3. Fundamental biomechanics of injury

Occupant protection engineering rests on a single quantitative question: for a given loading condition, will the human body be injured, and if so, how severely? Answering that question requires three distinct but connected bodies of knowledge. Injury mechanisms describe the physical and physiological processes by which tissue fails. Tolerance criteria convert those mechanisms into measurable mechanical quantities and threshold values. Injury risk functions express the probability of injury as a continuous function of the loading variable, allowing designers to trade off restraint performance against other vehicle attributes. This chapter builds the chain from mechanism to criterion to risk curve, and shows how each link is used in restraint system development.

Injury Mechanisms: How Tissue Fails

Injury occurs when the mechanical demand imposed on a tissue exceeds its capacity to deform, absorb energy, or maintain perfusion. The dominant mechanisms differ by body region and by loading mode.

• Brain — diffuse axonal injury (DAI): Rotational acceleration produces shear strain in the white matter. Axons tolerate stretch poorly; strains on the order of 10–20% sustained over tens of milliseconds are associated with functional disruption. DAI is driven primarily by angular acceleration, not linear acceleration.
• Brain — focal contusion and subdural hematoma: Linear acceleration causes the brain to move relative to the skull, producing coup and contrecoup pressures and bridging-vein rupture. These are pressure- and contact-driven.
• Skull fracture: Local contact force concentrated over a small area exceeds the bone's local strength. Force magnitude and contact area govern the outcome.
• Neck — fracture and dislocation: Axial compression combined with bending produces vertebral body fracture; tension combined with extension produces facet separation and ligamentous failure. The neck is highly sensitive to load direction.
• Thorax — rib fracture and lung contusion: Chest deflection compresses the rib cage; fracture occurs when rib strain exceeds roughly 1–2%. Lung contusion follows from the same compression event and is a strong predictor of subsequent mortality.
• Abdomen — solid organ rupture: Compression between the spine and an intruding object (belt, steering column) produces liver and spleen laceration. Belt geometry and belt load distribution are decisive.
• Lower extremity — axial load fracture: Femur and tibia fracture under axial compression, typically from knee bolster or footwell intrusion. The mechanism is column buckling and bending.

Two principles cut across all regions. First, rate dependence: biological tissue stiffens and becomes more brittle at higher strain rates, so a 20 g event lasting 5 ms is not equivalent to a 20 g event lasting 50 ms. Second, load direction and constraint: the same acceleration magnitude produces very different injury outcomes depending on whether the head is free to rotate, whether the torso is belted, and whether the occupant is in position.

Tolerance Criteria: From Mechanism to Measurable Threshold

A tolerance criterion is a scalar function of measured signals that predicts injury. Good criteria are mechanism-based, measurable with standard instrumentation, and validated against cadaver, animal, or volunteer data.

HIC illustrates the logic. It integrates resultant head acceleration over a time window, raises the mean to the 2.5 power to reflect the nonlinear severity of acceleration, and multiplies by the window duration. The 2.5 exponent and the 15 ms window were fitted to skull fracture and concussion data. HIC is a focal-injury criterion; it does not capture rotational injury, which is why BrIC was introduced for DAI. In practice, both are reported.

Nij is a normalized interaction criterion. F_zc and M_yc are critical values for axial force and bending moment, and the criterion sums their normalized contributions. Nij = 1.0 corresponds to a 50% risk of AIS 3+ neck injury in the reference data. The normalization allows tension-extension and compression-flexion to be compared on one scale.

The viscous criterion VC captures rate-dependent thoracic injury. It multiplies instantaneous chest deflection by deflection rate, so a fast, shallow compression can be as injurious as a slow, deep one. This is why belt load limiters and pretensioners are tuned together: pretensioning reduces deflection, while load limiting controls the rate at which the chest is loaded.

Injury Risk Functions: From Threshold to Probability

A threshold implies a binary outcome, but real injury data are probabilistic. Injury risk functions (IRFs) express the probability of a given injury severity as a function of the criterion value. The most common form is the cumulative normal (probit) model:

P(injury) = Φ( (x − μ) / σ )

where:
  x  = criterion value (e.g., HIC, Nij, chest deflection)
  μ  = mean of the tolerance distribution
  σ  = standard deviation of the tolerance distribution
  Φ  = standard normal cumulative distribution function

For HIC, a widely used IRF for AIS 3+ head injury gives μ ≈ 1000 and σ ≈ 300 in HIC units. Substituting HIC = 700 yields P ≈ 0.16; HIC = 1000 yields P ≈ 0.50; HIC = 1500 yields P ≈ 0.85. These values are illustrative and derived from specific datasets; they should not be treated as universal constants. The key engineering insight is that the risk curve is steep: a 30% reduction in HIC can cut injury probability by more than half.

IRFs are used in two ways. In design, they set targets: a restraint system might be required to keep AIS 3+ head injury risk below 10% across a matrix of crash pulses. In assessment, they convert measured or simulated criterion values into a single comparable risk metric, enabling trade studies across occupant sizes, seating positions, and restraint configurations.

Applying the Chain in Restraint Development

Consider a frontal offset crash pulse with a 50th percentile male occupant. The restraint engineer must decide belt load limit, pretensioner firing time, and airbag venting. The workflow proceeds as follows.

1. Define the loading environment. The crash pulse is characterized by delta-v and peak deceleration. For a 56 km/h ODB test, delta-v is approximately 56 km/h and peak sled deceleration is on the order of 30–40 g.
2. Select criteria and targets. Head: HIC₁₅ ≤ 700 and BrIC ≤ 1.0. Neck: Nij ≤ 1.0. Chest: deflection ≤ 63 mm and VC ≤ 1.0 m/s. These targets correspond to approximately 10–20% risk of AIS 3+ injury depending on the IRF used.
3. Run the simulation or sled test. Instrument the head, neck, chest, and femur with accelerometers and load cells. Record the time histories.
4. Compute criteria. For HIC, search all 15 ms windows in the head acceleration trace. For VC, differentiate the chest deflection signal and multiply by deflection at each time step.
5. Map to risk. Apply the appropriate IRF to each criterion value. If any risk exceeds the target, adjust the restraint parameters and repeat.

A common failure mode is a chest deflection that passes the peak deflection limit but fails VC because the deflection rate is too high. This typically occurs when the load limiter is set too high or the pretensioner fires too late. The remedy is to reduce the load limit or advance the pretensioner timing, then re-check head criteria because a softer belt may allow more head excursion.

Key Takeaways

• Injury mechanisms are region-specific and rate- and direction-dependent. The criterion must match the mechanism.
• HIC and BrIC address different head injury pathways; both are needed for a complete head assessment.
• Nij normalizes axial force and bending moment, enabling comparison across load directions.
• VC captures rate-dependent thoracic injury that peak deflection alone misses.
• Injury risk functions convert deterministic criterion values into probabilities, enabling quantitative design trade-offs.
• The probit form P = Φ((x − μ)/σ) is standard, but μ and σ must be sourced and justified for each application.