2. Restraint system components and modeling

An occupant restraint CAE campaign is only as credible as the component models it is built from. Before any sled or full-vehicle run can be trusted, each restraint device — airbag, seat belt, pretensioner, load limiter, seat, and steering column — must be represented with the correct kinematics, the correct force–displacement behavior, and the correct triggering logic. This section walks through the physical function of each component, the modeling approach typically used in an explicit LS-DYNA occupant-safety deck, and the parameters that most often decide whether a model correlates with test.

Airbags: from inflator output to bag pressure

An airbag module has three modeling layers: the folded bag geometry, the inflator gas supply, and the venting/leakage path. In CAE the bag is meshed as a membrane (fully integrated shell elements, often with a fabric material such as *MAT_FABRIC), folded either by explicit folding tools or by an initial-folding keyword, and inflated with a control-volume or particle method.

The control-volume (CV) approach is the workhorse for driver and passenger frontal bags. The inflator is characterized by a tank test: mass flow rate ṁ(t) and temperature T(t) versus time, entered through *AIRBAG_LOAD_CURVE or an equivalent inflator definition. The bag pressure is then computed from the ideal-gas relation

P = (γ − 1) · U / V        (adiabatic, no venting)
P = P_atm + (γ − 1) · U / V  (with ambient reference)

where U is internal energy, V is the instantaneous bag volume, and γ is the ratio of specific heats (typically 1.4 for the gas mixture). Vent holes are modeled with *AIRBAG_REFERENCE_GEOMETRY plus a vent orifice definition; leakage through seams is captured by a porosity or fabric leakage coefficient. The practical tuning knobs are the vent hole area, the fabric permeability, and the inflator mass-flow scaling factor.

Seat belts: webbing, slip, and geometry

The belt is modeled as a chain of 1D seatbelt elements (*ELEMENT_SEATBELT) or as shell strips, routed through sliprings and retractor definitions. Two behaviors dominate correlation:

• Webbing stiffness and strain rate. The force–strain curve is entered as a load curve; typical polyester webbing reaches roughly 10–12 kN at 10–12 % strain, with rate sensitivity that must be included for high-speed events.
• Slip and friction. Belt slip at the D-ring and buckle changes the effective payout. Friction coefficients are defined per slipring; a value near 0.1–0.2 is common for a steel D-ring, higher for coated hardware.

The retractor is represented by a spool with a locking condition (vehicle-sensitive or webbing-sensitive) and, when present, a torsion-bar force limiter. The pretensioner is a pyrotechnic or mechanical device that removes slack; in CAE it is modeled as a prescribed retraction stroke or a force–time curve applied at the retractor or buckle anchor, triggered by a sensor time T_sensor plus a firing delay.

Pretensioners and load limiters

These two devices are usually paired and must be modeled together, because the pretensioner sets the initial belt tension and the load limiter caps the peak force the occupant chest sees.

A common modeling error is to apply the load-limiter curve as a constant force. In reality the torsion bar yields progressively; using a flat cap over-predicts chest deflection early in the event and under-predicts it late. Always use the measured force–displacement curve from the component test.

Seats and steering column

The seat is not a rigid body in a restraint model. The cushion and back frame deform under occupant load, and the recliner can rotate. A practical representation uses:

• Rigid seat frame with a deformable cushion foam modeled by *MAT_LOW_DENSITY_FOAM or a simplified spring–damper.
• A recliner joint with a rotational stiffness and a yield moment, so the back frame can pitch forward under belt load.
• Seat track and mounting bolts as constraints with realistic failure loads if the seat is expected to remain attached.

The steering column contributes to driver chest and head loading through its collapse behavior. It is modeled as a telescoping column with a force–displacement curve (typically 2–4 kN collapse force over 100–150 mm of stroke), plus a tilt/telescope adjustment joint. The column force curve must be aligned with the airbag deployment timing: if the column collapses before the bag is fully inflated, the driver loads the bag at the wrong angle and the head may roll off the bag.

Building a consistent component set

The components above do not act independently; they share the occupant as a common load path. A reproducible modeling workflow therefore starts from a component parameter table and a trigger schedule, then verifies each subsystem in isolation before coupling them.

1. Collect component test data. Tank test for the inflator, webbing tensile test, torsion-bar force–displacement, seat cushion indentation, column collapse test.
2. Build and check each subsystem. Run a single-component model (e.g. bag-only inflation, belt-only pull test) and compare against the component test curve.
3. Assemble the full restraint deck. Route the belt, position the bag, define the seat and column, and set the sensor/fire schedule.
4. Run a baseline sled. Compare occupant responses (head acceleration, chest deflection, femur load) against the physical sled test.
5. Tune only the parameters that are physically uncertain. Vent area, friction, and fire timing are legitimate tuning knobs; fabric modulus and foam density are not, unless the component test itself is suspect.

Typical failure symptoms and their causes

Each of these symptoms points to a specific component parameter, which is why the component test data must be traceable in the CAE deck. When a model is delivered, the parameter table and the trigger schedule should travel with it, so that a later reviewer can tell whether a discrepancy comes from the model or from the test.