How can you model tire deformation in finite element analysis?

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Tire deformation is a complex phenomenon that affects the performance, safety, and durability of vehicles. To understand and optimize the behavior of tires under different load and road conditions, engineers often use finite element analysis (FEA), a numerical method that can simulate the stress, strain, and displacement of tire structures. In this article, you will learn how to model tire deformation in FEA using some basic steps and concepts.

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Tuan Manh NGUYEN

Innovative Engineering Solutions | CAE Consultant & Mentor | Driving Excellence ??

1 Choose a tire model

The first step in modeling tire deformation in FEA is to choose a suitable tire model that represents the geometry, material, and boundary conditions of the real tire. There are different types of tire models, such as rigid, flexible, or hybrid, depending on the level of detail and accuracy required. For example, a rigid tire model assumes that the tire does not deform and only considers the contact forces with the road, while a flexible tire model accounts for the deformation and stresses of the tire components, such as the tread, sidewall, and carcass. A hybrid tire model combines both rigid and flexible elements to balance the computational cost and accuracy.

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Tuan Manh NGUYEN

Innovative Engineering Solutions | CAE Consultant & Mentor | Driving Excellence ??
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I think the choice of a tire model for FEA depends on the needed detail and accuracy. Tire simulations can range from two-dimensional to three-dimensional, starting with a simpler 2D model for design validation before progressing to a more complex 3D representation. Tire modeling is challenging due to geometric and material nonlinearity, large deformations, and nonlinear contact conditions. Advanced hyperelastic models like neo-Hookean, Mooney-Rivlin, or Ogden are suitable for capturing nonlinear and large deformation behavior, especially in elastomeric materials like those found in tires. Anisotropic behavior in tires, attributed to materials like steel belts, can be addressed using anisotropic material models such as orthotropic models.

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2 Define the material properties

The next step in modeling tire deformation in FEA is to define the material properties of the tire components, such as the rubber, steel, and fabric. The material properties include the density, elasticity, damping, and friction coefficients, which affect how the tire responds to external forces and displacements. The material properties can be obtained from experimental tests, literature, or manufacturer data. However, some material properties, such as the hyperelasticity and viscoelasticity of rubber, are nonlinear and require special models and parameters to describe their behavior.

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Tuan Manh NGUYEN

Innovative Engineering Solutions | CAE Consultant & Mentor | Driving Excellence ??
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The tire plays a crucial role in automotive engineering, mainly crafted from rubber material with additional reinforced components. It's a bit tricky in FEA to choose the right material modeling to capture its unique characteristics. The rubber material is commonly simulated using the Mooney-Rivlin hyperplastic material model, chosen for its ability to handle large deformations and the nonlinear elastic behavior of rubber. Additionally, several reinforced components contribute to improving tire performance, typically represented as shell elements layered for anisotropic materials or some simple beads as beam elements.

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3 Apply the load and boundary conditions

The third step in modeling tire deformation in FEA is to apply the load and boundary conditions that simulate the real-world scenarios of the tire. The load conditions include the vertical load, inflation pressure, braking torque, and steering angle, which generate the contact forces and moments between the tire and the road. The boundary conditions include the constraints, such as the fixed or rotational nodes, that limit the degrees of freedom of the tire. The load and boundary conditions can be static or dynamic, depending on whether they change over time or not.

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4 Mesh the tire domain

The fourth step in modeling tire deformation in FEA is to mesh the tire domain, which means dividing the tire into smaller elements that can be solved by the FEA equations. The mesh quality and size affect the accuracy and efficiency of the FEA results. A finer mesh can capture more details and reduce the numerical errors, but also increases the computational time and memory. A coarser mesh can speed up the calculation, but also introduces more approximation and uncertainty. Therefore, a good mesh should balance the trade-off between accuracy and efficiency.

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5 Solve the FEA equations

The fifth step in modeling tire deformation in FEA is to solve the FEA equations, which are derived from the equilibrium and compatibility conditions of the tire elements. The FEA equations are usually nonlinear and coupled, meaning that they depend on each other and on the unknown variables, such as the stress, strain, and displacement. To solve the FEA equations, various numerical methods, such as the Newton-Raphson method, the finite difference method, or the finite volume method, can be used. The solution process involves iterations and convergence criteria, which determine when the FEA results are sufficiently accurate and stable.

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6 Analyze the FEA results

The final step in modeling tire deformation in FEA is to analyze the FEA results, which provide the information about the stress, strain, and displacement of the tire elements under the load and boundary conditions. The FEA results can be visualized using graphs, plots, or animations, which show the distribution and variation of the FEA variables. The FEA results can also be compared with experimental data, analytical solutions, or other FEA models, which can validate the accuracy and reliability of the FEA model. The FEA results can also be used to optimize the design and performance of the tire, such as reducing the rolling resistance, improving the traction, or enhancing the durability.

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Tuan Manh NGUYEN

Innovative Engineering Solutions | CAE Consultant & Mentor | Driving Excellence ??
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I think validation is a very important step for tire modeling and simulation. Make sure to compare what you get in your simulation with the experiments data. By looking at simple things such as load vs deformation or the footprint area when the load applied. If your simulation results looks good and reasonable but there is a huge difference, go back and double check how you've modeled the materials. Once you validate it, your tire model now can become like a virtual testing. And remember, you've also got to validate its dynamic behavior, that's equally important.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How can you model tire deformation in finite element analysis?

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3

4

5

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1 Choose a tire model

2 Define the material properties

3 Apply the load and boundary conditions

4 Mesh the tire domain

5 Solve the FEA equations

6 Analyze the FEA results

7 Here’s what else to consider

Mechanics

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How can you model tire deformation in finite element analysis?

1

2

3

4

5

6

7

1 Choose a tire model

2 Define the material properties

3 Apply the load and boundary conditions

4 Mesh the tire domain

5 Solve the FEA equations

6 Analyze the FEA results

7 Here’s what else to consider

Mechanics

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