4. Seatbelt design variables

The seatbelt is a closed-loop restraint system: webbing, retractor, pretensioner, load limiter, buckle, and anchors all interact, and the occupant response is rarely controlled by any single component. For a DOE on airbag and seatbelt design variables, the seatbelt side must therefore be parameterized as a set of physically meaningful, independently adjustable factors whose ranges are wide enough to produce a measurable response but narrow enough to remain buildable. This section defines the five seatbelt factor families used throughout the course — webbing stiffness, slip characteristics, retractor pretensioner, load limiter, and anchor point geometry — and shows how to map each one to a concrete LS-DYNA input so that the DOE matrix can be generated and post-processed without ambiguity.

Webbing stiffness

Webbing is a woven polyester strap whose force–strain response is strongly nonlinear: a compliant toe region at low load, a progressive stiffening as the weave consolidates, and a stiff, nearly linear region approaching the strap's breaking strength. In LS-DYNA the belt is normally modeled with seatbelt elements (*ELEMENT_SEATBELT) using *MAT_SEATBELT, where the keyword card ELASTIC or LOAD_CURVE option defines the force as a function of engineering strain. The DOE factor should be a scalar multiplier applied to the nominal force–strain curve, not a raw stiffness value, because the curve shape must be preserved to keep the model physical.

A practical parameterization is a single factor k_web in the range 0.85–1.15, applied by scaling the ordinates of the LCID curve referenced by *MAT_SEATBELT. A second, optional factor can scale the strain at which the curve reaches its knee, capturing weave construction differences between suppliers. Keep the two factors orthogonal in the DOE; if they are varied together, the main effect of stiffness becomes confounded with the toe-region shape. Typical response metrics that webbing stiffness influences most strongly are chest deflection, chest acceleration, and the timing of peak belt force.

Slip characteristics

Slip describes how webbing moves through the D-ring, the buckle latch, and the anchor routing. In the model this is controlled by friction between the belt and the slip-ring surfaces, defined through *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE or the seatbelt-specific contact with a friction coefficient FS, and by the routing geometry itself. The DOE factor is the friction coefficient at the D-ring and buckle, typically varied between 0.05 and 0.30. A low-friction D-ring lets the shoulder belt equalize tension between the lap and shoulder branches; a high-friction ring locks the distribution and can concentrate load on the chest.

Slip also governs how much webbing is pulled from the retractor during pretensioning and how the belt repositions over the pelvis and chest. Because friction is a contact property, it must be varied consistently across all belt-routing contacts; changing only the D-ring friction while leaving the buckle friction fixed produces a non-physical asymmetry. Record the friction pair as a single factor with a documented mapping to each contact definition.

Retractor pretensioner

The retractor pretensioner removes slack by rotating the spool at the onset of the crash. In LS-DYNA it is represented by *ELEMENT_SEATBELT_RETRACTOR with a *DEFINE_CURVE giving retraction force or pulled-in length versus time, plus a locking behavior defined by *ELEMENT_SEATBELT_PRETENSIONER with the PRETENSIONER type set to retractor. The DOE factors are the pull-in length (or force level) and the firing delay. A representative range is 60–120 mm of pull-in with a delay of 0–15 ms relative to the crash pulse.

Pretensioner timing interacts strongly with the airbag: too early and the occupant is pulled forward into the deploying airbag; too late and the slack is removed after the occupant has already moved. This interaction is exactly what a DOE is meant to expose, so pretensioner delay should be treated as a factor even when the airbag firing time is also a factor. The response metrics to watch are belt force at the shoulder, chest deflection, and head forward excursion.

Load limiter

The load limiter caps the belt force transmitted to the occupant, usually through a torsion bar in the retractor or a force-limiting stitch pattern in the webbing. In the model it is implemented as a force limit on the retractor element or as a *MAT_SEATBELT curve that plateaus at a defined force. The DOE factor is the limiting force, typically 3–6 kN for a front-row occupant, with an optional second factor for the force–displacement slope after the plateau (the "post-limit" stiffness).

Load limiter level is the single most influential seatbelt factor for chest injury metrics, but it trades directly against excursion: a lower limit reduces chest deflection while increasing forward travel and the risk of contact with the interior. The DOE must therefore include both chest deflection and head excursion as responses, otherwise the optimization will simply drive the limiter to its lowest value.

Anchor point geometry

Anchor geometry — the D-ring position, the buckle stalk position, and the outboard and inboard lap anchor locations — determines the belt path over the occupant and therefore the load distribution between pelvis and chest. In LS-DYNA these are node coordinates or rigid-body positions referenced by the seatbelt routing. The DOE factors are the three translational offsets of the D-ring (fore–aft, lateral, vertical) and the buckle position, each varied by ±20–40 mm around the nominal design.

