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A novel semi-analytical solution has been developed for the calculation of the static and dynamic response of an off road tire interacting with a deformable terrain, which utilizes soil parameters independent of the size of the contact patch (size-independent). The models involved in the solution presented, can be categorized in rigid and/or pneumatic tires, with or without tread pattern. After a concise literature review of related methods, a detailed presentation of the semi-analytical solution is presented, along with assumptions and limitations. A flowchart is provided, showing the main steps of the numerical implementation, and various test cases have been examined, characterized in terms of vertical load, tire dimensions, soil properties, deformability of the tire, and tread pattern. It has been found that the proposed model can qualitatively capture the response of a rolling wheel on deformable terrain.

The two-dimensional, frictional tyre-road contact interaction is investigated. A transient contact algorithm is developed, consisting of an analytical belt model, a non linear sidewall structure and a discretized viscoelastic tread foundation. The relationship between the magnitude/shape of the predicted two-dimensional pressure distribution and the corresponding belt deformation is identified. The effect of vertical load and the role of sidewall non linearity are highlighted. The modal expansion/reduction method is proposed for the increase of the computational efficiency and the effect of the degree of reduction on the simulation accuracy is presented. The qualitative results are physically explained through the participation of certain modes in the equilibrium solution, offering directions for the application of the modal reduction method in shear force oriented tyre models.