Contact Non-linearity

What Is It?

Contact non-linearity is the non-linearity introduced by interfaces that change state during the analysis — surfaces that open, close, slide or separate. Contact is inherently non-linear because the constraint on the structure depends on the deformation. When two surfaces are in contact, they transmit force and constrain relative motion. When they separate, the constraint is removed. This changing constraint alters the structural stiffness and the load path during the analysis, making the problem non-linear.

Why It Matters

Many engineering structures involve contact interfaces — bolted joints, pinned connections, sliding surfaces, support gaps, interference fits and assemblies of components. In each case, the contact state may change under load: a bolted joint may open under tension, a sliding surface may transition from sticking to sliding, a support gap may close under deflection. These changes alter the load path — force that was transmitted through contact may be redirected when the contact opens. A linear analysis with fixed contact assumptions cannot capture these changes and may produce results that do not represent the real structural behaviour.

Contact can change the load path during the analysis. A joint that opens redirects force to other load paths. A support that engages changes the boundary conditions. These changes are invisible to linear analysis.

Contact States

Normal and Tangential Behaviour

Contact behaviour is decomposed into normal and tangential components. The normal behaviour governs the transmission of force perpendicular to the contact surface — preventing penetration when in contact and allowing separation when the contact force becomes tensile (or zero, for standard contact). The tangential behaviour governs the transmission of force along the contact surface — friction. When the tangential force is below the friction limit, the surfaces stick (no relative motion). When the tangential force exceeds the friction limit, the surfaces slide.

Coulomb friction:

τ_limit  =  μ · p

where:
τ_limit  =  shear stress limit for sliding
μ        =  coefficient of friction
p        =  contact pressure (normal)

If τ < τ_limit:  sticking (no sliding)
If τ ≥ τ_limit:  sliding (kinetic friction)

Penalty-Based Contact

The penalty method is the most common contact enforcement approach in FEA. It introduces a stiff spring between the contact surfaces that resists penetration. When the surfaces are in contact and tend to penetrate, the penalty spring generates a force proportional to the penetration depth. The penalty stiffness determines how much penetration is allowed — a higher stiffness allows less penetration but can cause convergence difficulties; a lower stiffness allows more penetration but is numerically more stable. The penalty stiffness is a numerical parameter, not a physical property, and should be chosen to balance accuracy and stability.

CONTACT CONSIDERATION: Excessively stiff numerical contact can introduce artificial high-frequency response and unrealistic local forces. The penalty stiffness should be high enough to prevent significant penetration but not so high that it causes convergence problems or numerical artefacts.

Augmented Lagrangian Methods

The augmented Lagrangian method is an alternative to the pure penalty method. It combines the penalty approach with Lagrange multiplier corrections to reduce the sensitivity to the penalty stiffness. It typically allows less penetration than the pure penalty method for the same stiffness and may improve accuracy for contact pressure prediction. It is more computationally expensive per iteration but may improve convergence for difficult contact problems. Many FEA solvers offer augmented Lagrangian contact as an option.

Friction Coefficient Sensitivity

The friction coefficient can significantly affect the results of a contact analysis. A higher friction coefficient means more force is transferred in the tangential direction — the interface is closer to bonded. A lower coefficient means less tangential force — the interface slides more easily. For bolted joints, the friction coefficient affects load transfer between members. For sliding interfaces, it affects the force required to initiate sliding. The friction coefficient is often uncertain — it depends on surface condition, lubrication, temperature and wear. Sensitivity studies on the friction coefficient are advisable where the results are sensitive to it.

Contact Chattering

Contact chattering is a convergence problem where contact nodes oscillate between open and closed states across iterations. The contact opens in one iteration, closes in the next, opens again — preventing convergence. Chattering can be caused by contact stiffness that is too high, by oscillating loads, or by geometry that creates marginal contact conditions. Solutions include reducing the contact stiffness, using contact damping, smoothing the contact surface or switching to a different contact algorithm.

COMMON MISTAKE: Using a friction coefficient of zero when friction is physically present, or using a single friction coefficient without considering that it varies with surface condition, lubrication and temperature.

Initial Penetration and Gap

In a real structure, components may have initial interference (press-fit) or initial gaps (clearance). The FEA model must represent these initial conditions correctly. An initial penetration in the model that does not exist in reality will generate artificial contact forces at the start of the analysis. An initial gap that is too large or too small will affect when contact engages. Initial penetration should be checked and corrected — most solvers provide options to resolve initial overclosure or to account for initial gap.

Key Takeaways

• Contact non-linearity arises from interfaces that open, close, slide or separate during loading
• Contact changes the structural constraints and therefore the load path
• Penalty and augmented Lagrangian methods are the standard contact enforcement approaches
• Friction coefficient sensitivity should be assessed where results depend on it
• Initial penetration and gaps must be correctly represented in the model