Contact Mechanics
How FEM handles contact between parts — formulations, convergence, and practical tips.
Contact is one of the most common sources of nonlinearity in structural FEM. It models the interaction between two surfaces that can press against each other, slide, or separate — without the surfaces overlapping or passing through each other.
Why contact is hard
In a standard FEM model, each part is meshed independently. Without contact, parts have no knowledge of each other. The solver would let them overlap freely — which is physically wrong. Contact constraints prevent overlap (penetration) and optionally transmit friction forces.
The challenge: the solver doesn't know in advance which nodes will be in contact. It must iterate, checking and updating the contact state at each step.
Contact types
Bonded contact
The two surfaces behave as if they are glued together — no separation, no sliding. This is equivalent to merging the nodes of both parts.
Use it for: permanent welds, adhesive bonds, press fits that don't slip.
Benefit: Behaves linearly — no convergence iterations needed. Much faster to solve than frictional contact.
Frictionless contact
Surfaces can slide freely relative to each other but cannot penetrate. Normal forces are transmitted; no tangential forces.
Use it for: lubricated sliding surfaces, symmetry planes, initial contact studies.
Frictional contact
Surfaces resist relative sliding up to a friction limit (Coulomb friction). Once the tangential force exceeds μ × normal force, the surfaces slide.
Use it for: clamped joints, bolted connections, real mechanical contacts.
Frictional contact is the most computationally expensive contact type. It requires many iterations and can fail to converge if the friction coefficient is high or the contact area changes rapidly.
Contact formulations
Penalty method
A stiff spring is placed between the two surfaces. Some penetration is allowed (controlled by the penalty stiffness). Easier to converge but allows small overlaps.
Lagrange multiplier method
No penetration is allowed by definition. More accurate but harder to converge, especially with complex contact geometries.
Dr.Q uses augmented Lagrange by default — a hybrid that combines accuracy with reasonable convergence.
Practical guidelines
- Start with bonded contact and switch to frictional only if sliding is physically relevant to the result you need.
- Mesh consistently across the contact interface. Large element size mismatches cause contact pressure spikes and convergence problems.
- Check contact status in the results: are the surfaces actually in contact where you expected? Separated surfaces are a common modelling oversight.
- Avoid point contacts — a sharp edge pressing against a flat surface creates a singularity. Add a small fillet or distribute the load over an area.
Geometry requirements
Contact surfaces must be geometrically close — not touching, but within a small gap. Very large initial gaps require more iterations to close and can cause the solver to fail to find contact at all. Use assembly cleanup in the CAD system to ensure consistent small clearances (0.01–0.1 mm).