Hyperelastic Modeling of Wide-Base Tire and Prediction of Its Contact Stresses

Description of tire model development using the finite element (FE) method is presented. Three-dimensional tire-pavement contact stresses were predicted for braking, traction, and free rolling using the FE method. Measured load-deflection curves, contact area, and contact stresses were used for model outcome validation. Slide-velocity-dependent friction and accurate input regarding geometry and material properties were considered. The developed tire model, which helped in studying contact stresses variation in each direction, was used to explain the various phenomena taking place at the tire-pavement interface during straight-line rolling. The analysis matrix includes nine rolling conditions and various loads, tire inflation pressures, and speeds. Vertical contact stresses were not significantly affected by speed or slip ratio; however, contact stresses were greatly modified along the in-plane directions by rolling conditions. Analytical expressions were introduced to represent vertical and longitudinal contact stresses for full braking and full traction. Formulas are presented for low speed and full braking, which are relevant for roadway intersections design

Concrete Pavement Blowup Considering Generalized Boundary Conditions

An analytical expression for static stability of a rectangular slab with two simply supported and two elastically restrained edges is presented. The linear elastic isotropic slab can represent a rigid pavement resting on an elastic foundation and loaded by a uniform in-plane axial load per unit length along the edges. The partially restrained edges are connected to the ground by translational and rotational elastic springs; an appropriate magnitude of the springs can capture classical boundary conditions such as free, simply supported, and clamped edges. Results from classical boundary conditions and a finite-element model were used to validate the proposed stability equation. The generalized boundary conditions were found to change the critical load by a factor of two and greatly affected the first buckling mode shape of a typical concrete pavement. The critical load was not sensitive to the slab’s geometry if the length was four times longer than the width, but this was not the case for small aspect ratios. Finally, the translational spring was found to be a defining factor in determining the influence of the other variables on the critical load

Contact Phenomenon of Free-Rolling Wide-Base Tires: Effect of Speed and Temperature

The finite-element method was used to quantify the effect of temperature and speed on contact area, deflection, and three-dimensional contact stresses of a free-rolling wide-base tire. The tire model comprised material properties identified in the laboratory and/or provided by the tire manufacturer (hyperviscoelastic rubber and linear elastic reinforcement) and accurate geometry. The model was validated using measured deflection and contact area. The analysis matrix consisted of 81 cases resulting from a combination of three loads, tire-inflation pressures, speeds, and temperatures. Four criteria were used to compare contact stresses: range, average, root-mean-square error, and coefficient of determination. Speed and temperature influence the contact area more than deflection. Longitudinal contact stresses were the most affected, followed by transverse contact stresses. In general, under constant load and tire-inflation pressure, the influence of temperature was more significant on the considered output variables than the effect of speed

Closed-Form Solution for Curling Responses in Rigid Pavements

Closed-form expressions for calculating stresses and displacements of partially restrained concrete pavement caused by a linear temperature gradient are presented. Translational and rotational linear elastic springs along the slab edges defined the partial restraint. In addition to plate theory behavior, the model assumes linear elastic concrete and an infinitely long slab resting on a Winkler foundation. The solutions of curling stresses and displacements were validated using the finite-element (FE) method and quantified the effect of semirigid connections, slab and foundation material properties, and slab thickness and width on them. Rotational and translational restraints, which can be related to joint condition in concrete pavement, had significant influence on the magnitude and location of maximum curling stresses and deflections. In addition, Westergaard analysis, a particular case of the proposed solution when there is no restriction along the slab’s edges, resulted into the largest deflections at the center of the slab and the lowest maximum curling stresses. Adjustment factors that convert the theoretical findings from an infinitely long slab to a square slab are proposed

Semicoupled Modeling of Interaction between Deformable Tires and Pavements

The interaction between deformable tires and pavements was studied using finite-element modeling and a semicoupled approach. Three finite-element models were used: (1) a hyperelastic tire rolling on an infinitely rigid surface; (2) a three-dimensional pavement model; and (3) a hyperelastic tire rolling on a deformable viscoelastic body. The tire and pavement models have been successfully compared with experimental measurements. Tire interaction with a rigid surface provided contact stresses to excite the pavement model, and results of the pavement model defined the boundary conditions of the tire rolling on the deformable body. After that, the pavement loaded with the contact stresses from the tire interacting with the deformable body was run. This study focuses on issues related to pavement damage (tire–pavement contact stresses and critical pavement responses) and lifecycle assessment (rolling resistance). Transverse contact stresses were the most affected by pavement deformation, which translated into impact on the maximum vertical strain and the maximum shear strain in the asphalt concrete layer. The tire moving on a deformable body showed that the thin pavement created a higher rolling resistance force than thick pavements. In addition, dissipation-based and deflection-based approaches for calculating pavement contribution to rolling resistance were equivalent. Finally, for the range of values considered, changes in tire inflation pressure affected the rolling resistance force more than changes in applied load

