2. LS-DYNA model setup for DOE

A Design of Experiments study on an occupant-restraint system is only as trustworthy as the baseline model it starts from. Before any sampling plan is generated, the LS-DYNA input deck must be converted from a single-purpose run into a parametric model: a deck in which every quantity the DOE will vary is expressed as a named parameter, every parameter has a physically defensible range, and the unperturbed configuration runs cleanly and produces stable, repeatable responses. This chapter covers that conversion process for airbag and seatbelt design variables.

1. Selecting the Design Variables

Airbag and seatbelt DOE studies typically draw from three families of variables. Geometric variables describe the restraint hardware: airbag module position relative to the instrument panel or steering wheel, vent-hole diameter, tether length, seatbelt anchor locations, D-ring height, and buckle stalk angle. Inflation and material variables describe how the bag fills and behaves: inflator mass-flow rate, gas temperature, vent discharge coefficient, fabric permeability, and *MAT_FABRIC stiffness scaling. Deployment-timing variables describe when restraint action occurs: time-to-fire (TTF), the time offset between driver and passenger inflators, and pretensioner firing delay.

Not every candidate belongs in the study. A variable is worth including only if it (a) has a plausible effect on the response of interest, (b) can be changed independently of the others within manufacturing or calibration tolerances, and (c) has a range wide enough to produce a measurable signal but narrow enough to remain physically realizable. A vent-hole diameter that varies from 20 mm to 60 mm will swamp the response with an unrealistic bag pressure history; a range of 28–36 mm around a nominal 32 mm is more representative of production spread. Document the nominal value, lower bound, upper bound, unit, and the keyword card and field each variable maps to — this table becomes the single source of truth for the sampling script.

2. Parameterizing the Keyword Deck

LS-DYNA supports parameter substitution directly in the input deck using *PARAMETER and *PARAMETER_EXPRESSION. The convention is to define each DOE variable once, then reference it wherever the value appears. This eliminates the classic failure mode in which a value is edited in one card but a duplicate literal remains elsewhere in the deck.

*PARAMETER
$#   name       value
     VENT_DIA      32.0
     MFLOW_SCL      1.00
     TTF_DRV       18.0
     PRET_DLY       0.0
     DRING_H        0.0
*PARAMETER_EXPRESSION
$#   name       expression
     VENT_AREA  3.14159265*(VENT_DIA/2.0)**2
     TTF_DRV_S  TTF_DRV/1000.0

Downstream cards then reference the parameter names. For the simple airbag model, the vent area and the inflation curve are the two fields that matter most:

*AIRBAG_SIMPLE_AIRBAG_MODEL
$#     sid      sidtyp       rbid       lcid       lcidd      lciddr
         1          0          2          10          0          0
$#    aipos      aipos2       aipos3       aipos4       aipos5       aipos6
       0.0        0.0        0.0        0.0        0.0        0.0
$#   pvent      pvent2      pvent3      pvent4      pvent5      pvent6
  VENT_AREA       0.0        0.0        0.0        0.0        0.0

For the inflator mass-flow curve, the cleanest approach is to keep the curve shape fixed and scale it through a *DEFINE_CURVE with a parameterized ordinate, or to apply the scale factor in a *DEFINE_FUNCTION. For timing variables, the TTF is applied as an abscissa offset on the pressure/mass-flow curve, so a single parameter shifts the entire inflation event without editing the curve data. Pretensioner delay is handled the same way on the retractor force curve.

3. Preparing and Validating the Baseline

With the deck parameterized, run the baseline at nominal values and confirm three things before generating any DOE points. First, the model must terminate normally with no negative-volume, mass-scaling, or energy-error warnings that would indicate a fragile setup. Second, the energy balance must be sane: hourglass energy below roughly 5% of internal energy, and no unexplained external work. Third, the responses of interest — head acceleration, chest deflection, belt force, bag pressure — must be extracted at fixed, named locations so that every DOE run reports the same quantities in the same order.

Response extraction is best handled with *DATABASE_HISTORY_NODE and *DATABASE_HISTORY_BEAM sets whose IDs are stable across runs, plus a post-processing script that reads the nodout and elout files and writes a single CSV row per run. If the response is a derived quantity such as HIC or chest deflection rate, compute it in the post-processor from the same nodal history, not from a hand-picked peak value.

4. Structuring the Parametric Run Set

The final preparation step is to make the deck runnable as a batch. Each DOE point should be a self-contained directory containing the parameter include file, the shared keyword deck, and a run script that invokes the solver with a consistent termination time and output interval. The parameter file is the only thing that changes between runs; everything else is copied or symlinked. This structure makes the sampling matrix directly executable and keeps the baseline reproducible.

The diagram above summarizes the relationship between the three artifacts that make up a DOE-ready model: the design variable table (the specification), the parameter include file (the mechanism), and the shared keyword deck (the physics). The baseline validation gates sit between the parameterized deck and the run set, because a run set built on an unvalidated baseline will produce a sampling matrix full of failed or non-physical runs.

5. Practical Checks Before Handing Off to Sampling

Three quick checks catch most parameterization errors. First, run the baseline twice with identical parameters and confirm bit-identical response histories — any difference indicates a non-deterministic input such as a random seed or a time-dependent file read. Second, perturb one parameter by a small amount (e.g., VENT_DIA from 32 to 33) and confirm the response changes in the expected direction and magnitude; a null response usually means the parameter is not actually wired into the card. Third, inspect the generated d3hsp file to confirm the substituted values appear where expected, since LS-DYNA echoes the resolved parameter values at the top of the file.

Once these checks pass, the model is ready for the sampling stage: the design variable table defines the columns, the parameter include defines the substitution mechanism, the baseline defines the reference response, and the run-set structure defines how each DOE point is executed and harvested. The quality of every downstream sensitivity and optimization result depends on the rigor applied here.