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.
The thermomechanical behavior of pneumatic tires is a highly complex transient phenomenon that, in general, requires the solution of a dynamic nonlinear coupled thermoviscoelasticity problem with heat sources resulting from internal dissipation and contact and friction. This highly complex and nonlinear system requires indepth knowledge of the geometry, material properties, friction coefficients, dissipation mechanisms, convective heat transfer coefficients, and many other aspects of tire design that are not fully understood at the present time. In this paper, a simplified approach to modeling this system that couples all of these phenomena in a straightforward manner is presented in order to predict temperature distributions in static and rolling tires. The model is based on a one-way coupling approach, wherein the solution of a mechanical rolling contact problem (with friction and viscoelastic material properties) provides heat source terms for the solution of a thermal problem. The thermal solution is based on the thermodynamics of irreversible processes and is performed on the deformed tire configuration. Several numerical examples are provided to illustrate the performance of the method.
The Biot theory for the acoustics of porous media contains drag and virtual mass coefficients that depend on the physical properties of the fluid and solid constituents, the frequency, and the microstructure of the porous medium. Biot derived an equation for the drag coefficient as a function of frequency by assuming cylindrical pores. In this paper, the finite element method is used to obtain values of the drag and virtual mass coefficients for face-centered cubic granular materials with three different porosities and compare our numerical results to Biot’s analytical solutions. By making appropriate choices of three parameters in Biot’s analytical solution for cylindrical pores—the pore size parameter, the Kozeny parameter, and the tortuosity—the analytical solution matches these numerical results very well. This suggests that with appropriate choices of these parameters the analytical approach can predict the dependence of the drag and virtual mass coefficients on frequency for an arbitrary pore geometry. These results support a relation suggested by Hovem and Ingram for approximating the pore-size parameter for spherical grains, and they also agree with a relation suggested by Berryman for the dependence of the tortuosity on the porosity.
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