“…Simplified tire models with an analytical expression or purely empirically/semi-empirical formulae, such as the magic model [7], brush model [8], and LuGre model [9], etc., are used to investigate the longitudinal and lateral dynamics of the tire-road interactions with the computationally effective feature, while the structural elasticity and the flexible deformation of the tire belt and tire sidewall are ignored, leading to the existing deviation under certain manoeuvres. At the other extreme, taking the advantage the powerful computation and the composite characteristic [10], detailed tire models, such as the finite element tire model [6], absolute nodal coordinate formulation (ANCF) finite element tire model [11], and spectral element tire model [12], present the detail material feature and geometrical feature at the expense of much computation resource. Additionally, the detailed tire/road contacting feature can be investigated with the detailed tire and road model, while the large computation resource, the extensive finite element analysis (FEA)-oriented pre-processing, and the difficultly-obtained material parameters limit the extended application for vehicle dynamics.…”