Finite Element Formulation of Tire with Static Foundation Contact and Its Application

Abstract

Tire's are made up of a typical fiber–rubber composite structure. A finite element model of a tire with foundation contact is developed in this study. In this model, the rubber compounds are simulated by incompressible elements, which are treated using the Lagrangian multipliers method. The nonlinear mechanical properties of the elastomers are modeled by the Mooney–Rivlin model. The belts, carcass, and bead are modeled by an equivalent orthotropic material model in which the effective moduli are determined from the individual material properties of the rubber compound and cord based on the Halpin–Tsai equations. For composite elements consisting of multi-ply cord–rubber composites, three-dimensional effective elastic constants can be determined using the material model presented by Sun and Li. The contact constraint of the tire with a flat foundation and rigid rim is treated using the variable constraint method. For the large deformation description of the tire, the Lagrangian method is used here. The strain tensor and the stress tensor are selected as, respectively, the Green–Lagrangian strain tensor and the second Piola– Kirchhoff stress tensor. In finite element code, two kinds of three-dimensional elements are used – an eight-node brick isoparametric element (hexahedral element) and a six-node isoparametric element (pentahedral element). The present numerical results show that the reliability and convergence of the model are fairly good. Moreover, three groups of radial tires with different belt widths under inflation and static footprint loading are analyzed using the finite element method. Based on the detailed analysis for stress analysis parameters in the critical regions in the tires, the relative belt edge endurance is predicted.