3.2.1. Energy Distribution during Side Crash Simulation

The first law of thermodynamics is the law of conservation of energy. In an isolated system, the total energy remains constant, even when the energy changes from one form to another. The energy can be converted into various types in an automobile side impact, such as kinetic energy, potential energy, internal energy, or friction dissipation energy. In general, most kinetic energy in an automobile crash causes a considerable change in internal energy as a result of elastic and plastic deformation. Total energy can be measured as the sum of several energies according to Equation (13):

$$E\_{total} = E\_i + E\_k + E\_v + E\_f + E\_{c} \tag{13}$$

where *Ei*, *Ek*, *Ev*, *Ef*, and *Ee* are internal energy, kinetic energy, viscous dissipation energy, friction dissipation energy, and external work, respectively.

Figure 11 shows the distribution of the total energy during the side crash. The total energy is 142 kJ. First, the velocity of MDB decreased gradually as a result of friction between the ground and MDB before the collision. The *Ek* decreased sharply during the collision because the velocity of the MDB decreased, whereas the *Ei* was increased by plastic and elastic deformation, and *Ev* increased to 5.8 kJ as a result of material damping. During the collision, other energies increased, but total energies were maintained. For example, when the collision time was 0.0385 s, the *Ei.MDB*, *Ei.Sedan*, *Ek*, *Ev*, and *Ef* were 45.1 kJ, 45.7 kJ, 45.4 kJ, 2.9 kJ, and 5.9 kJ, respectively, as shown in Figure 11a,b. The value of *Ee* was 0 kJ because the external work had not yet occurred.

**Figure 11.** Energy conversion during side crash: (**a**) flow of energy distribution at t = 0.0385 s; (**b**) distribution of energies according to collision time; (**c**) distribution of energy conversion at t = 0.071 s.

Figure 11c shows the percentage of energy at t = 0.071 s, when MDB velocity was about 0 m/s. The *Ei.MDB* was 82.5 kJ, accounting 58.1% of the total energy, indicating that the 58.1% of total energy (142 kJ) was absorbed by the MDB during the side crash. On the other hand, the sum of *Ei.Sedan* absorbed by the doors, automobile body, and other frames was 44.6 kJ, with 5.4 kJ of energy absorbed by the center pillar and PW. According to the above data, the center pillar and PW took 12% of the sedan internal energy. The inner part of the center pillar was not included in this study. If the inner part of the center pillar been included, the center pillar, including the outer and inner portions, as well as the PW, would be expected to absorb 15~18% of the internal energy. The effect of PW and PS on energy distribution and intrusion resistance was investigated following, as reported below.
