C.H. Liu, P. Helnwein, G. Hofstetter, H.A. Mang:
"3D-Finite Element Analysis of Automobile Tires";
in: "Computational Mechanics '92 - Proceedings of the International Conference on Computational Engineering Science", Technology Publications, Atlanta, USA, 1992, 490.
Three-dimensional finite element analysis of automobile tires is a very challenging task. The structure of a tire is very complex, consisting of several different types of rubber, reinforced with cord layers. The analysis has to take into account incompressible material behavior and both large displacements and large strains.
The finite element program MARC permits the analysis of tires by means of three-dimensional rubber elements on the basis of incorporating the condition of incompressible material behavior by means of Lagrange multipliers. A drawback of this method is the increase of the number of degrees of freedom by the number of Lagrange multipliers.
In order to obtain an efficient formulation for three-dimensional analysis of tires, three-dimensional hybrid finite elements, based on a three-field Hu-Washizu principle, proposed by Simo, have been developed. The elements are characterized by treating the displacements, the hydrostatic pressure and the dilatation as independent variables. Assuming a discontinous approximation for the pressure and the dilatation field accros the element boundaries, a generalized displacement formulation is obtained. Hence, no additional degrees of freedom appear in the system of linear algebraic equations. Following the basic idea of the rebar elements, av displacements. These elements, consisting only of the cord layers, are characterized by having the same number of nodes and degrees of freedom as the rubber elements. Hence, they can be superimposed to the 3D rubber elements without the need of additional degress of freedom. Moreover, the application of rubber and rebar elements to describe the composite material of the tire yields a good numerical approximation of the stresses of both the rubber and the cord layers. Hence, this formulation is superior to the method using elements with average composite material properties.
The numerical study contains the 3D-FE analysis of an automobile tire.