2. Injury biomechanics fundamentals

Multi-metric occupant injury analysis begins with a single question: for a given body region, what mechanical quantity actually predicts injury, and how does the load reach that region? Injury biomechanics answers this by decomposing a crash event into load paths (how force and acceleration propagate through the body), tolerance thresholds (the level at which tissue fails), and injury criteria (normalized metrics that translate measured signals into a probability of injury). Without this foundation, a CAE model or a sled test produces numbers that cannot be interpreted, and tradeoff decisions between restraint parameters become guesswork.

Load paths: from belt and airbag to tissue

Every restraint system delivers load through a chain of interfaces. A three-point belt routes force through the clavicle and rib cage anteriorly, through the pelvis at the lap belt, and through the spine posteriorly. An airbag distributes pressure over the face and chest but also generates a rearward head acceleration that loads the cervical spine in extension. A knee bolster loads the distal femur and patella, and the floor pan loads the feet and tibia through the ankle.

The key engineering insight is that the same external force produces very different internal loads depending on contact area, load direction, and skeletal geometry. A 4 kN lap belt force spread over 80 cm² of pelvis is tolerable; the same force concentrated on the abdomen by a poorly routed belt can rupture the liver. Load path analysis therefore asks: where does the force enter, what structures carry it, and where does it concentrate? In a CAE model this is inspected through section forces and cross-section stress plots along the spine, rib cage, and femur; in a physical test it is inferred from belt load cells, accelerometer triads, and chest-band deflection gauges.

Head: HIC and the rotational gap

The head is the most consequential region for restraint tradeoffs because it drives both skull fracture and diffuse brain injury. The dominant translational criterion is the Head Injury Criterion (HIC), defined over a time window:

HIC = max over t1,t2 of [ (1/(t2-t1)) * ∫ a(t) dt ]^2.5 * (t2-t1)
where a(t) is the resultant head CG acceleration in g,
and t2 - t1 is limited to 36 ms (HIC36) or 15 ms (HIC15).

FMVSS 208 and Euro NCAP use HIC15 = 700 as a typical limit, while HIC36 = 1000 remains a common reference. HIC is purely translational and ignores rotation, yet real-world brain injury — especially diffuse axonal injury — correlates strongly with angular acceleration and angular velocity. This is why modern protocols add BrIC (Brain Injury Criterion), based on peak angular velocity components, and why head rotation is a central concern in oblique and far-side impacts. A restraint that reduces HIC by stiffening the airbag may increase angular velocity by creating an off-center contact, so the two metrics must be evaluated together.

Neck: Nij and the tension–compression–moment envelope

The neck transmits head inertia to the torso and is loaded in combined axial force and bending moment. The Nij criterion normalizes these against tolerance limits:

Nij = Fz / Fzc  +  My / Myc
where Fz is the axial force (tension or compression),
My is the sagittal bending moment,
and Fzc, Myc are the corresponding tolerance values
(e.g., tension 6.8 kN, compression 6.2 kN, flexion 310 Nm,
extension 135 Nm for a mid-size male in FMVSS 208).

Nij = 1.0 marks the tolerance boundary. The criterion is evaluated in four quadrants (tension–flexion, tension–extension, compression–flexion, compression–extension), and the governing quadrant depends on the impact direction. In rear impacts, extension dominates; in frontal impacts with airbag loading, compression–extension can occur as the head is driven back into the head restraint. Neck injury criteria are also sensitive to the head–torso relative motion, which is why seatback recline and head restraint geometry are tuned together.

Chest: deflection, not just acceleration

Chest injury is driven by rib deformation and the resulting strain on the rib cage and underlying organs. The most predictive metric is chest deflection (sternum-to-spine compression), often normalized as a percentage of chest depth. A common tolerance is 22–25% deflection for a mid-size male, with age and sex modifiers. The Chest Injury Criterion (Chest G) combines deflection and viscous response:

Chest G = max over time of [ (D(t) / Dmax) * (V(t) / Vmax) ]
where D(t) is instantaneous deflection,
V(t) is deflection rate,
and Dmax, Vmax are tolerance constants.

Acceleration alone is a poor chest metric because a stiff belt can produce high chest acceleration with modest deflection, while a loose belt can produce large deflection with lower acceleration. Belt load limiters and force-limiting retractors are tuned precisely to trade chest deflection against forward excursion — the classic restraint tradeoff.

Abdomen and lower extremities

Abdominal injury is dominated by compression and shear from belt loading, with the liver and spleen most vulnerable. There is no single universally adopted criterion comparable to HIC; instead, protocols use belt force limits, penetration depth, and the Abdominal Injury Criterion (AIC) derived from belt–abdomen interaction. In practice, the design lever is belt routing and pretensioner force, not a single scalar threshold.

Lower extremities are loaded through the floor and knee bolster. The dominant metrics are femur axial force (typically limited to around 10 kN for a mid-size male, with a knee–thigh–hip criterion), tibial index (combining axial force and bending moment at the tibia), and foot/ankle metrics. These are strongly sensitive to pedal and floor pan geometry, which is why lower-extremity injury is often a packaging problem rather than a restraint problem.

From criteria to tradeoff decisions

These criteria are not independent. A stiffer airbag reduces head excursion and HIC but raises neck compression and chest acceleration. A higher belt force limit reduces chest deflection but increases head forward excursion and the risk of head contact. A pretensioner that fires early reduces occupant kinematics but can raise belt force on the abdomen. The engineering task is to find the parameter set that keeps every metric below its threshold simultaneously — which is exactly why multi-metric analysis, rather than single-criterion optimization, is the correct framing.

A practical workflow for a frontal sled or CAE case looks like this. First, define the coordinate convention: +X forward, +Y lateral, +Z up, with head acceleration measured at the CG and chest deflection measured as sternum-to-spine compression along the local chest axis. Second, extract the time histories for head resultant acceleration, neck axial force and sagittal moment, chest deflection and deflection rate, belt forces, and femur/tibia loads. Third, compute each criterion over its specified window — HIC15 over any 15 ms interval, Nij at the instant of peak combined load, chest deflection as a percentage of chest depth. Fourth, compare against the applicable limits and record the margin. A result table for a hypothetical mid-size male frontal case might look like this:

In this illustrative case, chest deflection and abdominal belt force are the binding constraints, while the head and neck have comfortable margin. The correct response is not to stiffen the airbag further — that would buy head margin the design does not need while adding chest load. Instead, the lever is the belt force limiter and the pretensioner profile: a slightly lower force limit reduces chest deflection and abdominal load at the cost of a small increase in head excursion, which the head margin can absorb. This is the essence of multi-metric tradeoff reasoning: identify the binding constraint, then move the parameter that relieves it while monitoring the metrics that will degrade.

Finally, remember that tolerance thresholds are population references, not guarantees. They are derived from cadaver, PMHS, and volunteer data and carry substantial scatter; age, sex, stature, and bone density shift the effective threshold considerably. A design that sits at 95% of a limit for a mid-size male may exceed it for an older or smaller occupant. Multi-metric analysis should therefore be run across the occupant size and age range defined by the applicable protocol, and the reported margin should be the worst case, not the nominal case.