2. Injury mechanisms and tolerances

Injury criteria are the quantitative bridge between a physical loading condition and a biological outcome. A crash pulse, a helmet impact, or a seat-belt force is only meaningful for design once it is expressed as a metric that can be compared against a tolerance threshold. This chapter examines the three dominant families of criteria — strain-based, stress-based, and acceleration-based — and shows how each is converted into a design constraint that a component, restraint system, or protective structure can actually be engineered against.

Why the Criterion Family Matters

The choice of criterion is not cosmetic. Each family assumes a different dominant damage mechanism, and applying the wrong one produces either an over-conservative design or a dangerously permissive one. Strain-based criteria describe tissue deformation relative to its original length and are appropriate when the failure mode is tearing, rupture, or axonal stretching. Stress-based criteria describe force per unit area and are appropriate when the failure mode is fracture or crushing of a structure with a well-defined load path. Acceleration-based criteria describe the inertial response of a body or organ and are appropriate when the injury is driven by the mass of tissue being decelerated rather than by local contact force.

A useful rule of thumb: if the injury is caused by something pressing or pulling on tissue, think strain or stress; if it is caused by the body's own inertia during a rapid velocity change, think acceleration. In practice, real injuries often involve all three, and the analyst must decide which one dominates for the specific body region and loading direction.

Strain-Based Criteria

Strain is defined as the change in length divided by the original length, ε = ΔL / L₀, and is dimensionless. For soft tissue, the relevant tolerance is usually expressed as a maximum principal strain or a strain rate. Brain tissue, for example, is frequently assessed with a strain threshold in the range of 0.10–0.25 for mild traumatic brain injury, depending on the model and the strain rate considered; these values are illustrative and vary substantially between studies and finite-element material models.

The engineering translation is direct: a strain criterion becomes a deformation limit. If a helmet liner must keep cortical strain below a chosen threshold, the design constraint is the maximum allowable relative displacement between the skull and the brain, which in turn constrains liner thickness, stiffness, and the allowable bottoming-out displacement. The designer does not control strain directly; they control geometry and material compliance, and strain is the resulting field.

Stress-Based Criteria

Stress is force per unit area, σ = F / A, and is the natural criterion for hard or structural tissue: bone fracture, rib cracking, and skull failure. A rib fracture tolerance is often expressed as a force or a stress at the rib cross-section, with the well-known chest deflection and force limits used in crash testing being practical proxies for the underlying stress state.

Translating stress into design is a load-path problem. If a shoulder belt must not exceed a rib stress that corresponds to fracture, the constraint becomes a maximum belt force distributed over a minimum contact area, which then drives belt width, load-limiter force level, and the geometry of the belt-to-torso interface. The stress criterion is satisfied by controlling both the magnitude of the force and the area over which it is applied — a point that is frequently lost when designers focus only on peak force.

Acceleration-Based Criteria

Acceleration criteria treat the body or organ as a mass being decelerated. The classic example is the Head Injury Criterion (HIC), which integrates the resultant head acceleration over a time window:

HIC = max over t1,t2 of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt )^2.5 ]
      with (t2 - t1) ≤ 15 ms, a in g

A commonly cited threshold is HIC = 1000 for a 15 ms window, associated with a risk of severe head injury; lower values such as 700 are used where a more protective target is required. The 2.5 exponent means that short, high-amplitude spikes are penalized heavily, which is why padding that spreads deceleration over time is so effective.

The design translation is a deceleration-versus-time envelope. A restraint or energy-absorbing structure must keep the acceleration trace below the envelope for the relevant body region. This constrains the force–deflection curve of the energy absorber: it must be soft enough early in the stroke to limit peak acceleration, yet stiff enough later to absorb the required energy within the available stroke.

From Criterion to Design Constraint: A Worked Example

Consider a simplified head-impact protection problem. The input is a 5 kg headform striking a rigid surface at 6 m/s, with a 25 mm thick energy-absorbing liner available. The target is HIC ≤ 700. The analyst first estimates the average deceleration required to stop the head within the stroke: using v² = 2as with s = 0.025 m and v = 6 m/s gives a ≈ 720 m/s² ≈ 73 g average. Because HIC penalizes peaks, the actual peak must be kept close to this average, so the liner's force–deflection curve should be as rectangular as possible — near-constant force over the full stroke.

The resulting design constraint is a target crush force of approximately F = m·a = 5 kg × 720 m/s² ≈ 3.6 kN, held within a tolerance band over the 25 mm stroke. The designer then selects foam density or honeycomb cell size to hit that plateau, and verifies by simulating or testing the acceleration trace and computing HIC. If the measured peak acceleration is far above the average, the liner is bottoming out or is too stiff initially; if the stroke is not fully used, the liner is too soft and the head may reach the rigid surface.

Combining Criteria and Avoiding Common Errors

Real design problems rarely involve a single criterion. A frontal restraint system must satisfy chest deflection (a strain proxy), rib force (stress), and head acceleration (HIC) simultaneously. The constraints interact: softening the load limiter to reduce chest force may increase head excursion and head acceleration. The practical approach is to build a constraint table that lists each criterion, its threshold, the design parameter that most directly controls it, and the direction of the trade-off. The table below is a reusable template for that purpose.

Two errors are common. First, treating a threshold as a hard pass/fail line without accounting for its statistical basis: most tolerance values represent a probability of injury at a given level, not a sharp biological boundary, so a design that sits exactly at the threshold has a substantial injury risk. Second, mixing criteria from different loading regimes — for example, applying a quasi-static strain threshold to a high-rate impact — which can under- or over-predict injury by a large margin. Always confirm that the criterion was derived under loading conditions comparable to the design case.

Closing the Loop

Translating a criterion into a constraint is complete only when the constraint can be verified. For strain and stress criteria, verification typically means finite-element simulation of the tissue or structure under the design load case, followed by extraction of the peak strain or stress field and comparison against the threshold. For acceleration criteria, verification means measuring or simulating the acceleration trace, computing the metric (HIC or equivalent), and confirming margin. In both cases the deliverable is the same: a documented load case, a computed metric, a threshold with its source, and a stated margin. That four-part record is what allows a design decision to be defended and revised as new tolerance data become available.