# Prediction of Damage to the Vehicle Underbody due to Stone Chipping
## 1 Introduction  
In automobile development, a powertrain system change necessitates the design of modified peripherals, a revised layout, and a corresponding fuel system. There is no denying that electric vehicles will replace internal-combustion-engine vehicles in the coming decades. Most electric vehicles developed include a lithium-ion battery pack mounted at the underbody. When a lithium-ion battery is pierced, the lithium usually reacts with air, causing a fire or explosion [1]. Therefore, the severe design considerations of underbody shield against the impact of external bodies or random stone chipping needs to be made. As the driving performance of newly developed automobiles is rapidly improving and the maximum driving speed is gradually increasing, aerodynamic noise, vibration and harshness (NVH) become significant in passenger vehicles [2]. Moreover, most public roads, other than toll expressways, are difficult to maintain, and roads damaged by aging due to seasonal changes are rapidly destroyed. A driving vehicle is often in contact with the stones or gravel spattered by its own or the preceding vehicles. Dropped objects that pass under vehicle tires on aged roads continuously impact the underbody, which mainly protects the engine and powertrain, and the lower parts of vehicles. In addition, impact with massive objects damage the underbody relatively faster, leading to functional loss. The cumulative fracturing caused by these various impacts is called stone chipping, which results in long-term damage to the exterior and components of vehicles. The stone chipping problem can be passively solved by applying electroplating and ceramic coating for protecting the large body chassis against external impact [3]. However, it is difficult to design the external parts of a vehicle and set the safety factor for the parts exposed to the external environment. Unlike internal combustion engine driven vehicles, electric and hydrogen-fueled vehicleshave underbody spaces that are mostly occupied by batteries and fuel cells. Thus, underbody damage can lead to the loss of vehicle function, and if a fire develops in an extreme case, passenger safety cannot be guaranteed. Thus, as a countermeasure, the critical zones need to be analyzed for deriving a prediction model, and the underbody and batteries must be robustly designed to protect against stone chipping. [PERSON] [4] proposed a mathematical model for stone chipping and investigated its effects on the underbody parts by performing simulations using the model. However, the definition of the tire model was assumed to be a cylinder. Additionally, the variables of the mathematical model, such as the vehicle driving speed, the friction of tire and the air pressure, did not express the real driving environments. [PERSON] et al. [5] analyzed the damage tendency of the vehicle coating system by stone chipping considering several factors, such as the coating thickness, the number of layers and the chipping angle. There was good correlation between the results of image processing and the parameters extracted from an electrochemical impedance spectroscopy after stone chipping tests. [PERSON] et al. [6] studied the external impact resistances and tendencies of plastic underbody parts, such as the transmission oil pan, muffler housing, and fuel system protector. [PERSON] et al. [7] developed a mathematical model for the external impact of vehicle wheels, and conducted research and analyses, using it for verification. [PERSON] proposed a model for experimental verification, and compared the analytical and experimental results obtained according to the test criteria [8]. Furthermore, a study was conducted to determine the parameters by adjusting the shell structure, boundary conditions, and impact body speed for analyzing the response of a shell plate element to low-speed impact using commercial software [9]. In addition, [PERSON] et al. [10] proposed a nonparametric kernel density estimation method based on the plane characteristics of the linear distribution method. [PERSON] et al.