3. Crashworthiness simulation workflow

Bayesian optimization is only as trustworthy as the simulation it queries. If the finite element (FE) model produces noisy, unstable, or physically wrong crash responses, the optimizer will faithfully converge on the wrong design. This section walks through the complete crashworthiness simulation workflow — model setup, material and connection modeling, boundary conditions, and solver selection — with the specific goal of producing a deterministic, repeatable, solver-ready model that can be called hundreds of times by an optimization loop.

1. Geometry Preparation and FE Model Setup

Crashworthiness models typically start from CAD of a body-in-white (BIW) or a subassembly such as a front rail, bumper beam, or B-pillar. The first task is mid-surface extraction for thin-walled stamped parts (thickness 0.7–2.5 mm), followed by geometry cleanup: removing fillets smaller than 3–5 mm, repairing gaps, and suppressing features that do not influence collapse modes. A common rule of thumb is that the smallest element edge length should be at least 5 mm for full-vehicle models and 2–3 mm for component-level models, so any geometric detail below that scale is a candidate for defeaturing.

Meshing strategy directly controls both accuracy and runtime. Shell elements (e.g., Belytschko–Tsay, type 2 in LS-DYNA) dominate for sheet metal, while solid elements are reserved for castings, bushings, and foam. A typical full-frontal model contains 1–3 million elements; a component model for optimization might contain 50,000–300,000. For Bayesian optimization, keeping the component model under ~200,000 elements is often the difference between a 4-minute and a 40-minute single run.

2. Material Modeling for Impact

Crash simulation is strain-rate sensitive and failure-driven, so linear elastic models are inadequate. The most common choices are:

• MAT_024 (Piecewise Linear Plasticity) — the workhorse for mild and high-strength steel. Requires true stress–true plastic strain curve, Young's modulus, Poisson's ratio, density, and a strain-rate scaling table (e.g., Cowper–Symonds coefficients C and p).
• MAT_037 / MAT_054 — transversely anisotropic models for aluminum extrusions and rolled sheet, using Lankford coefficients r₀, r₄₅, r₉₀.
• MAT_123 / MAT_003 — kinematic/isotropic hardening for spot-weld and rivet connectors.
• MAT_057 / MAT_063 — crushable foam for energy-absorbing fillers and bumpers.

For a typical DP780 front rail, an example (illustrative, not measured) parameter set might be: ρ = 7.85×10⁻⁹ t/mm³, E = 210 GPa, ν = 0.3, yield = 550 MPa, ultimate = 780 MPa at 0.15 plastic strain, with Cowper–Symonds C = 40 s⁻¹ and p = 5. These values must be documented in a material card library so that every optimization sample uses identical constitutive data — otherwise the optimizer will exploit material noise rather than geometry.

3. Connection Modeling

Connections are the most frequent source of non-physical behavior in crash models. Spot welds are usually represented by MAT_100 (spot weld beam) or by tied contact with a failure criterion. Adhesive bonds use cohesive elements (MAT_186 or MAT_240) with a traction–separation law. Bolted joints are often simplified as rigid bodies (CONSTRAINED_NODAL_RIGID_BODY) or beam elements with preload. For optimization studies, it is critical that connection positions are either fixed or parameterized consistently — moving a weld without updating the tied node set will silently break the model.

*MAT_SPOTWELD
$#   mid        ro         e        pr        sigy      etan
         1  7.85E-9  210000.0       0.3       550.0      1200.0
$#   dt       tf        nrr        mtn       mcs
     0.0      0.0        0.0        0.0       0.0

4. Boundary Conditions and Loading

Crash boundary conditions must reproduce the physical test. For a frontal rigid-barrier impact, the vehicle is given an initial velocity (e.g., 56 km/h = 15.56 mm/ms) and the barrier is modeled as a rigid wall with a prescribed mass or as a fixed rigid plane. For a sled test, the pulse is applied via *BOUNDARY_PRESCRIBED_MOTION_RIGID using an acceleration–time curve. Symmetry planes (SPC on normal translation and two rotations) are used to halve model size when the structure and loading are symmetric.

Two conventions must be fixed and documented before any optimization run:

• Coordinate system: X = longitudinal (vehicle forward), Y = lateral, Z = vertical. All intrusion and force outputs are reported in this frame.
• Sign convention: compressive force is negative, intrusion is measured as displacement opposite to the impact direction.

5. Solver Selection and Execution

Explicit dynamics is the standard for crash. LS-DYNA, Radioss, Abaqus/Explicit, and Pam-Crash are the dominant codes. The stable time step is governed by the Courant condition Δt = L_min/c, where c is the wave speed. For steel, c ≈ 5.1 mm/ms, so a 5 mm element gives Δt ≈ 1 μs. A 100 ms event therefore requires ~100,000 time steps — this is why mass scaling (adding non-physical mass to small elements) is often applied, but it must be limited to keep added mass below 1–2% of total model mass.

For Bayesian optimization, the solver must be wrapped in a script that returns scalar objectives: peak intrusion, peak acceleration, energy absorbed, and mass. A typical run script looks like:

lsdyna i=rail_v03.k ncpu=8 memory=200m
# extract from d3plot / nodout:
#   max intrusion at node 10432
#   peak force from rcforc
#   total internal energy at t=0.08 s

6. Workflow Overview

The diagram below summarizes the data flow from CAD to solver-ready model, highlighting the four decision points that most affect optimization reliability.

7. Reproducibility Checklist for Optimization

Before handing the model to the Bayesian optimizer, verify the following. This checklist is deliberately short — it covers only the items that, if missed, will corrupt the optimization rather than merely slow it down.

Once these checks pass, the model becomes a reliable black-box function f(x) that maps design variables (thickness, material grade, bead depth, weld spacing) to crashworthiness responses (intrusion, peak force, energy absorbed). The next section introduces how Bayesian optimization constructs a surrogate for this function and selects the next design point to evaluate.