2. Crashworthiness responses and constraints

In a crash CAE design optimization study, the response surface is only as meaningful as the responses it interpolates. Before any DOE matrix is generated or any surrogate model is fitted, the engineer must decide what to measure from each simulation and how to express the design requirement as a mathematical constraint. Crashworthiness is multi-objective by nature: a structure that minimizes occupant intrusion tends to raise deceleration peaks, a structure that caps force may absorb less energy, and every countermeasure adds mass. This chapter establishes a consistent response taxonomy for RSM work — intrusion, acceleration, force, energy, and mass — and shows how each is extracted, signed, normalized, and constrained so that the optimizer receives a well-posed problem rather than a set of incomparable numbers.

Establishing a Consistent Reference Frame First

Every response in this chapter depends on a coordinate convention, and inconsistency between the CAE model, the post-processing script, and the optimization setup is one of the most common sources of sign errors in crash RSM studies. Adopt the following convention and state it explicitly in the study documentation: the vehicle coordinate system is ISO 4130-style, with +X forward, +Y to the left, and +Z upward. Intrusion is measured as displacement of a structural point relative to the occupant compartment reference, and is reported as a positive magnitude along the intrusion direction (typically −X for frontal barrier impact, i.e., rearward into the occupant space). Acceleration is reported in g with the crash pulse direction positive, so a frontal deceleration pulse appears as a positive value when the sensor axis is aligned with −X. Force is reported as the barrier or trolley reaction, positive in compression. Energy is always positive. Mass is always positive. Fixing these signs once prevents the classic failure mode where a constraint written as intrusion ≤ 120 mm is silently satisfied by a response that was extracted as a negative value.

Intrusion: The Occupant-Space Response

Intrusion is the response most directly tied to injury risk, because it reduces the survival space around the occupant and can load the occupant through the door, dash, or steering column. In RSM practice, intrusion is rarely a single scalar. A frontal study typically tracks several measurement points: toe pan rearward displacement, dash panel displacement at the steering column, brake pedal travel, and footwell lateral collapse. Each point becomes a separate response, and the constraint set becomes a vector inequality. For a surrogate model, this is handled either by treating each point as an independent response or by defining a scalar aggregate such as the maximum over the point set, I_max = max(I_1 … I_n). The aggregate is convenient for a single constraint but is non-smooth at the switch point between active locations, which can degrade gradient-based optimizers and kriging-based expected-improvement searches. A practical compromise is to keep the individual points as responses for the surrogate fit and apply the max only at the constraint-evaluation stage.

Intrusion responses are strongly nonlinear in time and are usually extracted as the peak value over the event window, not the final residual deformation. Report both: peak intrusion governs the constraint, while residual intrusion is useful for diagnosing whether the structure bottomed out or rebounded. A typical frontal constraint set for a passenger car might read I_toe ≤ 120 mm, I_dash ≤ 100 mm, and I_pedal ≤ 130 mm; these are illustrative values for a teaching example and must be replaced with the program-specific targets for a real vehicle.

Acceleration: Pulse Shape, Peaks, and the Filtering Trap

Acceleration responses are where RSM studies most often go wrong, because the raw signal is dominated by high-frequency structural ringing that has little to do with occupant loading. The standard practice is to apply the SAE J211 channel filter class appropriate to the measurement — CFC 60 for occupant-relevant accelerations, CFC 180 or CFC 1000 for structural component response — before extracting any peak. Extracting a peak from an unfiltered signal inflates the response, makes it mesh-sensitive, and produces a surrogate that is fitting numerical noise rather than physics.

Useful acceleration responses include the peak resultant at the B-pillar base, the peak at the seat track, the 3 ms clip value used in many occupant-protection criteria, and the pulse duration above a threshold. The 3 ms clip is defined as the maximum value of the filtered acceleration that is exceeded for a cumulative duration of 3 ms; it is more stable than a raw peak and is the preferred response for constraint formulation. A representative constraint might be a_3ms,B-pillar ≤ 60 g. Because acceleration and intrusion trade off directly — stiffer front structure lowers intrusion but raises the pulse — these two response families should always be included together in the same RSM study, never optimized in isolation.

