3. Characterize Pelvis Geometry Variability and Its Effect on Belt Engagement

Why Pelvis Geometry Variability Matters for Belt Purchase

In submarining assessment, the lap belt must first establish and maintain a load path across the anterior superior iliac spine (ASIS) region before pelvis rotation and belt migration can be evaluated. That load path is highly sensitive to pelvis geometry: a taller iliac crest gives the belt a larger vertical shelf to sit on, a more prominent ASIS creates a sharper anterior anchor that resists belt slip, and a wider pelvis changes the lateral belt wrap angle and thus the normal force distribution. If the abdomen-pelvis model is built with a single nominal pelvis, the resulting belt purchase may be optimistic or pessimistic relative to the population the countermeasure is meant to protect. This case parametrizes three geometric descriptors and quantifies how each one shifts lap-belt purchase before submarining onset.

Parametrization Strategy

We treat the pelvis as a rigid-body reference with three morphing parameters applied to the iliac and ASIS regions of the FE mesh. The parameters are defined relative to the baseline model from the previous case:

• Iliac crest height h_ic: vertical offset of the iliac crest ridge above the baseline crest line, in mm. Positive values raise the crest shelf.
• ASIS prominence p_asis: anterior protrusion of the ASIS node set along the model's +X (forward) axis, in mm. Positive values push the ASIS forward.
• Pelvis width w_pelvis: lateral scaling of the bi-iliac breadth about the midsagittal plane, expressed as a multiplier (1.00 = baseline).

Morphing is applied with a radial basis function (RBF) deformation controlled by three node groups: GRP_ILIAC_CREST, GRP_ASIS, and GRP_ILIAC_WING. The belt routing, seat cushion, and abdomen soft tissue are re-meshed or re-projected after each morph so that belt-to-pelvis contact is re-established rather than inherited from the baseline.

Design of the Variability Study

A full factorial over three parameters at three levels each would require 27 runs. For a screening study we use a face-centered central composite design (CCD) with 15 runs, which resolves main effects and two-factor interactions with far fewer simulations. The parameter ranges are chosen to bracket published adult pelvis anthropometry while staying within a range the morphing algorithm can handle without remeshing artifacts:

Each run uses the same belt pretension, seat cushion stiffness, and frontal deceleration pulse as the baseline so that differences in belt purchase are attributable to geometry alone. The belt is routed with a 4 kN pretensioner load and a lap-belt anchor geometry held fixed across runs; only the pelvis morphs.

Quantifying Belt Purchase

Belt purchase is measured by three quantities extracted from the first 60 ms of the simulation, before submarining onset is expected:

1. Belt–ASIS engagement length L_eng: the arc length of lap belt in contact with the ASIS node group at t = 20 ms, in mm.
2. Peak normal force on the iliac shelf F_n,peak: the maximum contact normal force summed over GRP_ILIAC_CREST, in N.
3. Belt slip rate v_slip: the relative tangential velocity between belt and ASIS surface averaged over 20–40 ms, in mm/ms. Lower is better.

These three metrics are combined into a normalized purchase index:

PI = 0.4 * (L_eng / L_eng,ref) + 0.4 * (F_n,peak / F_n,peak,ref) - 0.2 * (v_slip / v_slip,ref)

where the ref values are taken from the baseline run. A PI above 1.0 indicates better-than-baseline purchase; below 1.0 indicates degraded purchase and a higher risk of early submarining.

Extracting the Metrics in Post-Processing

The following Python snippet reads the belt and pelvis contact output from the solver's ASCII contact file and computes the three metrics for a single run. It assumes the contact file has columns time, node_id, part_id, fn, ft, slip and that the ASIS and iliac crest node groups are stored in a JSON sidecar.

import json
import numpy as np

def load_groups(path):
    with open(path) as f:
        return json.load(f)

def belt_purchase(contact_csv, groups_json, t_eng=20.0, t_slip=(20.0, 40.0)):
    groups = load_groups(groups_json)
    asis = set(groups["GRP_ASIS"])
    crest = set(groups["GRP_ILIAC_CREST"])

    data = np.genfromtxt(contact_csv, delimiter=",", names=True)
    t = data["time"]

    # Engagement length: belt nodes in contact with ASIS at t_eng
    mask_eng = (np.abs(t - t_eng) < 0.5) & np.isin(data["node_id"], list(asis))
    L_eng = float(np.sum(mask_eng)) * 2.0  # 2 mm per belt segment, example spacing

    # Peak normal force on iliac crest
    mask_crest = np.isin(data["node_id"], list(crest))
    F_n_peak = float(np.max(np.bincount(
        np.floor(t[mask_crest]).astype(int),
        weights=data["fn"][mask_crest])))

    # Belt slip rate over the slip window
    mask_slip = (t >= t_slip[0]) & (t <= t_slip[1]) & np.isin(data["node_id"], list(asis))
    if mask_slip.sum() > 1:
        v_slip = float(np.mean(np.abs(data["slip"][mask_slip])))
    else:
        v_slip = float("nan")

    return {"L_eng": L_eng, "F_n_peak": F_n_peak, "v_slip": v_slip}

if __name__ == "__main__":
    result = belt_purchase("run_07_contact.csv", "pelvis_groups.json")
    print(result)

Run this once per CCD point, collect the three metrics into a table, and normalize against the baseline run to obtain PI. The example below shows the expected direction of the response, not measured values:

Reading the Response Surface

The SVG below summarizes the expected interaction between iliac crest height and ASIS prominence on belt purchase, with pelvis width shown as a secondary modifier. The key engineering insight is that crest height and ASIS prominence are not independent: a tall crest with a flat ASIS can still produce poor purchase because the belt slides forward off the shelf, while a prominent ASIS with a low crest can concentrate load on a narrow ridge and promote local slip. The diagonal band of high PI in the figure marks the combinations where the belt is captured between a raised shelf and a forward anchor.

Interpreting the Results and Setting the Model Range

After running the CCD, fit a second-order response surface to PI and inspect the main effects. Two practical outcomes drive the next modeling decision:

• If h_ic dominates and p_asis is secondary, the countermeasure study should carry at least a low-crest and a high-crest pelvis variant forward, because the low-crest variant is the worst-case for belt purchase and the most likely to submarine early.
• If the h_ic × p_asis interaction is significant, a single nominal pelvis is not defensible; the study must use a small ensemble (typically three to five pelvis variants) that spans the high-purchase band and the low-PI corners.

Pelvis width acts mainly as a modifier: widening the pelvis reduces the normal force on the iliac shelf because the belt wraps around a larger circumference, so a wide pelvis with a low crest is the most adverse combination for purchase. That combination should be included explicitly in the countermeasure matrix even if it is not the population mean.

Deliverable: Pelvis Variant Matrix

The output of this case is a small, defensible set of pelvis variants for the countermeasure study, each with its morphing parameters and its measured purchase metrics. A completed matrix has the following form:

Fill the metric columns from the post-processing output, confirm that P-01 yields the lowest PI and P-02 the highest, and carry P-00, P-01, and P-02 into the countermeasure simulations. If the interaction variants P-03 and P-04 fall outside the band predicted by the main effects, add a fifth variant at the observed worst interaction point before proceeding.