4. Reviewing contact definitions for energy consistency

In an explicit or implicit virtual test, contact definitions are the most common source of non-physical energy. A contact that looks visually plausible can still inject or dissipate energy through an over-stiff penalty, an under-damped normal response, or a friction model whose parameters were copied from a different load case. This chapter treats the contact definition as an energy budget: every penalty stiffness, damping coefficient, and friction parameter must be traceable to a physical stiffness, a measured damping ratio, or a validated friction coefficient, and the resulting contact energy must be reconcilable against the global energy balance.

Why contact parameters break the energy balance

Penalty contact replaces a hard constraint with a compliant spring. The penalty stiffness k_p is not a physical property of the material; it is a numerical stiffness chosen large enough to keep penetration small relative to element size, yet small enough to keep the stable time increment acceptable. In an explicit solver the stable increment scales roughly with sqrt(m/k_p), so doubling k_p to reduce penetration by half also halves the stable increment and doubles the cost. More importantly, an over-stiff penalty converts penetration into a large elastic restoring force, and the resulting contact spring energy E_c = ½ k_p δ² can dominate the energy balance even when the visible penetration is sub-millimetre.

Damping in the normal direction is intended to dissipate the high-frequency ringing that penalty contact produces at impact. It is usually specified as a damping coefficient c or as a critical damping fraction ξ relative to the contact's effective mass. If ξ is set too high, the contact behaves like a dashpot and removes energy that should have been transferred into the structure; if it is zero, the ringing persists and contaminates the internal energy history. Friction parameters — the friction coefficient μ, the elastic slip stiffness, and the static-to-kinetic transition — determine how much tangential work is converted into heat. A friction coefficient that is too high locks the interface and produces spurious tangential forces; one that is too low lets the interface slide when it should stick, and the missing tangential reaction shows up as an energy deficit.

The energy-consistency review workflow

The review proceeds in four passes, each of which can be completed before the full transient run is trusted. First, extract the contact definition from the input deck and tabulate every parameter with its source. Second, compute the contact's characteristic stiffness and damping and compare them against the adjacent element stiffness and the expected damping ratio. Third, run a short instrumented probe — a single impact or a single sliding cycle — and read the contact energy channels directly. Fourth, reconcile the contact energy against the global energy balance and decide whether the parameter set is admissible.

For the tabulation pass, the relevant fields are the penalty stiffness (or the stiffness scale factor and the underlying element stiffness), the normal damping coefficient or critical damping fraction, the friction coefficient, the elastic slip stiffness, and the contact thickness or search tolerance. Each field should carry a provenance note: measured, derived from material data, inherited from a template, or assumed. Parameters marked "assumed" are the first candidates for the sensitivity study.

For the characteristic-value pass, a useful sanity check is to compare the penalty stiffness with the stiffness of the contacting elements. A common rule of thumb is that k_p should be one to two orders of magnitude above the element stiffness k_e ≈ EA/L in the contact direction, but not so high that the stable increment collapses. For a steel block of cross-section 100 mm² and length 10 mm, k_e ≈ 210 GPa × 100 mm² / 10 mm = 2.1 × 10⁶ N/mm; a penalty stiffness of 2 × 10⁷ N/mm is a reasonable starting point, while 2 × 10⁹ N/mm is almost certainly over-stiff and will show up as a large contact spring energy spike at first impact.

Reading the contact energy channels

Most explicit solvers expose contact energy as a separate history variable, often split into normal spring energy, damping dissipation, and friction dissipation. The review should read these channels rather than infer them from the total. A healthy normal contact shows a spring-energy spike at first impact that decays within a few oscillations as damping removes the ringing; the damping dissipation rises monotonically and then plateaus. If the spring energy keeps growing after the impact, the penalty stiffness is too high or the contact is being re-detected at a new location each increment. If the damping dissipation rises without bound, the damping coefficient is too large and the contact is acting as a brake.

Friction work deserves separate attention because its sign is diagnostic. In a well-posed sliding contact, the friction work should be non-negative and should increase only while slip is occurring. A friction work that oscillates in sign indicates that the elastic slip stiffness is too high relative to the element size, so the interface is alternating between stick and slip every increment. A friction work that stays flat while the normal force is clearly non-zero indicates that the friction coefficient is effectively zero — often because the friction model was defined on a contact pair that never actually enters the active set.

Worked example: a bolted bracket under shock

Consider a steel bracket (E = 210 GPa, ρ = 7850 kg/m³) bolted to a base plate and subjected to a 50 g half-sine shock. The contact between bracket foot and plate is modelled with penalty contact. The initial definition uses a penalty scale factor of 1.0 relative to the element stiffness, a critical damping fraction of 0.0, and a friction coefficient of 0.3 inherited from a static template. The probe run shows a contact spring energy that reaches 8 % of the peak internal energy and does not decay, and a friction work that oscillates in sign during the first 2 ms.

The diagnosis is twofold. The zero damping leaves the impact ringing undamped, so the spring energy persists; the oscillating friction work points to an elastic slip stiffness that is too high for the 2 mm element size at the foot. The re-tune sets the critical damping fraction to 0.3, reduces the elastic slip stiffness so that the maximum elastic slip is about 10 % of the element size, and keeps the friction coefficient at 0.3 pending a sensitivity run at 0.2 and 0.4. After the re-tune, the contact spring energy peaks at 2.5 % of the peak internal energy and decays within 1.5 ms, and the friction work is monotonic. The global energy drift stays below 1 % of the peak internal energy, which is the acceptance criterion for this model.

Parameter review checklist

The review is complete when every contact parameter has a stated physical anchor, the probe run shows decaying contact spring energy and monotonic friction work, and the global energy drift is within the model's acceptance budget. Parameters that cannot be anchored should be flagged as assumptions and covered by a sensitivity run before the virtual test is used for a design decision.