Force, Energy, and the Consistency Check

Force responses describe the load path: barrier force, cross-member force, and the force transmitted into the occupant compartment through the dash or floor. Energy responses describe absorption: internal energy in the front rail, hourglass energy, and the ratio of absorbed energy to initial kinetic energy. These two families are linked by the work integral, and that link is the single most valuable sanity check in a crash RSM study. If the surrogate predicts a force–displacement curve whose integral does not approximately equal the kinetic energy that must be dissipated, the response extraction is wrong regardless of how good the fit statistics look.

Hourglass energy deserves explicit treatment as a constraint rather than a diagnostic. In under-integrated shell meshes, hourglassing can absorb a large fraction of the impact energy and produce a surrogate that appears to satisfy intrusion targets while the physical structure would not. A common practice is to constrain E_hourglass / E_internal ≤ 0.05 and to reject any DOE run that violates it before fitting. Energy responses are also the natural place to express the design requirement that the front rail absorb a target fraction of the initial kinetic energy, for example E_rail / E_kinetic ≥ 0.55.

Mass: The Objective That Bounds Everything

Mass is simultaneously an objective and a constraint, and the RSM formulation must be explicit about which role it plays in each study. In a typical crashworthiness optimization, mass is minimized subject to intrusion, acceleration, and force constraints, with the constraint set defining the feasible region. The mass response itself is usually computed as a linear function of gauge and geometry variables, which makes it a poor candidate for surrogate modeling — it can be evaluated exactly and cheaply. The practical consequence is that mass should be carried as an analytical response in the optimization layer, not as a fitted surface, while the crash responses are fitted. Mixing the two without noting the distinction leads to surrogate error being attributed to mass when it actually originates in the nonlinear responses.

Putting the Responses Together: A Constraint Set for a Frontal Study

The table below shows a complete, internally consistent response and constraint set for a teaching example of a frontal barrier study. All values are illustrative and chosen to demonstrate the formulation, not measured results.

The SVG below maps how these responses flow from the simulation through filtering and extraction into the constraint set and the mass objective, and highlights the two consistency checks that must pass before a run enters the DOE.

Practical Extraction Workflow and Failure Symptoms

A reproducible extraction workflow for this response set looks like the following. The input is the run directory containing the LS-DYNA d3plot and nodout/glstat/matsum outputs plus a measurement-point definition file listing node IDs for each intrusion location and accelerometer node sets with their axes. The execution step applies the CFC filter, computes peaks and 3 ms clips, integrates barrier force over displacement, and reads internal and hourglass energy from glstat at the end time. The expected output is a single CSV row per run with one column per response, plus a pass/fail flag from the two acceptance gates. Verification is straightforward: rerun the extraction on a known-good baseline and confirm the values match the hand-checked report.

Typical failure symptoms and their causes are worth memorizing. If intrusion values are negative, the sign convention in the measurement-point file disagrees with the post-processor axis. If the 3 ms clip is implausibly high and changes when the mesh is refined, the filter class is wrong or was not applied. If the work–energy check fails by a large margin, the force history was taken from a contact definition that does not cover the full barrier interface, or the displacement used in the integral was taken from a different reference node than the force. If hourglass ratio exceeds the gate on only a few DOE runs, those runs should be excluded from the fit rather than down-weighted, because the surrogate would otherwise learn a non-physical response. Each of these is diagnosable from the CSV row itself, which is the main argument for keeping extraction scripted and auditable rather than manual.

With the response set defined, signed, filtered, and gated, the RSM study has a well-posed target: a feasible region bounded by intrusion, acceleration, force, and energy constraints, with mass as the objective to be driven down. The next step — choosing design variables and a DOE that resolves these responses — depends on this taxonomy being fixed first, because the number of responses directly determines the sampling budget required for a trustworthy surrogate.