Tire-Pavement Interaction Modeling: Hyperelastic Tire and Elastic Pavement

The interaction between deformable tire and pavement was studied using the validated finite element model; the full understanding of tire–pavement contact has implications for pavement damage prediction and pavement life-cycle assessment (fuel consumption estimation). The tire’s rubber and reinforcement were considered hyperelastic and linear elastic, respectively, with material constants obtained from the tire manufacturer (rubber) and laboratory testing (reinforcement). On the other hand, the pavement was assumed linear elastic supported by linear elastic springs. This assumption was made as a first step to examine the impact of using a deformable-on-deformable tire–pavement system to predict energy in the tire and contact stresses. The effect of the pavement stiffness on contact area, tire deflection, three-dimensional contact stresses, surface deflection, internal energy of the tire and its components, the work performed by the contact forces, and dissipation caused by friction was also studied. The elastic modulus of the pavement affected the contact area, while the elastic constants of the springs were more relevant for tire deflection. In addition, stiffness of the pavement had a varying effect on each component of the three-dimensional contact stresses: vertical contact stresses remained almost constant and longitudinal ones were the most affected. The symmetry of the surface deflection decreased and the friction dissipation increased 10.2% as the elastic modulus changed from the smallest to the highest value. Finally, the work performed by the vertical contact forces was significantly higher than by the in-plane loads, and the stiffness of the pavement affected rolling resistance force, which is related to fuel consumption

Effect of Surface Friction on Tire-Pavement Contact Stresses during Vehicle Maneuvering

Accurate modeling of tire-pavement contact behavior plays an important role in the analysis of pavement performance and vehicle stability control. A threedimensional (3-D) tire-pavement interaction model was developed using the finite element method (FEM) to analyze the forces and contact stresses generated during vehicle maneuvering (free rolling, braking/acceleration, and cornering). A pneumatic radial-ply tire structure with rubber and reinforcement was simulated. The steady-state tire rolling process was simulated using an Arbitrary Lagrangian Eulerian (ALE) formulation. An improved friction model that considers the effect of sliding speed on friction coefficients was implemented to analyze the effects of pavement surface friction on contact stresses, friction forces, and cornering forces. The results show that the magnitudes and non-uniformity of contact stresses are affected by vehicle maneuvering conditions. As the pavement surface friction increases, the tangential tire-pavement contact stresses at various rolling conditions (free rolling, braking/acceleration, and cornering) and the vertical contact stresses at the cornering condition increase. It is reasonable to use the constant friction coefficient when predicting tire-pavement contact stresses at the free rolling condition or at the cornering condition with small slip angles. However, it is important to use the sliding-velocity-dependent friction model when predicting the friction force at tire braking

Development of Domain Analysis to Predict Multi-Axial Flexible Airfield Pavement Responses Due to Gear and Environmental Loadings

Flexible pavement design procedures use maximum mechanistic strains to predict service life via empirical transfer functions. The conventional method of using predefined point locations for potential damage may not accurately represent realistic pavement scenarios. For instance, flexible airfield pavement analysis mainly considers the critical strain at the bottom of the asphalt concrete (AC), which may not characterize near-surface cracking potential. In lieu of point strains, domain analysis, a new method, accounts for the multi-axial behavior of pavements, as inherently excited by three-dimensional (3-D) and nonuniform aircraft tire–pavement contact stresses. Initially applied on highway pavements considering truck tire loading, this approach is an initial breakthrough for implementing domain analysis on flexible airfield pavements; in this study, A-380 and F-16 landing gear tire loads were considered. As anticipated, speed and temperature had significant influence on cumulative domain stress and strain ratios. The decrease in speed and increase in temperature not only increased the cumulative ratios up to 1.81, but nonlinearity of the problem became more prevalent at worst loading conditions (8 kph and 45°C). Minimal difference in ratios for F-16 cases suggests that the National Airport Pavement Test Facility pavement structure became less sensitive to conditions under low loads. Point response analysis revealed that critical strains were not significantly influenced by the tire-inflation pressure, for example, tensile strain at the bottom of the AC only increased up to 13.6% (considering 8 kph speed), whereas domain analysis quantified the increase with respect to 3-D stress or strain states

Baseline Rolling Resistance for Tires’ On-Road Fuel Efficiency Using Finite Element Modeling

Calculation of truck tires rolling resistance, using the finite element method and considering variables such as incompressible visco-hyperelastic rubber materials, accurate tire geometry and steady temperature distribution, is presented. The model was validated using experimentally measured contact area and contact stresses. Rolling resistance was calculated for three values of axle load, tire inflation pressure, temperature and speed. In addition, regression analysis was used to propose a mathematical expression for predicting rolling resistance as a function of the considered variables. Finally, the contribution of tire’s rubber components to the internal energy was quantified, and it was found that sidewall and subtread were the most relevant. The results of this study will help differentiate the contribution of pavement parameters, such as mean profile depth and international roughness index, to fuel efficiency