2. Restraint system design variables in LS-DYNA

Before a DOE matrix can be generated, every factor in that matrix must map to a real, editable quantity inside the LS-DYNA keyword deck. In restraint system simulation, the design space is not defined by abstract labels such as "aggressive" or "soft" — it is defined by numeric fields on specific keyword cards. This chapter establishes that mapping: which airbag, seatbelt, pretensioner, and load limiter parameters are typically varied in a restraint DOE, where they live in the keyword file, and how their units and dependencies constrain the ranges you can legitimately sample.

Airbag parameters and their keyword representation

An airbag in LS-DYNA is most commonly modeled with the uniform pressure (control volume) approach: the bag geometry is defined by *AIRBAG cards, and the inflation is driven by an *AIRBAG_INFLATOR definition referenced through *AIRBAG_REFERENCE_GEOMETRY and the associated *AIRBAG keyword. For a restraint DOE, the parameters that most directly influence occupant response are:

• Mass flow rate and temperature curve — defined on *AIRBAG_INFLATOR via LCID (load curve of mass flow rate versus time) and the inflator gas temperature T. Scaling the mass flow curve is the standard way to represent a "hotter" or "colder" inflator.
• Venting — *AIRBAG card fields for vent hole area (PVENT / vent area) and the vent orifice coefficient. Vent area is a first-order lever on bag pressure and therefore on occupant loading.
• Bag volume and geometry — set by the *AIRBAG_REFERENCE_GEOMETRY node set and the initial gas volume V on the *AIRBAG card. In a DOE, volume is often varied indirectly through a scale factor applied to the reference geometry rather than by rebuilding the mesh.
• Fabric leakage — the leakage coefficient LCC / LCR on the *AIRBAG card, representing porosity of the bag material.

A representative snippet for a driver airbag inflator looks like this:

*AIRBAG_INFLATOR
$#  lcid       t       lcd       ...
         101    900.0
$#  lcIdM     lcIdT
         102      103

Here LCID = 101 is the mass flow rate curve, T = 900.0 is the gas temperature in Kelvin, and the optional LCIDM/LCIDT curves allow mass and temperature to vary with time. When you build a DOE factor for "inflator output," you are almost always scaling the ordinates of curve 101 — for example, a factor range of 0.85 to 1.15 on mass flow rate. Note that the curve is referenced by ID, so a DOE driver must either rewrite the curve data or point to a different curve ID per run; the latter is cleaner because it preserves the baseline deck.

Seatbelt characteristics

Seatbelt modeling in LS-DYNA uses *MAT_SEATBELT (or the older *MAT_FABRIC with belt-specific options) combined with *ELEMENT_SEATBELT and *ELEMENT_SEATBELT_SLIPRING / *ELEMENT_SEATBELT_RETRACTOR. The belt material card carries the load-extension behavior through a load curve:

*MAT_SEATBELT
$#    mid       ro        e      pr       c        n
         5   1.0e-9   2000.0     0.3
$#   lcid      ...
         201

The LCID (201) defines force versus strain for the webbing. In a DOE, belt stiffness is varied by scaling this curve's ordinates, typically within ±10–15%. Two practical cautions apply. First, the belt load curve is defined in force units consistent with the model's unit system (commonly N, mm, tonne, s, so force is in N and stress in MPa); scaling must respect that. Second, the belt routing — sliprings, retractor anchor, buckle position — is geometry, not a material parameter, and is usually held fixed in a restraint DOE unless the study explicitly targets routing.

Belt pretension and load limiting are handled by the retractor and slipring definitions rather than the material card, which is where the next two parameter families live.

Pretensioner settings

A pyrotechnic pretensioner is modeled with *ELEMENT_SEATBELT_RETRACTOR, which pulls belt webbing into the retractor according to a prescribed pull-in curve:

*ELEMENT_SEATBELT_RETRACTOR
$#   sid1      sid2      sid3      sid4      sid5      sid6      sid7      sid8
         1         2
$#   lcid      ...
         301

The load curve LCID = 301 gives retractor pull-in (length) versus time. DOE factors for the pretensioner are typically the total pull-in stroke (scaling the curve's peak ordinate) and the trigger time (shifting the curve along the time axis). Trigger time is a particularly sensitive factor because it interacts with the airbag firing time and the occupant's forward excursion; a 5 ms shift can change chest deflection measurably. When you define a trigger-time factor, express it as an absolute time offset in milliseconds and apply it consistently to every retractor and inflator curve that shares the firing event.

Load limiter settings

The load limiter is the force-limiting element in the belt path, usually modeled as a *ELEMENT_SEATBELT_SLIPRING with a force limit, or as a dedicated retractor force-limiting curve. In the slipring formulation, the limiting force is set by a load curve or a constant:

*ELEMENT_SEATBELT_SLIPRING
$#   sid1      sid2      ...
         3         4
$#   lcid      ...
         401

Curve 401 defines the force limit versus slip distance. The DOE factor here is the limit force level — for example, 3.0 kN to 4.5 kN in a passenger belt. This is one of the most influential restraint variables for chest deflection and is almost always included in a restraint DOE. Because the limiter and pretensioner act in series, their factors interact: a high pretensioner stroke combined with a low limit force produces a different occupant response than either alone, which is exactly the kind of interaction a well-designed DOE matrix is meant to expose.

How the variables connect

The figure below shows the restraint signal chain and where each DOE factor enters the keyword deck. Reading left to right, the crash pulse drives the occupant forward; the pretensioner and load limiter act on the belt path; the airbag inflator and venting act on the bag pressure; and all of them combine at the occupant interface to produce the injury metrics that the DOE will ultimately regress against.

Units, dependencies, and DOE range discipline

Three practical rules keep a restraint DOE valid. First, fix the unit system before defining factors. LS-DYNA is unit-agnostic; a deck built in mm-tonne-s uses N for force and MPa for stress, while an m-kg-s deck uses N and Pa. A load limiter factor of "3.5 kN" must be entered as 3500 in the first system and 3500 in the second only if the curve is in N — but the belt material modulus and density will differ by orders of magnitude. Record the unit system in the DOE metadata and never mix decks. Second, respect parameter dependencies. The pretensioner trigger time and the airbag firing time are coupled through the crash event; if you vary one, hold the other fixed or vary both as a deliberate two-factor study. Similarly, vent area and mass flow rate both affect bag pressure, so a DOE that varies both without accounting for their interaction will produce confounded results. A fractional factorial or D-optimal design is usually the right choice when such interactions are expected. Third, keep factor ranges physically meaningful. A mass flow scale of 0.85–1.15, a belt stiffness scale of 0.90–1.10, a load limit of 3.0–4.5 kN, and a pretensioner stroke of 80–140 mm are representative engineering ranges for a passenger restraint study; they are illustrative, not universal. Ranges should be justified by supplier data, regulatory corridors, or the design team's tolerance stack — not chosen arbitrarily to fill a matrix.

Verification before matrix generation

Before committing to a DOE, run a single baseline simulation and confirm that each factor's keyword reference resolves correctly. A missing load curve ID, a retractor referencing a nonexistent slipring, or a unit mismatch will silently produce a zero-force belt or an un-inflated bag, and the DOE will then regress against garbage. Check the d3hsp file for warnings on unresolved curve IDs, confirm that the airbag pressure history reaches a plausible peak (typically 150–250 kPa for a driver bag in this unit system), and verify that belt force at the retractor rises to the expected pretension level. Only after the baseline is clean should the factor table be frozen and the matrix generated.