#### Problem Definition

The interaction of rolling tires with hard pavement and soft soil presents a challenging numerical modeling problem. Using the capabilities of the multi-physics code LS-DYNA, PEC has developed well-defined approaches for accurate yet efficient modelling of the most demanding class of tires in the world: aircraft tires. To take one example, the bottoming load of the Boeing 737 main-gear tire is about 120,000 lbs, which is equal to the weight of roughly forty sedans. The inflation pressures are an order of magnitude higher than car tires, at 200-psi or more. Meanwhile, the running speeds for aircraft tires rival those of race cars.

#### Numerical Modelling Approach

Finite element models of aircraft tires were developed using a simplified approach that employs a smeared-property orthotropic carcass material, using *MAT_ORTHOTROPIC_ELASTIC. The smeared properties represent the combination of the different components: tread, bulk rubber, reinforcement plies, and so on. The specified pressure for each tire is modeled with *AIRBAG_SIMPLE_PRESSURE, which allows the pressure in the tire to fluctuate depending on the applied vertical load as the tire rolls over obstacles. Detailed features like tire tread blocks have been omitted from the model owing to their limited relevance in the problems of interest.

Material Axes for Carcass Orthotropic Constitutive Law

#### Tire Model Calibration

The geometry of the tires is based on manufacturer data sheets, and the dimensions vary depending upon inflation pressure. Matching the inflated dimensions and load-deflection behavior of the tire model requires a balance between initial uninflated geometry and material properties, which is determined through an iterative modeling process. PEC has developed efficient approaches that optimize the procedure. The parameters of the tire material model are determined with LS-OPT to match the pushdown load-deflection experimental data and inflated dimensions provided by the tire manufacturers.

Examples of Tires that were Numerically Simulated with LS-DYNA

#### Summary

Overall, the tire models that are developed using this approach meet three main criteria for capturing the effects of rolling tires on hard or soft surfaces. Those criteria are:

• Correct geometry at the rated inflation pressure
• Numerical stability while the tire rolls and experiences high dynamic loads

This modelling approach is attractive due to its simplicity and produces the correct deformation within the loading range of interest.