2. Restraint system design variables in LS-DYNA

Before a single DOE matrix can be generated, the design space must be expressed as a set of numeric, keyword-level parameters that LS-DYNA can actually consume. In a restraint-system model, the occupant safety outcome is governed by a relatively small number of physical design variables: how fast the airbag inflates, how much gas escapes, when the pretensioner fires, how much belt force the load limiter allows, and where the anchors sit. Each of these maps to specific keywords, and each has a defensible range, a physical meaning, and a characteristic effect on occupant response. This chapter establishes that mapping so that later matrix generation operates on meaningful, well-scaled factors rather than arbitrary numbers.

Airbag inflator mass flow

The inflator is modeled with *AIRBAG_SIMPLE_PRESSURE_VOLUME or, more commonly for DOE work, *AIRBAG_HYBRID / *AIRBAG_HYBRID_JETTING, where the mass-flow rate curve is supplied as a load-curve ID. The physical design variable is the total inflator output and its temporal shape. In practice, DOE factors are expressed as a scaling multiplier on the baseline mass-flow curve rather than as raw kg/s values, because the curve shape is fixed by the inflator supplier and only the magnitude is a design freedom. A typical factor is INFLATOR_SCALE ranging from 0.85 to 1.15, applied by scaling the ordinate of the *DEFINE_CURVE referenced by the inflator definition.

The observable effect is on bag pressure rise and hence on occupant chest acceleration and head excursion. Higher mass flow inflates the bag earlier, reducing forward excursion but raising the loading rate on the occupant. The DOE must therefore capture the trade-off, not simply maximize inflation. A practical caution: mass-flow scaling changes the internal energy of the bag, so the *AIRBAG reference geometry and the PV (pressure-volume) work must remain consistent; scaling the curve without checking the resulting peak pressure against the venting model can produce non-physical bag behavior.

Venting

Venting is defined through the vent hole area and discharge coefficient in the airbag keyword, or through *AIRBAG_SIMPLE_AIRBAG_MODEL parameters. The design variable is the effective vent area, usually expressed as a multiplier on the baseline vent area, with a typical DOE range of 0.7 to 1.3. Venting controls how quickly the bag deflates after peak inflation and therefore governs the rebound phase and the late-time occupant interaction.

Venting and inflator mass flow are strongly coupled: increasing both raises peak pressure while shortening the sustained pressure plateau. This coupling is exactly why a DOE is preferable to one-factor-at-a-time tuning, and it is why the matrix must sample the two factors jointly rather than independently. In the keyword deck, the vent area appears as a geometric parameter on the bag surface; the DOE driver should modify the area value, not the mesh, so that the model remains topologically identical across runs.

Seatbelt pretensioner timing

The pretensioner is modeled with *ELEMENT_SEATBELT_PRETENSIONER, where the firing time is set by the TIME (or TDEL) parameter and the retraction is driven by a *DEFINE_CURVE of pull-in force or displacement versus time. The design variable is the pretensioner trigger time, typically referenced to the crash pulse origin. A representative DOE range is 8 ms to 20 ms after T=0, with the baseline at 12 ms.

Timing is a genuinely temporal factor, and its effect is non-monotonic. Firing too early removes belt slack before the occupant has begun to move forward, which can pull the occupant into an unfavorable posture; firing too late leaves slack that allows excessive forward excursion before the load limiter engages. The DOE must therefore sample the timing range densely enough to resolve the optimum, and the response metric should include both chest deflection and forward excursion so the trade-off is visible.

Load limiter force

The load limiter is represented by the belt force limit in the retractor or buckle element, supplied as a force level in *ELEMENT_SEATBELT_RETRACTOR or through a force-limiting slip element. The design variable is the limit force, typically 2.5 kN to 4.5 kN for a front occupant, with the baseline at 3.5 kN. Lower limit force reduces chest loading but permits greater forward excursion; higher limit force restrains the occupant more firmly at the cost of higher chest deflection.

Because the load limiter and pretensioner act in sequence, their interaction is a first-order DOE concern. The pretensioner must remove slack before the limiter pays out force; if the limiter force is set too low relative to the pretensioner pull-in, the belt may pay out during the pretensioning phase and negate the pretensioner's benefit. The matrix should therefore include the pretensioner timing and load limiter force as a paired factor block.

