2. Crashworthiness requirements and assessment metrics

Crashworthiness is not a single number; it is a set of regulatory and consumer requirements, each expressed through measurable physical quantities. A virtual crash test is only useful if every one of those quantities can be extracted from the simulation output and compared against a defined threshold. This section establishes the three families of metrics that dominate crash assessment — occupant injury criteria, structural integrity measures, and the mapping between them and the signals a solver actually produces — and shows how to build that mapping explicitly so that a simulation result can be judged, not merely inspected.

Occupant injury criteria and their physical basis

Injury criteria compress a complex kinematic history into a scalar that correlates with a probability of injury. The most common ones in frontal and side impact assessment are:

• HIC (Head Injury Criterion) — computed from the resultant translational acceleration at the head centre of gravity over a 36 ms window: HIC = max[(t₂−t₁)(1/(t₂−t₁))∫a dt]^2.5. The 2.5 exponent makes HIC strongly sensitive to short, high-amplitude spikes, so filtering and sampling rate matter as much as the physical response.
• a₃ms — the maximum resultant acceleration at the head or chest sustained over any 3 ms interval, used where a simple peak limit is more appropriate than HIC.
• Chest deflection and V·C — chest compression (mm) and the viscous criterion, the product of compression rate and instantaneous compression, capturing soft-tissue injury under high-rate loading.
• Nij and Nkm — normalised neck injury criteria combining axial force and bending moment, each normalised by an injury reference value and summed.
• Femur force and tibia index — axial compressive force limits and a combined bending/axial index for lower-leg injury.

Each criterion has a defined measurement location, a defined filter (commonly CFC 600 or CFC 1000 per SAE J211), and a defined sign convention. A virtual test that reports HIC without stating the filter class and the head CG definition is not comparable to a regulatory result. The first discipline of virtual assessment is therefore to record the measurement chain alongside the number.

Structural integrity measures

Structural metrics describe what the vehicle body does to manage energy and preserve the occupant compartment. They are not injury criteria, but they govern the boundary conditions under which the occupant criteria are achieved:

• Intrusion — displacement of occupant-compartment boundaries (toe pan, dash, A-pillar, door inner panel) relative to the undeformed vehicle coordinate system. Intrusion reduces the survival space and changes the restraint interaction.
• Deceleration pulse — the rigid-body or B-pillar acceleration history that the restraint system must work against. Its shape (peak, duration, rise time) determines airbag and belt timing.
• Energy absorption — the integral of force over crush distance in the front or side structure, and the proportion of kinetic energy absorbed by each load path.
• Structural integrity / no-splitting — absence of spot-weld separation, hinge failure, or door opening that would compromise the restraint or allow ejection.

These measures are the causal layer: they explain why an occupant metric passed or failed. A HIC of 720 against a 700 limit is not diagnosable from the HIC alone; the intrusion history and the pulse shape tell you whether the head contacted the A-pillar, the airbag, or the steering wheel.

Mapping requirements to virtual outputs

The mapping is the core engineering artefact of this chapter. Every requirement must be traced to a specific output channel, a specific post-processing operation, and a specific acceptance rule. The diagram below shows that trace for a frontal impact case: the physical requirement on the left, the solver output channel in the centre, and the post-processing and acceptance rule on the right.

The mapping is not merely bookkeeping. It forces three decisions that determine whether the virtual test is defensible. First, the coordinate system must be fixed: intrusion is measured in the vehicle coordinate system, while occupant kinematics are reported in the occupant or sled frame. Mixing them produces plausible-looking but wrong intrusion values. Second, the filter and sampling must match the criterion's definition; a HIC computed from unfiltered 1 kHz data will differ materially from one computed at CFC 1000. Third, the acceptance rule must state whether the limit is a hard regulatory threshold or a target with margin, because a virtual test used for design guidance needs margin tracking, not just pass/fail.

Worked example: extracting and judging a frontal result

Consider a 50 km/h full-frontal virtual test of a passenger car with a Hybrid III 50th-percentile driver. The solver outputs, among others, the head CG acceleration history, the chest band deflection, the toe pan node displacement, and the B-pillar acceleration. The post-processing sequence is:

1. Filter the head CG resultant acceleration at CFC 1000 and compute HIC over the 36 ms window. Suppose the example result is HIC = 640 against a 700 limit — a 60-unit margin.
2. Extract peak chest deflection and V·C. Suppose peak deflection is 44 mm against a 50 mm limit, but V·C reaches 0.95 m/s against a 1.0 m/s limit — the deflection margin is comfortable while the rate margin is thin.
3. Read toe pan intrusion in the vehicle coordinate system. Suppose the maximum is 132 mm against a 150 mm limit, located at the driver's left footwell.
4. Check the B-pillar pulse against the restraint timing envelope: airbag contact should occur before the pulse peak. Suppose contact occurs 8 ms after peak — a timing flag.

The judgement is not "pass." The thin V·C margin and the late airbag contact are coupled: a slightly stiffer toe pan would raise the pulse peak earlier and worsen the timing, while a softer toe pan would reduce intrusion margin. The virtual test has produced a diagnosis, not just a verdict, because the structural and occupant channels were mapped together. This is the practical value of the mapping table: it turns a set of numbers into a causal story that a design change can act on.

Acceptance boundaries for virtual assessment

Finally, the metrics must be read against the boundary of what the virtual test can claim. Three boundaries apply. Model fidelity: the occupant criteria are only as trustworthy as the dummy model's validation status for the loading direction and rate. Output completeness: a criterion that cannot be extracted from the available channels — for example, a neck criterion requiring a moment channel the model does not output — cannot be assessed, and the gap must be declared rather than approximated. Correlation status: a virtual result is an assessment only when the model has been correlated against a physical test of the same configuration; before correlation, the numbers are predictions with an unquantified bias. The acceptance rule should therefore carry a correlation flag alongside the pass/fail value, so that a reader knows whether the margin is a validated margin or a predicted one.

With the requirement-to-output mapping established and the boundaries declared, the next question is how the virtual test itself is set up so that these channels are produced with the fidelity the criteria demand — which is the subject of the modelling and boundary-condition work that follows.