## 3 The Finite Element Model of the Tire Established in ABAQUS
### Validation of the Tire Finite Element Model  
To validate the effectiveness of the tire finite element model, several static contact and stiffness tests were conducted on a 205/55 R16 radial tire using the MTM-2 Tire Comprehensive Strength Tester (Tire and Automotive Rubber Products Research Institute, Jiangsu University, Zhenjiang, China). The tests were conducted under a rated load of 4821 N and a rated inflation pressure of 0.24 MPa, in accordance with the GB/T 23663-2009 standard [26]. All tests were performed under consistent conditions, and the average values were used as the final results. The tire contact patch under static loading was obtained using an ink-printing method, and the tire finite element simulation was carried out using ABAQUS. A comparison between the experimental and finite element simulation results of the tire contact patch is shown in Figure 2. The corresponding characteristic parameters are listed in Table 1. The comparison of experimental and simulation results for the tire radial, longitudinal, and lateral stiffness is shown in Table 2.  
statically refined along the transverse direction and divided into four distinct areas: the crown area, shoulder area, sidewall area, and rim area, as shown in Figure 3. Using the longitudinal groove \(G_{1}(G^{\prime}{}_{1})\) of the tire tread as a boundary, the area covered by the tread pattern is divided into the crown area and shoulder area. These two areas are in direct contact with the road surface and provide the required traction or grip for real-time driving, braking, and steering. \(G_{0}\) represents the center of symmetry for the crown area, and \(G_{2}(G^{\prime}{}_{2})\) indicates the end point of the tread pattern. The region between \(G_{2}(G^{\prime}{}_{2})\) and \(G_{3}(G^{\prime}{}_{3})\) is defined as the sidewall area, which remains out of contact with external components. The region from \(G_{3}\) (the termination point of the \(G^{\prime}{}_{3}\) treadwear rubber outer contour) to \(G_{4}(G^{\prime}{}_{4})\) at the end of the tire bead is designated as the rim area, which directly interfaces with the rim. As the tire rolls over the road surface, the crown area deforms and leaves a flat footprint, known as the contact patch area. The ground deformation area of the tire is dynamically refined along the circumferential direction and divided into three sub-areas: entry into contact patch area A (\(D_{1}D_{2}\)), contact patch area B (\(D_{2}D_{3}\)), and exit from contact patch area C (\(D_{3}D_{4}\)), as shown in Figure 4. \(D_{1}\) and \(D_{4}\) correspond to the maximum response locations, namely acceleration, strain, and displacement, before entering and after exiting the contact patch area, respectively. \(D_{0}\), \(D_{2}\), and \(D_{3}\) represent the symmetric center and the front and rear critical boundaries of contact patch area B, respectively. \(\theta_{d}\) and \(\theta_{c}\) are defined as the deformation angle and the contact angle of the rolling tire, respectively.  
The ground deformation area of the tire inner liner is unfolded into a plane and divided into 21 smaller areas along the transverse and circumferential directions. \"L\" and \"R\" represent the left and right sides of the tire, respectively, as shown in Figure 5.  
Figure 4: Circumferential dynamic partitioning of the tire ground deformation area for refinement.  
Figure 3: Transverse static partitioning of the tire inner liner for refinement.