2. Contact artifact taxonomy in virtual tests

In a virtual test, contact is never a single number. It is a relationship between two discretized surfaces, a contact algorithm, a time integrator, and a set of material and geometric assumptions. When that relationship breaks down, the solver does not stop and tell you "the contact model is wrong." Instead it produces artifacts: interpenetration, floating gaps, force spikes, or energy that appears from nowhere. Learning to classify these artifacts is the first step toward diagnosing them, because each class has a distinct physical signature, a distinct numerical cause, and a distinct set of remedies.

This chapter builds a working taxonomy. The goal is not to memorize definitions but to develop a diagnostic reflex: when you see a suspicious contact result, you should be able to name the artifact class, identify the likely mechanism, and choose a targeted verification step rather than blindly tightening tolerances.

Why a Taxonomy Matters

Contact artifacts are frequently misattributed. A force spike is often blamed on "stiff contact," when the real cause is a time step that is too large relative to the contact stiffness. A gap is often blamed on "penetration tolerance," when the real cause is a missing contact pair or an inverted shell normal. A non-physical energy source is often blamed on "damping," when the real cause is a penalty stiffness that injects energy during a chattering contact event.

Because the symptoms overlap, the taxonomy must be organized around what is physically impossible rather than around what the solver reports. Four classes cover the vast majority of contact artifacts in explicit and implicit virtual tests:

• Penetration — material overlap that exceeds what the contact formulation permits.
• Gaps — separation where contact should exist, or a persistent standoff that never closes.
• Force spikes — transient contact forces that are discontinuous, oscillatory, or orders of magnitude above the expected load path.
• Non-physical energy sources — energy that increases in a system that should be conservative or dissipative, or energy that appears at the contact interface without a corresponding work input.

The figure below maps these four classes onto the contact signal chain, from geometry and detection through to the force and energy outputs that a reviewer actually inspects.

Penetration: When the Constraint Is Too Soft

Penetration is the most visible artifact because it is geometric. In a penalty contact formulation, the contact force is proportional to the penetration depth: F_n = k_n · δ, where k_n is the penalty stiffness and δ is the overlap. Some penetration is therefore by design — the method trades a small, controlled overlap for numerical robustness. The artifact appears when δ exceeds the tolerance you have declared acceptable for the test.

Consider a representative example: a rigid indenter pressed into a 2 mm thick shell coupon modeled with a penalty stiffness of k_n = 1.0 × 10⁶ N/mm and an expected contact force of 500 N. The equilibrium penetration is δ = 500 / 1.0 × 10⁶ = 5 × 10⁻⁴ mm, which is negligible. If the same model is run with k_n = 1.0 × 10³ N/mm, the penetration becomes 0.5 mm — a quarter of the coupon thickness. That is no longer a numerical tolerance; it is a modeling error that will corrupt the stress field and the reported stiffness.

The diagnostic question is not "is there penetration?" but "is the penetration consistent with the declared penalty stiffness and the applied load?" If it is not, check three things in order: whether the contact pair was actually detected, whether the time step is small enough to resolve the contact event, and whether the penalty stiffness is appropriate for the material stiffness of the contacting bodies. A useful rule of thumb is that k_n should be one to two orders of magnitude below the effective stiffness that would destabilize the explicit time step.

Gaps: The Silent Failure

Gaps are more dangerous than penetration because they produce no visible overlap and often no warning. A gap artifact means that two surfaces which should be in contact are not, so the load path is broken and the structure behaves as if a joint were missing. The result is an overly compliant response, underestimated stresses, and — in energy terms — a system that appears to absorb work without a corresponding contact force.

The most common causes are geometric rather than numerical. An inverted shell normal will cause the contact search to look on the wrong side of the surface. A search tolerance smaller than the initial standoff will cause the pair to be missed at initialization. A contact pair defined between the wrong part instances — for example, between two copies of the same rigid body — will never generate a force. In explicit analyses, a gap can also appear when the time step is so large that a node passes entirely through the contact surface between two increments, a phenomenon known as tunneling.

Verification is straightforward and should be routine: at t = 0, confirm that every intended contact pair reports a detected status and a finite initial gap. If a pair reports "not detected," fix the geometry or the search tolerance before running the full analysis. During the run, monitor the gap distance at a few representative locations and confirm that it closes when the load path requires it.

Force Spikes: Discontinuity in the Load Path

Force spikes are transient contact forces that are discontinuous, oscillatory, or far above the expected load. They are the signature of a contact event that the time integrator cannot resolve. In an explicit analysis, the contact force is applied over a finite number of increments; if the contact stiffness is high and the time step is large, the force overshoots, the surfaces separate, the force drops to zero, and the cycle repeats. The result is chattering — a high-frequency oscillation superimposed on the true contact force.

A practical example: a drop test of a 1 kg component onto a rigid floor, modeled with a penalty stiffness of 5 × 10⁵ N/mm and a stable time step of 2 × 10⁻⁷ s. If the time step is increased to 2 × 10⁻⁶ s to reduce runtime, the contact event is resolved by roughly ten increments instead of one hundred, and the force history shows spikes of several times the expected peak. The fix is not to add damping — that masks the symptom — but to restore an adequate time step, reduce the penalty stiffness to a value consistent with the stable increment, or use a contact formulation that is less sensitive to the time step.

Force spikes also appear in implicit analyses, where they usually indicate a contact status change that the Newton iteration cannot converge through. In that case, the remedy is typically a smaller load increment, a contact stabilization term, or a change from a hard to a soft contact formulation.

Non-Physical Energy Sources: The Accounting Check

The energy ledger is the most powerful single diagnostic in contact review. For a system with no external work input, the total energy — internal strain energy plus kinetic energy plus dissipated energy — must be non-increasing. If it rises, energy is being created, and the contact interface is a prime suspect.

Penalty contact is the classic source. The penalty spring stores energy during penetration and releases it during separation; if the contact chatters, the spring can do net positive work on the system over a cycle. Hourglassing in reduced-integration elements can also inject energy, and mass scaling in explicit analyses changes the kinetic energy budget in ways that must be accounted for explicitly. The diagnostic procedure is to plot the energy components separately: if the internal energy rises while the external work is flat, the excess is coming from the contact formulation or the element formulation, not from the load.

A Reviewer's Checklist

The taxonomy translates directly into a review sequence. Before inspecting any contact result, confirm the geometry and normals. Then confirm that every intended pair is detected at initialization. Then compare the contact force history against the expected load path, looking for discontinuity and oscillation. Finally, reconcile the energy ledger. Each step isolates one artifact class, so a failure at any step points to a specific mechanism rather than a vague "contact problem."

The four classes are not independent. A penalty stiffness that is too low produces penetration; a penalty stiffness that is too high produces force spikes; both can inject non-physical energy; and a missed pair produces a gap that looks like a compliant joint. The value of the taxonomy is that it forces the reviewer to name the mechanism before choosing a remedy, which is the difference between a defensible virtual test and a result that merely looks plausible.