_Applied_  
_sciences_  
_Article_  
Modelling the Interaction between a Laterally Deflected Car  
Type and a Road Surface  
[PERSON] 1,*,*\({}^{\text{\LARAR  
An approach to predicting the slippage of a tractor's driving tyres, including a numerical expression of the tyre inflation pressure, was discussed in [4]. [PERSON] [5] used a hyper-elastic model of a tyre to predict energy in the tyre and contact stresses. A study of friction in the case of rubber sliding on smooth glass, concrete and asphalt road surfaces was presented by [PERSON] et al. [6]. There have been significant efforts to understand tyre-soil interactions. [PERSON] et al. [7] studied the dependence on wheel pressure and external vertical loads in the case of wheel interaction with a terrain surface. [PERSON] and [PERSON] [8] presented stochastic soil-tyre models which could serve as tools for predicting model responses due to various uncertainties. The tyre-sand interaction has been investigated by several authors [7; 8; 9; 10]. A tyre-sand interaction model was also proposed in [11] and showed good agreement with experimental data. [PERSON] et al. [10] presented experimental data on the motion of a vehicle travelling on dry sand. Their work also contains comparisons with theoretical research; the values of tyre forces are also given. Several papers investigated snow-influenced conditions [12; 13; 14; 15]. [PERSON] [12] calibrated and validated a tyre-snow interaction model, [PERSON] et al. [13] presented a numerical investigation of snow traction characteristics, [PERSON] et al. [14] presented a general analysis of tyre-road contact in winter conditions and [PERSON] et al. [15] performed modelling of tyres on snow. The work of [PERSON] et al. [16] was focused on the temperature dependence of traction on ice and snow. These authors also derived the limiting curve of force transmission on ice and snow. In [17], thermal effects and a strong correlation between thermal conditions and transmittable forces on a sand road were found by monitoring temperatures on a tyre surface using a high-speed infrared camera. Most physically adjusted theoretical relationships are of semi-empirical character, that is, they were obtained based on experimental results. Due to the large number of parameters, experimental validation of theoretical results can be problematic. Generally, the most important tyre parameters are estimated by manufacturers by conducting tyre dynamics tests. However, these tests cannot fully characterise the tyre in special conditions, for example, dynamic behaviour under low inflation pressure [18]. Due to the high costs of experimental tests, numerical simulation has become an important alternative to physical testing. Substantial progress in computer hardware and the improvement of numerical discrete analysis methods has stimulated the development of advanced software tools able to solve complicated physical problems, including tyre-road interactions. Novel software technology makes theoretical analysis methods more feasible. Physical data that have not been measured experimentally may be inferred using numerical analysis. However, the numerical analysis of tyres involves several difficulties stemming from geometric complexity and the use of materials exhibiting a high degree of nonlinearity. The remarkable differences in the sizes of tyre structures cause the most trouble in the creation of numerical schemes. The required fine discretisation of the tread part of the tyre substructures and inhomogeneous road or pavement layers in the contact zone become more crucial in the 3D case. Different approaches have been proposed for discretisation of both tyre and terrain and their coupling. The characteristics of tyres on wet surfaces were examined by [PERSON] and [PERSON] [19]. Their work used the finite element method (FEM) and the smoothed-particle hydrodynamic method. The multiscale approach presents the most general strategy formulated by coupling the discrete element method and the FEM models on the contact surface.