3. Airbag design variables

In an LS-DYNA airbag simulation, the inflator is not modeled as a pressure boundary condition. Instead, it is represented as a mass source that injects gas into a control volume (CV) or a finite element (FE) airbag. The physical behavior of the deployed bag is therefore governed by four coupled design variables: the mass flow rate history, the temperature of the injected gas, the venting characteristics, and the fabric permeability. Each of these variables maps to specific fields in the *AIRBAG keyword family, and understanding that mapping is the prerequisite for any DOE study on restraint performance.

Mass Flow Rate: The Inflator Signature

The mass flow rate ṁ(t) describes how much gas enters the bag per unit time. In LS-DYNA it is supplied through *AIRBAG_HYBRID (for pyrotechnic inflators) or through a user-defined load curve referenced by *AIRBAG_SIMPLE_PRESSURE_VOLUME and *AIRBAG_SIMPLE_AIRBAG_MODEL. The most common parameterization is a tabulated curve of mass flow rate versus time, defined with *DEFINE_CURVE and referenced by the LCID field. For a driver-side inflator, a representative example curve might rise from zero to roughly 0.6–1.2 kg/s within 5–10 ms and decay to zero by 40–60 ms; these values are illustrative and must be replaced by the inflator supplier's tank-test data.

Two practical points matter for DOE. First, the integral of ṁ(t) must equal the total gas mass delivered, so scaling the curve amplitude and shifting its duration are not independent factors — a DOE that varies both without constraint will produce physically inconsistent designs. Second, the curve is often parameterized by a small set of shape factors (peak rate, rise time, decay time) rather than by individual ordinates, which keeps the design space low-dimensional and the surrogate model tractable.

Gas Temperature and the Energy Equation

The injected gas temperature Tinj enters through the TEMP field of the airbag keyword and, for CV-based models, through the *AIRBAG_THERMAL or *AIRBAG_ADIABATIC options. Temperature affects the bag pressure through the ideal-gas relation p = mRT/V: for a fixed mass and volume, a 10% increase in absolute temperature raises pressure by roughly 10%. In practice, pyrotechnic inflators deliver gas at 800–1200 K, and the bag cools as gas expands and heat transfers to the fabric. LS-DYNA's CV model tracks this through the CP and CV (specific heat) fields and the heat-transfer coefficient, so Tinj should be treated as a DOE factor only when the thermal model is active; otherwise it is a constant that merely scales pressure.

Venting: Area, Coefficient, and Opening Pressure

Venting is the dominant energy-loss mechanism after peak inflation. In *AIRBAG_SIMPLE_AIRBAG_MODEL and *AIRBAG_SIMPLE_PRESSURE_VOLUME, venting is defined by the vent hole area Avent (field PVENT or AREA depending on the keyword variant), the discharge coefficient Cd, and optionally an opening pressure Popen. The mass flow through the vent follows the orifice equation

ṁ_vent = C_d · A_vent · sqrt(2 · ρ · (p_bag − p_amb))

where ρ is the gas density at bag conditions. Because the flow scales linearly with Avent and with Cd, these two parameters are strongly correlated in their effect on bag pressure; a DOE that varies both will show near-collinearity in the response surface. A common and defensible practice is to fix Cd at a calibrated value (typically 0.6–0.8) and treat only Avent as the design variable. Vent area is usually expressed in mm² and ranges from about 200 mm² for a passenger bag to 1500 mm² or more for a driver bag with aggressive venting.

Fabric Permeability

Fabric permeability describes leakage through the weave itself and is distinct from venting. In LS-DYNA it is specified with *AIRBAG_POROUS or through the PERM field of the simple airbag model, using a permeability curve of volumetric flow per unit area versus pressure differential. Permeability is strongly rate-dependent: coated fabrics may show near-zero leakage below 20 kPa and then rise sharply, while uncoated nylon leaks measurably from the start of inflation. For DOE purposes, permeability is best parameterized by a multiplier on the baseline curve (e.g., 0.8×, 1.0×, 1.2×) rather than by individual curve ordinates, because the curve shape is a material property that should not be arbitrarily distorted.

Parameterization Strategy for DOE

The four variables above are not equally suitable as DOE factors. Mass flow rate and vent area are the primary levers on bag pressure and are almost always included. Gas temperature is a secondary factor that matters mainly when the thermal model is active. Fabric permeability is a material-level factor that is often fixed by the fabric supplier and varied only in a robustness study. A defensible baseline DOE for a driver airbag might use a three-factor, three-level Box-Behnken design with peak mass flow rate (0.8×, 1.0×, 1.2× of baseline), vent area (400, 600, 800 mm²), and permeability multiplier (0.8×, 1.0×, 1.2×), giving 13 runs plus center-point replicates.

Each factor must be mapped to a concrete keyword edit. For the mass flow rate, scale the ordinates of the *DEFINE_CURVE referenced by LCID while preserving the time abscissa. For vent area, edit the PVENT or AREA field directly. For permeability, scale the ordinates of the *DEFINE_CURVE referenced by the PERM field. Keeping these edits scripted — for example, with a Python driver that rewrites the keyword deck per run — is what makes the DOE reproducible and auditable.

Reading the Response

The response quantities that close the loop are bag pressure at a reference point, occupant chest acceleration or chest deflection (from a Hybrid III or THOR dummy), and the time of peak pressure. A well-posed DOE will show that vent area dominates peak pressure decay, mass flow rate dominates time-to-peak, and permeability has a modest effect on late-phase pressure. If the main-effect plots show mass flow rate and vent area as nearly interchangeable, the design space is confounded and the factor ranges should be widened or the design augmented. These observations are the basis for the surrogate model built in later chapters.