Anchor geometry is the factor family most likely to violate packaging constraints, so each DOE run must be checked against a feasible envelope before the matrix is accepted. A D-ring moved too far inboard will route the belt across the neck; too far outboard and the belt may slip off the shoulder. These are not numerical failures but design failures, and they should be flagged in post-processing rather than silently averaged into the response.

Define a consistent sign convention before generating the matrix: for example, +X forward, +Y toward the vehicle centerline, +Z upward, with all anchor offsets measured from the nominal CAD position. State this convention in the DOE documentation and use it unchanged in every plot and table.
Seatbelt DOE Factor Map: Inputs, Keyword Mapping, and Responses DOE FACTORS Webbing stiffness k_web = 0.85 – 1.15 Slip characteristics FS = 0.05 – 0.30 Retractor pretensioner pull-in 60–120 mm, delay 0–15 ms Load limiter F_limit = 3 – 6 kN Anchor geometry D-ring / buckle offsets ±20–40 mm LS-DYNA MAPPING *MAT_SEATBELT LCID curve ordinate scale *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE FS on D-ring and buckle *ELEMENT_SEATBELT_RETRACTOR *ELEMENT_SEATBELT_PRETENSIONER Retractor force limit or plateau in *MAT_SEATBELT Node / rigid-body coordinates referenced by belt routing RESPONSE METRICS Chest deflection Chest acceleration Belt force at shoulder Lap/shoulder load split Head forward excursion Peak belt force timing Chest deflection (dominant) Forward travel trade-off Belt path / neck contact Packaging feasibility Key interactions to preserve in the DOE matrix Pretensioner delay × airbag firing time | Load limiter level × forward excursion | D-ring friction × lap/shoulder load split Anchor offsets must be screened against the feasible packaging envelope before runs are accepted

Building the factor table

The five families above translate into a DOE factor table with documented levels, keyword locations, and response assignments. The table below is a representative starting point for a front-row driver-side study; the levels are illustrative and must be replaced with values validated against the actual hardware and CAE model.

Factor Symbol Low Nominal High LS-DYNA location
Webbing stiffness scalek_web0.851.001.15*MAT_SEATBELT LCID ordinates
D-ring / buckle frictionFS0.050.150.30Belt contact definitions
Pretensioner pull-inL_pre60 mm90 mm120 mm*ELEMENT_SEATBELT_RETRACTOR curve
Pretensioner delayt_pre0 ms7 ms15 msPretensioner firing time
Load limiter forceF_lim3.0 kN4.5 kN6.0 kNRetractor force limit / plateau
D-ring fore–aft offsetdx_D−30 mm0+30 mmRouting node coordinates
D-ring vertical offsetdz_D−20 mm0+20 mmRouting node coordinates
Buckle lateral offsetdy_B−25 mm0+25 mmBuckle rigid-body position

With eight factors at three levels, a full factorial is 6561 runs — impractical for a full-vehicle model. A screening design such as a 27-run Plackett–Burman or a 33-run definitive screening design resolves the main effects and the strongest two-factor interactions, after which a response-surface design on the four or five significant factors refines the optimum. The pretensioner delay and load limiter force should always be retained in the refinement stage because their interaction with the airbag is the dominant coupling in the system.

Execution and verification

Each DOE run is a complete LS-DYNA deck with the factor values substituted into the keyword cards listed above. Automate the substitution with a parameterized include file and a script that writes one deck per run, then launch the runs in batch. A minimal parameterized include looks like this:

*PARAMETER
k_web    1.00
fs_dring 0.15
l_pre    90.0
t_pre    7.0
f_lim    4.5
dx_dring 0.0
dz_dring 0.0
dy_buckle 0.0
*MAT_SEATBELT
$# mid  ro  e  pr  lcid  ...
     1  1.0e-9  0.0  0.0  &lcid_belt
*ELEMENT_SEATBELT_RETRACTOR
$#  sid  lcid  ...
     1  &lcid_retract

Verify each run before accepting it into the response database: confirm that the belt does not slip off the shoulder, that the retractor does not reach its spool limit, and that the pretensioner fires at the intended time. A run in which the belt slips off the shoulder is a design infeasibility, not a numerical outlier, and must be recorded as such rather than averaged into the response surface. Typical failure symptoms and their causes are: negative belt force or element inversion (contact penetration at the D-ring), premature retractor lock (pull-in curve too steep), and chest deflection that is flat across all load limiter levels (the limiter is not actually engaged because the belt force never reaches the plateau).

Do not vary the load limiter force and the webbing stiffness simultaneously in a screening design without checking their correlation. Both raise belt force, and a confounded pair will produce a response surface that attributes the effect to the wrong factor.

Once the runs are complete, extract the response metrics at the standard occupant-injury measurement locations and assemble them into a run-by-response matrix keyed to the factor table. That matrix is the input to the statistical analysis covered in the following sections, and its integrity depends entirely on the discipline applied here: one factor, one keyword location, one documented level range, and one consistent sign convention.

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