plastic deformation is the most efficient way for ductile materials to absorb energy, the energy dissipated by viscous deformation, friction or fracture is not considered here. \(W_{human}\) is the work completed by the impact on the occupant. \(W_{other}\) is the energy absorbed by other structures of the seat except the key energy-absorbing structure during the collision. \(E\) is the kinetic energy after the collision.  
Since this paper intended to study of the key energy-absorbing structure of the seat, the other structures of the seat remained unchanged. Therefore, \(W_{other}\) is considered as approximately a constant value even through the key energy-absorbing structure changes. In the equivalent simplified model which is established according to the energy dissipation condition of the human-seat coupling system, all structures of the seat except the key energy-absorbing structure are regarded as a rigid body-damping system. As is shown in Equation (3), the energy absorbed by the damping is used to represent the energy absorbed by structures of the seat except the key energy absorbing structure. The damping device works only when \(\mathbf{F}_{y}\) is greater than the pre-set critical force.  
\[W_{other}=\int_{s}\mathbf{F}_{y}(\mathbf{u})\cdot\mathrm{d}\mathbf{u} \tag{3}\]The key energy-absorbing structure is connected to the outer frame by bolts at point C and point D. See Figure 2 for details. The structure is simplified to a V-shaped beam in the following paragraphs. Point A and point B are the front-most point and the inflection point, respectively.  
On the basis of the above, the mechanical model of the human-seat coupling system during collision is shown in Figure 3. The imaginary line A'B'C in the figure indicates the key energy-absorbing structure after deformation and it is only a schematic diagram. The red area is considered to be between the pelvis and the lumbar column of the ATD. \(\mathbf{F}_{p}\) is resultant of the external forces on it. The arrow in the figure is only a schematic representation and does not indicate the true direction and magnitude of the force. A section view of the ATD is shown in Figure 4. The green area between the lumbar column and the pelvis is used to measure the compressive load.  
Figure 4: The section view of the FEM model of the Hybrid III 50 th Percentile Male ATD.  
Figure 3: Mechanical model of the human–seat coupling system during the collision.  
Figure 2: Partial enlargement of main structures.