Anchor positions

Anchor positions are geometric design variables: the D-ring (shoulder anchor), the buckle anchor, and the lap anchor. In LS-DYNA these are node coordinates on the seatbelt path or on the *ELEMENT_SEATBELT slip-ring definitions. The DOE factors are typically small translations, on the order of ±20 mm in the fore-aft and vertical directions, expressed as offsets applied to the baseline coordinates.

Anchor position changes the belt routing geometry and therefore the belt force vector on the occupant. A D-ring moved forward increases the angle of the shoulder belt, altering the chest loading direction; a buckle moved upward changes the lap-belt path across the pelvis. These are geometric factors and must be applied consistently to both the belt elements and any contact definitions that reference the anchor nodes, otherwise the model becomes inconsistent between runs.

Keep every DOE factor as a dimensionless multiplier or a small offset from a validated baseline. This preserves model integrity, keeps the design space physically plausible, and makes the resulting response surfaces interpretable in engineering units.
Restraint Design Variables → LS-DYNA Keywords → Occupant Response Inflator mass flow scale 0.85–1.15 Vent area scale 0.7–1.3 Pretensioner timing 8–20 ms Load limiter force 2.5–4.5 kN Anchor positions ±20 mm offsets *AIRBAG_HYBRID mass-flow curve ID *AIRBAG_SIMPLE_AIRBAG_MODEL vent area / Cd *ELEMENT_SEATBELT_PRETENSIONER TIME / TDEL *ELEMENT_SEATBELT_RETRACTOR force limit *ELEMENT_SEATBELT / slip-ring node coordinates Airbag response bag pressure rise peak pressure rebound / deflation head excursion Belt response slack removal belt force vector chest deflection forward excursion coupled sequenced Dashed links mark factor pairs that must be sampled jointly in the DOE matrix. All factors are applied as multipliers or offsets from a validated baseline model.

Building a consistent factor set

The five variables above are not independent in their effect, and the DOE matrix must reflect that. A workable approach is to define each factor as a named parameter in the LS-DYNA input deck, for example through *PARAMETER and *PARAMETER_EXPRESSION, so that the matrix generator only needs to substitute scalar values. The following fragment shows the pattern for the inflator and vent factors:

*PARAMETER
INFL_SCALE   1.00
VENT_SCALE   1.00
PRET_TIME    0.012
LL_FORCE     3500.0
D_RING_DX    0.0
*DEFINE_CURVE
         101         0       1.0       1.0
     0.000,     0.0
     0.005,   ${INFL_SCALE*0.6}
     0.015,   ${INFL_SCALE*1.0}
     0.030,   ${INFL_SCALE*0.4}
*ELEMENT_SEATBELT_PRETENSIONER
         201         1         0         0
${PRET_TIME},       0.0,       0.0,       0.0

With the deck parameterized this way, each DOE run is a single substitution of the five scalars, and the model topology, mesh, and contact definitions remain identical. This is the precondition for a valid matrix: if the geometry changes between runs, the response differences cannot be attributed to the design variables.

Ranges, baselines, and what to watch

The table below summarizes the recommended factor definitions for a front-occupant frontal-impact study. The ranges are engineering starting points, not validated optima; they should be narrowed after a screening run.

Design variable LS-DYNA keyword Baseline DOE range Primary response
Inflator mass flow *AIRBAG_HYBRID 1.00 0.85–1.15 Bag pressure, head excursion
Vent area *AIRBAG_SIMPLE_AIRBAG_MODEL 1.00 0.70–1.30 Deflation rate, rebound
Pretensioner timing *ELEMENT_SEATBELT_PRETENSIONER 12 ms 8–20 ms Slack removal, excursion
Load limiter force *ELEMENT_SEATBELT_RETRACTOR 3.5 kN 2.5–4.5 kN Chest deflection
Anchor position *ELEMENT_SEATBELT nodes 0 mm ±20 mm Belt force vector, routing
Two failure modes are common when these factors are introduced into a DOE. First, scaling the inflator curve without re-checking the vent model can drive the bag into a non-physical pressure regime; always inspect the bag pressure history for the extreme corner of the matrix before trusting the response surface. Second, moving anchor nodes without updating the associated slip-ring and contact definitions produces a model that runs but no longer represents the intended belt routing; verify belt path continuity in the extreme anchor-position runs.

Once these five factors are parameterized, ranged, and checked at their extreme corners, the design space is well defined and the matrix generation step can proceed on a sound footing. The key discipline is to keep every factor as a controlled multiplier or offset from a validated baseline, to sample the coupled pairs jointly, and to confirm that the extreme runs remain physically plausible before any response surface is fitted.

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