Recent advances in the development of a general three‐dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure‐volume. Several new test problems and examples of tire analysis are presented.
A steady state formulation of the rolling contact problem with friction that allows the analysis of free rolling, cornering, acceleration, and braking is presented. This formulation is applied to the finite element analysis of tires. A layered shell finite element with shear deformation that allows for large deflection and rotation is developed. In each layer, orthotropic Hookean materials or Mooney‐Rivlin type materials with fiber reinforcements can be used and the incompressibility constraint is enforced with Lagrange multipliers. The contact constraint is enforced with a penalty and the friction term, instead of the usual Coulomb friction, is regularized by a differentiable form that makes it more suitable for numerical analysis. A numerical example for a typical tire is also given.
Mathematical models of finite deformation of a rolling viscoelastic cylinder in contact with a rough foundation are developed in preparation for a general model for rolling tires. Variational principles and finite element models are derived. Numerical results are obtained for a variety of cases, including that of a pure elastic rubber cylinder, a viscoelastic cylinder, the development of standing waves, and frictional effects.