2. Airbag modeling fundamentals in MADYMO

An airbag is not a rigid body that simply appears in front of an occupant. In MADYMO it is represented as a deformable control volume whose internal pressure, venting behavior, and contact stiffness evolve over a few tens of milliseconds. Getting the deployment physics right depends on three modeling decisions that are largely independent of each other: how gas enters and leaves the bag, how the fabric resists stretching and leaking, and whether the internal gas state is treated as a single uniform pressure or as a spatially resolved flow field. This chapter explains each decision, how they interact, and how to choose between the uniform-pressure and Eulerian gas-flow approaches.

Gas flow models: inflator output and venting

MADYMO does not simulate the propellant chemistry. Instead, the inflator is characterized by a gas inflow definition that supplies mass flow rate and temperature as functions of time, or by a tank-test-derived pressure curve that is converted internally. The two common input forms are:

• Mass flow and temperature tables — TIME, MASS_FLOW (kg/s), and TEMP (K) columns. This is the most physically transparent option and is preferred when inflator data come from a closed-tank or open-jet test.
• Pressure-based inflator — a TIME–PRESSURE curve referenced to a specified tank volume, from which MADYMO back-calculates mass flow using the ideal-gas relation.

Gas leaves the bag through two mechanisms. Venting is modeled with vent holes defined by an effective area and a discharge coefficient; the mass flux follows a compressible orifice relation driven by the pressure difference between the bag and ambient. Porosity (fabric leakage) is a distributed loss through the membrane and is usually specified as a leakage coefficient rather than discrete holes. Both paths remove mass and enthalpy, so they directly control the pressure peak and the decay that the occupant feels.

Fabric material definitions

The bag membrane is defined as a membrane (no bending stiffness) with an orthotropic linear-elastic or user-defined stress–strain law. The essential parameters are:

Because the fabric is nearly inextensible once taut, the choice of modulus mainly shifts the timing of the pressure rise rather than the final shape. A common error is to use a stiff modulus to make the bag "look right" in a static inflation; this suppresses the initial unfolding and produces an unrealistically early pressure peak. Calibrate the modulus against a static or dynamic deployment test before tuning the inflator.

Uniform pressure versus Eulerian gas flow

This is the central modeling distinction in MADYMO airbag simulation.

In the uniform-pressure (UP) approach, the entire bag is a single control volume. One pressure, one temperature, and one density describe the gas at every point. The pressure is computed from the ideal-gas law using the instantaneous volume, the accumulated mass, and the energy balance. Contact forces on the occupant are derived from the local membrane geometry and this single pressure. The UP model is fast, numerically robust, and accurate when the bag is fully inflated and the internal state is nearly homogeneous.

In the Eulerian gas-flow approach, the bag interior is discretized into a mesh of gas cells. Mass, momentum, and energy are transported between cells, so pressure and temperature vary spatially and in time. This captures the jet of gas leaving the inflator, the pressure wave that travels to the bag extremities, and the non-uniform loading that occurs during the first few milliseconds of deployment. The cost is a much larger model, tighter time-step control, and greater sensitivity to mesh quality.

Choosing the right approach

The decision is driven by the time window of interest and the occupant's proximity to the bag. During the first 10–20 ms, the inflator jet has not yet filled the bag uniformly; a UP model will under-predict the force on an occupant who is close to the module (out-of-position, or OOP). For a mid-position occupant who contacts the bag after it is largely inflated, the UP model is usually sufficient and far cheaper.

A practical workflow is to start with UP, validate the overall pressure history against a tank or static deployment test, then switch to Eulerian only for the OOP or early-contact cases where the pressure gradient matters. When switching, keep the same inflator mass-flow table and the same fabric properties so that the comparison isolates the gas model.

Worked example: a driver-side bag

Consider a 60 L driver airbag with a pyrotechnic inflator. The mass-flow table rises to a peak of about 2.5 kg/s at 15 ms and decays to zero by 45 ms. The fabric is a 470 dtex nylon 6.6 with E₁ = E₂ = 2.0 GPa, thickness 0.35 mm, and a leakage coefficient calibrated from a static leak test. Two vent holes of 25 mm effective diameter with a discharge coefficient of 0.8 are placed on the rear panel.

Run the UP model first. Plot bag pressure versus time and check that the peak falls in the expected range for the inflator class (roughly 180–220 kPa gauge for this example). If the peak is too high, increase vent area or leakage; if the pressure rise is too slow, check the mass-flow table and the bag volume. Then run the Eulerian model with the same inputs and compare the pressure at the module-side and occupant-side cells. A large early difference confirms that the jet has not yet homogenized, which is exactly the regime where the Eulerian model is needed.

Typical failure symptoms and their causes:

• Pressure oscillates or the solution diverges — time step too large for the Eulerian mesh; reduce the time step or coarsen the gas mesh.
• Bag inflates but never reaches target pressure — vent area or leakage coefficient too high, or the mass-flow table is truncated.
• Occupant force is unrealistically high at early contact — UP model used where a pressure gradient exists; switch to Eulerian.
• Bag shape is wrong but pressure is plausible — fabric modulus or initial folding is incorrect; the gas model is not the cause.

Mastering these three decisions — gas inflow and venting, fabric definition, and the UP-versus-Eulerian choice — gives you a defensible airbag model. The next step is to couple that model to the occupant and verify the interaction against physical test data.