3. Full-order finite element models for airbags and seatbelts
Before any reduced-order model can be trusted, it must be anchored to a high-fidelity reference. In occupant safety simulation, that reference is the full-order finite element (FE) model: a discretized representation of the airbag fabric, the seatbelt webbing, the retractor, the buckle, and the surrounding occupant and interior geometry, solved with explicit time integration. This chapter explains how such models are structured, why they are expensive, and how they are typically driven through a complete simulation workflow. The goal is not to teach you to build one from scratch, but to give you a clear mental model of the reference solution that every ROM in this course is measured against.
Model structure: what a full-order model actually contains
A production airbag/seatbelt FE model is a system of coupled subsystems, not a single mesh. The airbag side typically consists of a folded fabric envelope meshed with membrane or shell elements, an inflator represented as a mass-flow or pressure–time source, internal contact definitions between folded layers, and a gas model (uniform pressure, or a control-volume/ALE approach for out-of-position cases). The seatbelt side consists of webbing modeled as membrane or 1D elements with a defined force–strain response, a retractor with locking and pretensioner logic, a load limiter (torsion bar or adaptive), a buckle with a defined release behavior, and slip rings or D-rings that route the belt over the occupant. The occupant itself is a crash dummy FE model (Hybrid III 50th percentile, THOR, or a human body model) with its own contact and joint definitions.
The critical structural feature is that these subsystems interact through contacts and constraints: fabric-to-fabric self-contact inside the folded bag, bag-to-occupant contact, belt-to-occupant friction, and belt-to-retractor slip. These interactions are what make the model physically meaningful and computationally heavy at the same time. A useful way to see the architecture is as a signal-and-load path: the inflator drives the bag, the bag loads the occupant, the occupant loads the belt, and the belt feeds back through the retractor and load limiter. The SVG below shows this coupled structure with the dominant cost drivers annotated.
Why full-order models are computationally expensive
Three mechanisms dominate the cost. First, explicit time-step stability: the stable increment is governed by the smallest element characteristic length divided by the wave speed in the material. Thin fabric shells and fine webbing meshes push the stable step into the sub-microsecond range, so a 120 ms event may require hundreds of thousands to millions of increments. Second, contact: folded airbags generate large numbers of self-contact pairs that must be searched and resolved every increment, and belt-to-occupant contact adds further penalty. Third, mesh size: resolving the fold pattern, the seam geometry, and the vent holes requires a fine discretization that multiplies both element count and contact pairs.
As a rough order of magnitude for a single restraint-system load case, a full vehicle occupant model with a detailed folded driver airbag and a three-point belt commonly runs in the range of several hours to a few days on a modern multi-core node, depending on mesh density and contact settings. These figures are illustrative, not measured results; the actual number depends heavily on the model. The practical consequence is that design-space exploration, optimization, and hardware-in-the-loop studies cannot afford to call the full-order model thousands of times — which is precisely the motivation for reduced-order modeling.
Typical simulation workflow
A full-order run is not a single command; it is a sequence with several decision points. A representative workflow looks like this:
- Geometry and mesh preparation. Import the CAD of the airbag envelope, belt routing, and interior. Mesh the fabric with membrane elements, define the fold pattern (often from a pre-processing fold tool), and mesh the webbing. Assign thickness and material cards.
- Material and gas definition. Assign fabric constitutive behavior (orthotropic, with permeability), webbing force–strain curves, and the inflator mass-flow or pressure–time table. Define the gas model and the venting behavior.
- Assembly and contact setup. Position the folded bag in the module, define self-contact with appropriate thickness offsets, set belt-to-occupant friction, and configure the retractor, pretensioner, and load limiter.
- Initial and boundary conditions. Apply the crash pulse (deceleration vs. time) to the vehicle structure, set the dummy initial posture, and define the seat and floor boundary conditions.
- Solve and monitor. Run the explicit solver, monitor energy balance (hourglass, internal, kinetic, contact energy), check for negative volumes or excessive penetration, and confirm the time step is stable.
- Post-process and verify. Extract occupant kinematics, belt force–time history, airbag pressure, and injury criteria; compare against physical sled or vehicle test data where available.
What to watch for in practice
Two failure modes are common enough to mention explicitly. Fold-induced contact instability appears as sudden penetration or explosive separation of fabric layers at deployment onset; it usually traces back to insufficient contact thickness or an over-aggressive initial fold. Time-step collapse appears as the solver slowing dramatically mid-run; it is typically caused by a single distorted element in the folded region, and the fix is local remeshing or a mass-scaling check rather than a global change. Both are worth catching before the model is used as a ROM training reference, because a corrupted reference silently propagates error into every surrogate built from it.
The full-order model is therefore both the ground truth and the bottleneck. Understanding its structure, its cost profile, and its workflow is what allows you to judge which physics a reduced-order model must preserve and which it can safely approximate.