3. Occupant injury criteria and biomechanical targets

In restraint system development, CAE correlation is not judged by whether the simulation "looks like" the test. It is judged by whether the model reproduces the physical quantities that regulators, rating programs, and internal biomechanical targets actually use to decide pass or fail. Those quantities are the injury criteria. Each one is a scalar (or a small set of scalars) computed from time-history channels recorded on the dummy, and each has a defined normalization, filtering, and windowing procedure. If the CAE post-processor applies a different filter, a different time window, or a different sign convention than the test lab, the correlation will fail even when the underlying kinematics are correct.

HIC: Head Injury Criterion

HIC is derived from the resultant translational acceleration at the head center of gravity, expressed in g, and is defined as:

HIC = max over (t1, t2) of [ (t2 - t1) * ( 1/(t2-t1) * ∫ a_res dt )^2.5 ]
      subject to t2 - t1 ≤ 15 ms

HIC15 = the same expression with the 15 ms window constraint
HIC36 = the same expression with a 36 ms window constraint

The acceleration must be filtered with a CFC 1000 low-pass filter (SAE J211 channel class) before the integral is evaluated. The 2.5 exponent makes HIC strongly sensitive to short, high-amplitude spikes, which is why a single 3 ms pulse difference between test and CAE can shift HIC by hundreds of units. Typical targets: FMVSS 208 requires HIC15 ≤ 700 for the 50th percentile male driver; Euro NCAP and many OEM internal targets use HIC15 ≤ 500–650 depending on the assessment protocol. When correlating, always compare the filtered resultant acceleration trace first, then the HIC value, then the time window (t1, t2) that produced the maximum. A matching HIC with a different (t1, t2) window indicates a different injury mechanism and should be investigated.

Nij: Neck Injury Criterion

Nij combines axial neck force and bending moment into a single dimensionless number. It is computed at the occipital condyle and is defined separately for tension–extension, tension–flexion, compression–extension, and compression–flexion:

Nij = Fz / Fzc + My / Myc

where Fz  = upper neck axial force (N), tension positive
      My  = upper neck bending moment (N·m)
      Fzc = critical axial force (N), e.g. 6800 N tension, 6160 N compression
      Myc = critical moment (N·m), e.g. 310 N·m extension, 135 N·m flexion

The critical values are interpolation functions of the dummy size (the "Nij intercept" curves in FMVSS 208 / ECE R94). Nij must be ≤ 1.0. Because the criterion is a sum of two normalized terms, a model that over-predicts force but under-predicts moment can still produce a plausible Nij. For correlation, decompose Nij into its Fz/Fzc and My/Myc components and compare each separately. The moment sign convention is critical: extension moments are positive in the FMVSS formulation, and a flipped sign in the CAE output will invert the criterion.

Chest Deflection and Chest Acceleration

Chest deflection is measured by the chest potentiometer or IR-TRACC (Infra-Red Telescoping Rod for Assessment of Chest Compression) in the Hybrid III and THOR dummies. The raw signal is filtered at CFC 180 and reported as absolute deflection in millimeters, or as a percentage of the chest depth. FMVSS 208 limits chest deflection to 63 mm for the 50th percentile male; Euro NCAP uses a scaled limit and also evaluates the deflection rate. Chest acceleration (3 ms clip) is a separate criterion, filtered at CFC 180, with a typical limit of 60 g. In CAE, chest deflection is one of the hardest channels to correlate because it depends on ribcage stiffness, belt routing, and the interaction between the belt and the chest flesh. A common failure mode is a model that matches chest acceleration but over-predicts deflection, indicating the belt is loading the chest too locally or the rib stiffness is too low.

Femur Load and Knee Load

Femur load is measured by load cells in the femur shaft and is filtered at CFC 600. The axial compressive force is the primary criterion, with FMVSS 208 limiting it to 10 kN per leg (or 8 kN for the 5th percentile female). The load is signed: compression is positive. In CAE, femur load is sensitive to knee bolster stiffness, footwell intrusion, and the interaction between the knee and the instrument panel. A model that matches femur load but not knee slider displacement usually has a knee bolster model that is too stiff or too soft. Knee load is a secondary channel, typically limited to 6 kN, and is used to diagnose load path issues.

Using Injury Criteria as Correlation Metrics

The practical workflow is to treat each criterion as a correlation metric with a defined tolerance. A typical internal target is ±10% on peak value and a peak-time shift of less than 5 ms for HIC, Nij, chest deflection, and femur load. The correlation should be evaluated on the filtered channel, not the raw signal, and the filter class must match between test and CAE. The table below summarizes the key parameters.

Visualizing the Correlation Chain

The diagram below shows how the raw dummy channels are filtered, transformed into injury criteria, and compared against test data. The key point is that the comparison must happen at the criterion level, not at the raw signal level, and that each criterion has its own filter and window.

Practical Correlation Checklist

Before declaring a correlation acceptable, verify the following for each criterion:

• The filter class matches between test and CAE (CFC 1000 for head and neck, CFC 600 for femur, CFC 180 for chest).
• The sign convention is consistent: tension positive for neck Fz, compression positive for femur load, extension positive for neck My in the FMVSS formulation.
• The time window for HIC is reported (t1, t2) and matches between test and CAE.
• The peak value and peak time are compared, not just the peak value.
• The shape of the filtered trace is compared over the loading phase, not just at the peak.
• If a criterion fails, the raw channel is inspected to determine whether the discrepancy originates in the model or in post-processing.

In the next stage of the correlation workflow, these criterion-level comparisons become the acceptance criteria for the CAE model. A model is considered correlated when all criteria are within tolerance across the agreed load cases, not when a single channel matches. This criterion-based approach is what makes the correlation defensible to regulators and rating bodies, and it is the foundation for using CAE to support restraint system design decisions.