How can you model contact and friction in nonlinear FEA?

1 Contact types

Contact is the interaction between two or more bodies that are in contact or close proximity and can be classified into different types based on the relative motion and the contact surface geometry. Node-to-surface contact is the simplest type, where a node on one body contacts a surface on another body. This type of contact is often used for point loads, supports, or small contact areas. Surface-to-surface contact is the most general type, where any point on a surface on one body can contact any point on a surface on another body. This type of contact is more realistic and accurate, but also more computationally expensive and sensitive to mesh quality. Edge-to-edge contact is a special type of contact, where an edge on one body contacts an edge on another body. This type of contact is useful for modeling sharp corners, cracks, or thin features.

2 Contact algorithms

Contact algorithms are the methods used to enforce the contact conditions and determine the contact forces and displacements. These algorithms can be divided into two categories: penalty-based and Lagrange multiplier-based. Penalty-based algorithms utilize a penalty stiffness to apply a force proportional to the penetration depth between the contacting bodies. This stiffness can be determined by the user or calculated automatically based on material properties and mesh size. These algorithms are simple and robust, but they may cause artificial stiffness and oscillations in the solution. On the other hand, Lagrange multiplier algorithms use Lagrange multipliers to impose the non-penetration constraint between contacting bodies. While these algorithms are more accurate and stable, they can increase system size and computational cost.

3 Friction models

Friction is the resistance to the relative motion between two contacting surfaces, which can have a significant effect on the structural response and energy dissipation. To quantify this, friction models are mathematical expressions that relate the friction force to the normal force and sliding velocity. Common friction models include the Coulomb friction model, where the friction force is proportional to the normal force and independent of sliding velocity, and the viscous friction model, which accounts for the effect of sliding velocity on friction force. Lastly, there is the combined friction model that combines both Coulomb and viscous models, capturing the transition from stick to slip regime and variation of friction force with velocity. The proportionality constants for each model are material properties that depend on surface roughness, lubrication, and other surface properties.

4 Mesh considerations

Mesh quality is an important factor that affects the accuracy and convergence of nonlinear FEA with contact and friction. To achieve a good mesh, it should have adequate resolution to capture contact geometry and stress distribution; compatible elements for the contacting surfaces; and a smooth transition from fine to coarse regions. A coarse mesh can lead to inaccurate contact detection, stress concentration, and numerical errors, while incompatible elements can cause artificial contact stiffness, contact pressure, and stress discontinuity. Mesh distortion, element locking, and numerical instability can occur with sudden changes in element size or aspect ratio. A mesh refinement study can help to determine the optimal mesh size for a given problem.

5 Tips and tricks

Modeling contact and friction in nonlinear FEA can be more effective and efficient with the following tips and tricks. Consider using symmetry and simplification to reduce the size and complexity of the model, but be wary of losing important features or effects that can affect the contact behavior. Employ contact pairs and sets to organize and manage multiple contact interfaces, which can help to avoid conflicts, errors, and redundancies in your contact definition. Utilize initial contact and adjustment to correct initial gaps or penetrations between your contacting surfaces. Contact controls and options can also be used to improve difficulties or issues with your contact solution. These parameters control the contact algorithm, while features modify the contact behavior. With these tips and tricks, you may achieve better results for modeling contact and friction in nonlinear FEA.

6 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?