## 4 Results and Discussion
### Discussion on Simulation Results for Varying Droplet Diameter  
The von Mises and S33 stress vary exponentially, allowing the development of empirical relations describing the evolution of these two crucial factors. The exponential fitting of von Mises and S33 stresses is assumed as,  
* von Mises stress exponential relation: \[\sigma_{\text{vs}}=a[e^{bx}-e^{cx}]\] (3) where \(\sigma_{\text{vs}}\) is the von Mises stress at the top surface of the LEP. After curve fitting, \(a=66\) MPa, \(b=-0.04\), and \(c=-1.5\). * S33 exponential relation: \[\sigma_{33}=ae^{bx}+d\] (4) where \(\sigma_{33}\) is the S33 stress at the top surface of the LEP. After curve fitting, \(a=-85\) MPa, \(b=-0.6\), and \(c=100\) MPa. In both cases, a is the interception with the Y axis, and b and c are the exponents. D is the offset in the Y direction. \(x=\left(\frac{dt}{dL}\right)\) is a non-dimensional variable where dl represents the current diameter and dL the normalisation reference diameter of 1 mm. To verify the robustness of Equations (3) and (4), Figures 10 and 11 compare the von Mises and normal S33 stresses of the numerical FE results with the MATLAB R2022b exponential fitting, for varying diameters from 0.5 mm to 5 mm. The comparison between empirical fitting equations and the numerical FE results is found to agree well with each other. Figure 10: S33 for varying droplet diameters, 0.5 mm–5 mm. (MATLAB Fit vs. Numerical FE values). Figure 9: von Mises stress for different droplet diameters, 0.5 mm–4.5 mm. Figure 10 illustrates the evolution of S33 stress for droplet diameters ranging from 0.5 mm to 5 mm. The S33 maximum peak value reaches around 100 MPa for 5 mm diameter droplets. Unlike the von Mises stress, the larger the droplet, the more important the S33 stress. The increase in S33 with larger droplet diameters leads to higher normal stress acting on the surface, probably due to the higher kinetic energy and mass of bigger droplets. This will cause more perpendicular, direct, and localised damage. Figure 11 illustrates the evolution of von Mises stress for droplet diameters ranging from 0.5 mm to 5 mm. The overall trend shows a von Mises maximum peak value of around 60 MPa for droplet diameters of 2.5 mm, decreasing to 50 MPa for 5 mm droplet diameters. The von Mises trend shows limitations as the droplet diameter exceeds 2.5 mm, where the curves start decreasing. The von Mises criterion measures the yielding potential of the material. The maximum von Mises stress at a 2.5 mm droplet diameter suggests that the stress state of the principal and shear stresses is at its maximum to cause failure and deformation. However, studying the behaviour of S33 over time in Figure 10 does not fully explain the trend seen in the von Mises stress. Beyond this specific droplet size, although the S33 stresses increase, other factors, such as the principal stresses S11, S22, S12, S23, and S13, may limit further increases in von Mises stress. Specifically, it means that a 2 mm droplet will cause more damage in multiple directions, while a larger droplet, despite being less critical for yielding, causes more unidirectional stress. Similarly, the computational analysis conducted by [PERSON] and [PERSON] [PERSON] and [PERSON] (2014) illustrates von Mises curves that decrease as the droplet's mass fraction increases. However, other researchers like [PERSON] et al. [PERSON] et al. (2016) have proven it unrealistic since the bigger the droplet, the more critical for material damage. Indeed, their experimental simulation compares the relationship between droplet diameter, ranging from 0.76 mm to 3.5 mm and the specific impacts. The non-dimensional specific impacts used in [PERSON] et al. (2016) may be considered equivalent to the number of load cycles sustained by a material element. In this case, the lower the specific impact, the less it would withstand the loads applied by the raindrop impact. Moreover, [PERSON] et al. [PERSON] et al.