2. LS-DYNA restraint model setup

Before any DOE or multi-objective injury optimization can be meaningful, the restraint system must be modeled so that its force–displacement behavior matches the physical hardware. In LS-DYNA occupant safety simulations, the restraint model is not a single entity but a chain of interacting components: the belt webbing path, the retractor and pretensioner, the load limiter, the airbag inflator and fabric, and the contact definitions that govern how these components interact with the dummy and the interior. Errors in any one link propagate directly into injury metrics such as HIC, chest deflection, and neck force, and those errors will corrupt the DOE response surface. This chapter focuses on building that chain correctly.

Seatbelt Elements and Routing

Seatbelts are typically modeled with *MAT_SEATBELT (or the older *MAT_FABRIC with belt-specific options) assigned to shell or seatbelt elements created with *ELEMENT_SEATBELT. The belt is discretized along the actual webbing path: shoulder belt from the D-ring through the chest to the buckle, lap belt from the buckle across the pelvis to the anchor. Two modeling decisions dominate accuracy:

• Element formulation and mesh density. Seatbelt elements are 1D tension-only elements. A typical spacing of 10–15 mm along the belt path resolves the interaction with the dummy chest without excessive cost. Too coarse a mesh causes the belt to "cut through" the chest surface; too fine a mesh increases contact cost and can introduce instability.
• Routing and slip rings. The belt must pass through *ELEMENT_SEATBELT_SLIPRING definitions at the D-ring and buckle so that belt material can slide from the shoulder segment to the lap segment during loading. Without slip rings, the belt behaves as a fixed-length loop and the shoulder/lap force split becomes physically wrong.

A practical starting point for webbing is a Young's modulus around 2–4 GPa with a defined failure strain, but the more important calibration is the force–strain curve of the actual webbing, since belt stretch directly shifts occupant excursion. If test data from a belt pull test is available, fit the LOAD curve in the material definition to that data rather than relying on nominal modulus.

Retractor, Pretensioner, and Load Limiter

The retractor is modeled with *ELEMENT_SEATBELT_RETRACTOR, which controls belt payout and locking. Two parameters deserve attention: the locking behavior (which determines when the belt stops paying out) and the retractor force limit. The pretensioner is defined through *ELEMENT_SEATBELT_PRETENSIONER, which pulls a specified length of belt (or applies a force/time curve) at a trigger time. A typical pyrotechnic pretensioner removes 60–120 mm of belt slack within 10–20 ms of firing; the exact value must come from the supplier's characterization, not from a generic default.

The load limiter is the component most often mis-modeled. Physically it is a torsion bar or tear-stitch arrangement in the retractor that caps belt force at a designed level, typically 3–6 kN for a front occupant. In LS-DYNA it is represented by a force-limiting function on the retractor or by a dedicated *ELEMENT_SEATBELT_LOAD_LIMITER-style definition, depending on the version and modeling approach. The key point is that the limiter must produce a plateau in belt force, not a linear spring: the whole purpose is to trade chest deflection against forward excursion. If the plateau level is set too high, chest deflection rises; too low, and the occupant moves forward into the airbag or interior. This trade-off is precisely what the later DOE will explore, so the baseline model must represent it faithfully.

Airbag Modeling

Airbags are modeled with *AIRBAG keywords. Two approaches are common: the uniform pressure (UP) method, where the bag is a control-volume chamber with a prescribed mass flow and temperature, and the particle/ALE or corpuscular method for out-of-position or complex deployment studies. For a standard frontal driver airbag in a DOE study, the UP approach is usually sufficient and far cheaper.

The critical inputs are the inflator mass-flow curve (*AIRBAG_..._INFLATOR or a LOAD curve of gas mass versus time), the initial gas temperature, the vent area, and the bag fabric properties. A representative driver inflator reaches roughly 90% of its gas mass within 25–35 ms. The vent hole area controls the pressure decay after peak and therefore the bag's "catch" behavior. Fabric leakage and porosity should be included if the bag is a coated or uncoated design, since leakage changes the pressure history measurably.

Bag folding and initial geometry matter for contact timing. A poorly folded bag may deploy asymmetrically and contact the dummy earlier on one side, producing a spurious lateral load. Where deployment kinematics are important, use the folded geometry from the supplier's CAD rather than a simplified sphere.

Contact Definitions

Contacts tie the restraint chain to the occupant and interior. The essential definitions are:

Friction on the belt–dummy contact is not a nuisance parameter: it governs how much of the belt force is converted into chest compression versus sliding. A value that is too low lets the belt slide and under-predicts chest deflection; too high and the belt "grabs," over-predicting local penetration. Calibrate against a belt pull or sled test where possible.

Modeling Chain and Verification

The figure below summarizes how the restraint components connect and where the calibration checkpoints sit. Each checkpoint corresponds to a measurable quantity in a sled or component test, which is what makes the model trustworthy enough to serve as the baseline for a DOE.

Verification should proceed in the same order as the chain. First, run a belt-only model (no airbag) and compare belt force at the shoulder and lap anchors against a belt pull or sled test; this isolates the retractor, pretensioner, and load limiter. Second, add the airbag and check bag pressure history and the time of first dummy contact. Third, run the full model and compare chest deflection, HIC, and neck force. Only when the baseline matches the test within an agreed tolerance—commonly 10–15% on peak injury metrics—should the model be used to generate DOE samples. A baseline that is off by 20% on chest deflection will produce an optimization that is precise but wrong.

Finally, keep the restraint parameters that will later become DOE factors clearly separated in the input deck: pretensioner pull length, load limiter force level, vent area, inflator mass scale, and belt friction. Naming these as parameterized variables from the start avoids reworking the model when the DOE matrix is generated, and it makes the mapping from design variables to LS-DYNA keywords explicit and auditable.