4. Injury criteria and biomechanical metrics

In virtual testing and certification (VTC), a crash simulation produces a time history of accelerations, forces, moments, and displacements for each occupant model. Those raw signals are not directly comparable to regulatory limits. Injury criteria convert them into normalized, physically interpretable scalars that can be compared against thresholds. This chapter explains the five metrics most frequently used in frontal and frontal-oblique occupant evaluation — HIC, chest deflection, Nij, femur force, and the associated chest acceleration limit — and shows how each is computed, where the reference frame matters, and how to judge a result against a threshold.

Head Injury Criterion (HIC)

HIC is defined over a time window within the acceleration pulse measured at the head center of gravity, expressed in units of g:

HIC = max over (t1, t2) of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt )^2.5 ]
subject to t2 - t1 ≤ 15 ms (HIC15) or ≤ 36 ms (HIC36)

In practice the resultant acceleration a(t) = sqrt(ax² + ay² + az²) is used, and the integral is evaluated numerically at the simulation output step. Two implementation details dominate result quality. First, the acceleration must be filtered with the channel frequency class specified by the regulation — CFC 1000 for head acceleration in FMVSS 208 and UN R94/R137 — before HIC is computed; computing HIC on unfiltered data inflates the peak and produces non-reproducible values. Second, the search must cover all valid windows, not only the window around the global peak, because a lower but longer pulse can yield a higher HIC.

Thresholds in common use: HIC15 ≤ 700 for the driver and passenger in FMVSS 208 frontal rigid-barrier tests, and HIC36 ≤ 1000 in UN R94. In VTC evaluation, report HIC15 and HIC36 separately and state the filter class and output sampling rate, since a 10 kHz output is generally required to resolve the CFC 1000 signal without aliasing.

Chest Deflection and Chest Acceleration

Chest deflection is the peak lateral or anteroposterior compression of the rib cage, measured between the sternum and the spine in the Hybrid III or THOR dummy, or between corresponding nodes in a human body model. It is usually normalized by the half-chest depth to give a percentage. The threshold is direction- and dummy-dependent: FMVSS 208 specifies 63 mm for the Hybrid III 50th percentile male in frontal impact, while UN R94 uses a deflection criterion of 42 mm for the 50th percentile in its frontal test. For the THOR dummy, the chest deflection limit is typically 63 mm with an additional deflection-rate criterion.

Chest acceleration, filtered to CFC 180, is limited to 60 g for a 3 ms cumulative duration (the "3 ms clip"). This is a separate criterion from deflection and must be evaluated independently: a restraint that spreads load well can pass deflection while still producing a sharp acceleration spike, and vice versa.

Neck Injury Criterion (Nij)

Nij combines the axial force and bending moment at the occipital condyle into a single normalized value:

Nij = Fz / Fzc + My / Myc

where Fz is the axial force (tension positive), My is the flexion/extension moment,
and Fzc, Myc are the corresponding critical values from the regulation.

The critical values differ for tension, compression, flexion, and extension, so four combinations must be evaluated: NTE (tension-extension), NTF (tension-flexion), NCE (compression-extension), and NCF (compression-flexion). The threshold is Nij ≤ 1.0. Because the criterion is a sum of normalized terms, a moderate force combined with a moderate moment can exceed 1.0 even when neither term alone looks alarming — this is the most common reason a neck result fails in VTC when the individual channels appear acceptable.

Sign conventions are critical. Fz is positive in tension; My is positive in flexion for the Hybrid III neck. If the model or the post-processing script uses the opposite sign for My, the flexion and extension cases are swapped and the wrong critical values are applied. Always verify the sign convention against the dummy definition before interpreting Nij.

Femur Force

Femur force is the axial compressive load transmitted through the femur, measured at the knee or femoral shaft load cell. The threshold is 10 kN per femur in FMVSS 208 and UN R94 for the 50th percentile male, with lower limits for smaller occupants. Femur force is a direct indicator of lower-extremity injury risk and is strongly influenced by knee bolster geometry, knee-to-instrument-panel clearance, and the presence of a knee airbag. In VTC, report the peak force for each leg separately and note whether the load path is through the knee bolster or through direct femur contact.

Reading the Metrics Together

The five metrics are not independent. A stiffer restraint increases chest acceleration and may increase Nij through the head-neck inertia, while a softer restraint increases chest deflection and forward excursion, which can raise femur force through knee contact. The evaluation task is therefore to identify which metric is closest to its threshold and to understand the trade-off that produced it.

Worked Example: Interpreting a Frontal VTC Result

Consider a 50th percentile male occupant model in a 56 km/h frontal rigid-barrier simulation with a force-limiting retractor and a knee airbag. The post-processing script reports the following illustrative values (these are representative example numbers, not measured results): HIC15 = 612, chest deflection = 58 mm, chest 3 ms clip = 54 g, Nij = 1.08 (NCF case), femur force = 8.4 kN left and 9.1 kN right.

Normalizing each against its threshold gives HIC 0.87, deflection 0.92, chest acceleration 0.90, Nij 1.08, and femur 0.91. The governing metric is Nij, which exceeds 1.0. The correct next step is not to soften the whole restraint — that would raise deflection and femur force — but to examine the NCF case specifically: compression force combined with flexion moment. A common cause is head contact with the airbag while the neck is still in forward flexion, producing a compression-flexion couple. Reducing the airbag inflation rate or adjusting the venting to delay head contact can lower the flexion moment without increasing chest loading. After the change, re-run and confirm that Nij falls below 1.0 while deflection and femur force remain below their limits.

Practical Checklist for Metric Evaluation

• Confirm the filter class per channel: CFC 1000 for head acceleration, CFC 180 for chest acceleration, CFC 600 for neck force and moment, CFC 600 for femur force.
• Verify sign conventions for Fz and My against the dummy definition before computing Nij; check all four cases (NTE, NTF, NCE, NCF).
• Compute HIC over all valid windows up to the specified duration, not only around the peak.
• Report chest deflection in millimeters and as a percentage of half-depth, and state the dummy or model used.
• Report femur force per leg and identify the load path (knee bolster, knee airbag, or direct contact).
• Present the governing ratio (criterion / threshold) for every metric so the design trade-off is visible.

With these five metrics computed consistently and compared against the correct thresholds, the VTC result becomes a design tool rather than a pass/fail stamp: the governing ratio tells you which restraint parameter to change, and the trade-off between metrics tells you what will happen to the others when you change it.