4. Identifying uncertainty sources in virtual crash models
A virtual crash assessment claim is only as credible as the uncertainty budget behind it. Before any single number can be defended — a peak intrusion, a HIC value, a restraint load — the analyst must first enumerate every mechanism that can move that number away from the physical truth. This chapter establishes a systematic identification framework across the four dominant source families in crashworthiness simulation: geometry variability, material scatter, boundary conditions, and solver approximations. The goal is not yet to quantify each contribution, but to build a complete, traceable inventory that later chapters will populate with distributions and sensitivities.
Why identification precedes quantification
Uncertainty quantification methods — Monte Carlo sampling, interval analysis, polynomial chaos — are mathematically indifferent to what they are fed. If a source is omitted from the inventory, no sampling scheme will recover it, and the resulting budget will be confidently wrong. Identification is therefore a completeness problem, not an accuracy problem. A practical discipline is to walk the model's construction chain in reverse: start from the output quantity of interest (QoI), trace back through the solver, the boundary definitions, the material cards, and finally the geometric representation, asking at each stage "what was assumed, measured, or idealized here?" Every answer that involves a judgment call is a candidate source.
Two attributes should be recorded for each candidate source from the outset: whether it is aleatory (irreducible physical randomness, such as sheet metal thickness variation within a coil) or epistemic (reducible lack of knowledge, such as an untested strain-rate regime). This classification drives later decisions — aleatory sources are propagated probabilistically, epistemic ones may be bounded or refined with additional testing — and misclassifying a source early is expensive to correct.
Geometry variability
Geometry in a crash model is never the nominal CAD surface. It is a mesh approximation of a manufactured part, and both the manufacturing and the approximation introduce deviation. The most consequential geometric source in body-in-white models is sheet thickness: rolled steel and aluminium carry mill tolerances typically on the order of ±3–5% of nominal, and this variation directly scales bending stiffness and axial crush force. A 1.2 mm rail at the low end of tolerance can reduce the initial peak force by several percent compared with nominal — enough to shift the timing of the crash pulse and, in a full-frontal event, the occupant loading phase.
Stamping springback and residual forming effects are subtler. A formed part carries through-thickness stress gradients and work-hardened material that a flat-shell idealization does not reproduce. If the model uses nominal flat geometry with as-received material properties, the effective stiffness of the formed part is misrepresented. Weld and flange positions add a discrete scatter: a spot weld placed 5 mm from nominal changes the local load path and can alter the failure sequence of a joint under bending. Finally, mesh idealization itself — fillet radii collapsed to sharp corners, small features removed — is an epistemic source whose magnitude depends on element size and should be checked with a mesh-refinement study rather than assumed negligible.
Material scatter
Material uncertainty enters at two levels. The first is batch-to-batch and within-coil scatter of basic properties: yield strength, ultimate strength, and elongation for a given grade typically show coefficients of variation of 3–8%, with the upper tail of yield strength being particularly important because it raises peak force. The second level is the constitutive and failure description. Strain-rate sensitivity parameters are usually fitted from a limited set of tensile tests at discrete rates; extrapolation to the rates actually experienced in a crash (10²–10³ s⁻¹) is an epistemic gap. Fracture strain and spot-weld failure loads are notoriously scattered — weld failure load can vary by 20% or more between nominally identical joints — and they govern the transition from stable folding to tearing, which is often the difference between a passing and failing assessment.
A practical identification step is to build a material-source register that lists, for each card in the model, the property, its nominal value, the evidence basis (test report, handbook, supplier certificate), and the observed or assumed scatter. Properties with no test evidence behind them should be flagged as epistemic and given a conservative bound rather than a fabricated distribution.
Boundary conditions
Boundary conditions in a crash model are where the analyst's assumptions are most exposed. Impact velocity is usually well controlled in a physical test (within ±0.5 km/h), but yaw and pitch alignment of the vehicle relative to the barrier are not: a 1° yaw at 50 km/h introduces a lateral velocity component of roughly 0.9 km/h and can asymmetrically load the front structure. Barrier face friction, rarely measured, affects the post-impact rebound and the longitudinal force trace. On the occupant side, the H-point and posture of the ATD or human body model, seat cushion compliance, pretensioner firing time, and airbag trigger delay all shift occupant metrics such as HIC and chest deflection by amounts comparable to the design margins being claimed. These are predominantly aleatory in a real fleet but epistemic in the sense that the analyst chooses a single nominal value; the identification task is to record the plausible range and the basis for the nominal.
Solver approximations
Numerical sources are entirely epistemic and, unlike physical scatter, they are controllable — but only if they are recognized. Element size governs the resolution of folding wavelengths; a coarse mesh can artificially stiffen a section or suppress local buckling. Hourglass control settings trade numerical stability against added artificial stiffness. Contact penalty stiffness affects penetration and force oscillation at interfaces. Mass scaling, used to raise the stable time step, adds inertia that is negligible for quasi-static events but not for high-rate crush. Constitutive integration schemes (for example, explicit vs. implicit stress update) introduce small but systematic biases in yield-surface return. The standard identification technique is a verification matrix: run the same load case with systematically varied numerical settings and record the spread in the QoI. Any setting whose variation moves the QoI by more than a pre-agreed threshold (commonly 1–2%) belongs in the budget.
Consolidating the inventory
The output of this chapter is a source register, not a number. A workable register has one row per source with the following fields: identifier, source family, affected model input, affected QoI, aleatory/epistemic classification, nominal value, plausible range or distribution with evidence basis, and a proposed quantification method (sampling, interval, or verification study). The register becomes the input to the sensitivity screening in the next stage, where sources with negligible influence are screened out and the remainder are propagated. Getting the register complete and honestly evidenced is the single highest-leverage step in the entire budget: every later claim of confidence inherits its validity from this list.