1. Restraint system DOE and injury optimization overview

Occupant safety development in LS-DYNA sits at the intersection of explicit finite element crash simulation, statistical design of experiments (DOE), and multi-objective optimization. A restraint system — seat belts with pretensioners and load limiters, airbags, seat structures, and the surrounding trim — must absorb occupant energy within a tightly constrained package while satisfying regulatory and consumer-rating injury criteria. Because these requirements conflict (a stiffer restraint reduces excursion but raises chest loading), engineers rarely tune one parameter at a time. Instead they build a parametric LS-DYNA occupant or sled model, sample the design space with a DOE, fit surrogate models to the injury responses, and search those surrogates for a design that balances competing metrics. This chapter establishes the vocabulary, the metrics, and the end-to-end workflow that the remaining chapters implement in detail.

Where LS-DYNA Fits in Occupant Safety

LS-DYNA is an explicit nonlinear dynamic solver used across the crashworthiness chain: full-vehicle frontal and side impact, body-in-white stiffness, and — most relevant here — occupant restraint simulation. Two model families dominate restraint work. A sled model applies a prescribed acceleration pulse (from a full-vehicle or barrier test) to a buck containing seat, restraint, and a crash dummy, isolating restraint behavior from structural crush. A full-vehicle model couples the occupant to the deforming body, capturing steering-wheel and knee-bolster intrusion. Sled models are the workhorse for DOE because they run in minutes to a few hours and their boundary conditions are stable across design changes.

The dummy itself is a validated finite element occupant — the Hybrid III 50th percentile male is the standard frontal occupant, with THOR and the Hybrid III 5th percentile female used for advanced and small-occupant studies. LS-DYNA provides these through the LSTC/FTSS dummy libraries, and the restraint hardware is modeled with belt elements (*MAT_SEATBELT), sliprings, retractors, pretensioners, and airbag fabrics using *AIRBAG_ keywords with uniform-pressure or particle/CPM gas models. The fidelity of these components — belt routing, friction, retractor locking, airbag fold and venting — determines whether the DOE responses are physically meaningful.

Key Injury Metrics

Optimization needs scalar, comparable responses. The three most common frontal metrics are:

  • HIC (Head Injury Criterion) — computed from the resultant head center-of-gravity acceleration a(t) over a 36 ms window: HIC = max over t₁,t₂ of [(t₂−t₁)(1/(t₂−t₁)∫a dt)²·⁵]. The regulatory limit is HIC₁₅ ≤ 700 and HIC₃₆ ≤ 1000; consumer protocols often target lower values. HIC is highly sensitive to airbag timing and head-to-airbag contact velocity.
  • Chest deflection — peak sternal deflection in millimeters, measured by the dummy's chest potentiometer or IR-TRACC. FMVSS 208 limits 50th-percentile chest deflection to 63 mm (with a 76 mm upper bound in some configurations); Euro NCAP and C-NCAP apply their own thresholds. Deflection correlates with belt load-limiter force and airbag pressure.
  • Femur force — axial compressive load in each femur, limited to 10 kN (roughly 2250 lbf) per leg in FMVSS 208. Femur force is driven by knee-bolster stiffness, seat pan geometry, and belt lap-path routing.

Additional responses — neck Nij, chest acceleration (3 ms clip), abdomen force, and combined injury probability (e.g., a weighted AIS-based risk) — are often added as secondary objectives or constraints. The choice of metrics defines the optimization problem, so it must be fixed before the DOE is generated.

Report each metric with its window and normalization convention. HIC₁₅ and HIC₃₆ are not interchangeable, and chest deflection measured at the sternum differs from rib-level IR-TRACC output. Consistent definitions are a prerequisite for comparing DOE runs.

The Optimization Workflow

The workflow below is the backbone of this course. Each stage has a distinct failure mode, and skipping a stage usually produces a design that looks optimal on the surrogate but fails on the FE model.

Restraint DOE → Surrogate → Multi-Objective Optimization Loop 1. Parametrize belt limit force, pretensioner, airbag 2. DOE Sample LHS / CCD, N runs 3. LS-DYNA Runs sled / full vehicle, extract HIC, chest, femur 4. Surrogate Fit RSM / Kriging, R², RMSE check 5. Optimize NSGA-II / Pareto front 6. Verify Candidate in LS-DYNA re-run FE with optimal parameters compare predicted vs. simulated injury refine DOE / add runs Responses extracted per run HIC₁₅ / HIC₃₆ · chest deflection (mm) · femur force (kN) + Nij, chest 3 ms clip, abdomen force (secondary)

Stage 1 — Parametrize. Identify the design variables and their bounds. Typical restraint variables include belt load-limiter force (e.g., 3–6 kN), pretensioner stroke and firing time, airbag vent diameter, inflator mass-flow rate, airbag fold and tether length, and seat-pan angle. Each variable must be exposed as a keyword parameter (*PARAMETER) so the DOE driver can rewrite the input deck without manual editing.

Stage 2 — DOE sampling. Choose a sampling scheme that covers the space efficiently. Latin Hypercube Sampling (LHS) with 30–60 points is common for 4–8 variables; a central composite design (CCD) is used when a quadratic response surface is expected. The sample size must exceed the number of surrogate coefficients by a comfortable margin — a rule of thumb is at least 1.5× the coefficient count, and more for noisy responses.

Stage 3 — LS-DYNA execution. Each sample becomes one input deck. A driver script (Python with lasso-python, LS-OPT, or a custom shell loop) substitutes parameter values, launches lsdyna i=run_XX.k, and parses the nodout, rcforc, and dummy-specific output files. Injury metrics are extracted with a post-processing script — for example, reading head acceleration from the dummy's accelerometer node set and integrating over the 36 ms window to compute HIC. Runs that terminate abnormally (negative volume, contact instability) must be flagged, not silently averaged into the surrogate.

Stage 4 — Surrogate construction. Fit a response surface (polynomial RSM) or a Kriging/Gaussian-process model to each injury metric. Validate with leave-one-out cross-validation and report R² and RMSE. A surrogate with R² below roughly 0.9 on HIC is usually too weak to optimize against; add runs or narrow the bounds.

Stage 5 — Multi-objective optimization. Because HIC, chest deflection, and femur force trade off, solve for a Pareto front rather than a single optimum. NSGA-II or a weighted-sum sweep over the surrogates produces a set of non-dominated designs. The engineer then selects a candidate based on program priorities — for instance, minimizing chest deflection subject to HIC ≤ 650 and femur force ≤ 8 kN.

Stage 6 — Verification. Re-run the FE model with the selected parameters. If the simulated injury metrics deviate materially from the surrogate prediction, the surrogate is inadequate and the DOE must be refined. This feedback loop is not optional; it is the quality gate that separates a defensible optimization from a numerical exercise.

What Makes a Restraint DOE Defensible

Three practices distinguish a credible study. First, fix the metric definitions and output extraction before sampling — changing the HIC window or chest measurement location mid-study invalidates comparisons. Second, keep the FE model stable across the design space; a parameter range that causes belt element inversion or airbag self-contact produces garbage responses that corrupt the surrogate. Third, document the pulse, dummy, and boundary conditions so the optimization is reproducible and its conclusions transferable to the full-vehicle program. The chapters that follow apply this workflow to concrete restraint variables, surrogate types, and Pareto selection strategies.

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