Designing a Better Crumple Zone

Rand Simulation — Applications Engineering AI
Automotive · Ansys LS-DYNA + optiSLang · 8 min read

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Two of the tube designs the search tried, crushed axially in Ansys LS-DYNA by the same 275 kg mass at 15 m/s. Color is plastic strain — the bright rings are the fold hinges. The two designs soak up the same hit in very different ways: that difference is the whole study.

The result: instead of designing one crush tube, we let optiSLang drive Ansys LS-DYNA and design 36 of them — a space-filling sweep of wall thickness, taper and trigger-bead depth, then a metamodel that mapped the trade-off and a handful of real solves to confirm its picks. The search learned that wall thickness alone sets the peak force (it explains 81 % of it), a trigger bead trades that peak away for energy absorbed, and taper barely matters. What comes out is not one answer but a Pareto front: pick how hard the hit is allowed to be, and it tells you the lightest tube that survives it.

This is a companion to our crush-tube study. That one crushed a single thin-walled tube and validated the physics against the textbook mean-crush-force formula. Here we kept the same solver and the same validated tube and changed only one thing: who chooses the next design. A script and an optimizer did, 36 times over, unattended.

A crumple zone has two jobs that fight

The rails and crush cans in a car’s front end have to do two things that pull in opposite directions. They must absorb energy — turn the car’s motion into crushed metal so it doesn’t reach the people — and they must do it without spiking the force, because peak force is what the occupants feel as deceleration. A tube that is too stiff absorbs plenty but hits like a wall; a tube that is too soft is gentle but bottoms out before it has soaked up the crash. The good designs live on a curve between those extremes, and finding that curve is the job.

Here the “crash” is a fixed one: a 275 kg mass at 15 m/s, about 31 kJ of kinetic energy, dropped onto a AA6060-T4 tube fixed at its base. Every design in the sweep has to swallow the same energy; what changes is the force it charges to do it, and the mass of metal it needs.

Letting the search drive

The workflow is the point. One tube was piloted first to fix the solver settings and the per-case cost — the folding contact, the mass scaling, the run time — and to check the mean crush force against the closed-form value from the base study (about 21.1 kN; the model lands within roughly 20 % of it, the expected direction for a dynamic, untriggered crush). Then optiSLang 26.1.0 took over. It laid down a space-filling set of 28 designs across wall thickness, taper and bead depth, LS-DYNA crushed every one, and the responses came back to fit a metamodel — a fast surrogate that stands in for the solver so the optimizer can explore thousands of designs it never has to run.

The honest part is the last step. A metamodel’s prediction does not count until a real solve confirms it, so the search took its predicted best trade-offs and crushed them for real in LS-DYNA — 36 converged solves in all, 36 of them clean. That is the difference between a search and a guess: the front you see was drawn by the surrogate but every corner of it was checked against the actual solver.

Why not simply grid it? A full factorial over three variables, even at a coarse five levels each, is well over a hundred solves — and most of them land in regions no sensible design would occupy, thick walls with deep triggers that are both heavy and weak. The space-filling sample spends its solves spread across the whole box, the metamodel covers the gaps between them for free, and the confirmations are aimed only at the front that actually matters. That is the same reasoning optiSLang applies at industrial scale, where one solve can be an hour of cluster time and a brute-force grid is simply not affordable. Here it is the difference between a few dozen crushes and several hundred for the same map.

What the search found

Specific energy absorption versus peak crush force for every design — Every design the search crushed, plotted as energy absorbed per kilogram against peak crush force, colored by wall thickness. The orange line is the Pareto front — the designs where you cannot get more energy absorption without accepting a harder hit. Peak force ran from about 19.7 to 85.0 kN across the set; specific energy absorption from 10.1 to 18.7 kJ/kg.

The colors tell the first story on their own: peak force is almost entirely a wall-thickness effect. Thin-walled tubes sit on the left (gentle) and thick ones on the right (hard), in a clean gradient, because a thicker wall simply takes more force to fold. There is no free lunch hiding in taper or bead depth that lets a thick wall hit soft.

The trigger bead earns its keep

Peak, mean crush force and energy absorbed, with and without a trigger bead — The same 2 mm-wall tube with and without a 2 mm trigger groove — the only change between them. The groove gives the first fold somewhere to start, and the whole crush force drops: the peak by about a third, and the mean with it. The tube hits softer, and gives up some of its energy absorption in the trade.

This is the knob that buys a designer something wall thickness cannot. Wall thickness moves you along the trade-off — harder and heavier, or softer and lighter. Adding a trigger groove to a fixed wall instead drops the whole crush force at once. One honest surprise from the model: the ratio of peak to mean force barely moved — in this dynamic crush the groove lowers the entire force level rather than just shaving the opening spike the way the quasi-static rule of thumb suggests. That softer crush is paid for in energy absorbed, and across the search the bead is the second-largest lever on absorption after wall thickness — the one variable that lets a thin, light tube reach the gentle corner of the front at all.

Reading the metamodel honestly

Sensitivity of energy absorption and peak force to each design variable — How much each shape variable moves each response, from the metamodel. Peak force is almost all wall thickness (81 %); energy absorption is a wall-and-bead affair (54 % wall, 42 % bead). Taper barely registers on either — a genuinely useful null result.

The surrogate itself reports how much to trust it. Peak force was highly predictable — its metamodel scored a coefficient of prognosis of 0.96 on held-out designs, meaning a simple surface captures it almost perfectly, which fits a quantity dominated by one variable. Energy absorption was harder, at 0.59: folding is a nonlinear, contact-driven process, and a smooth surface only partly captures it. That gap is worth stating plainly rather than hiding — it is why the front’s corners were confirmed with real solves, not read off the surrogate. The taper result is the quiet win: the search spent solves learning that a variable a designer might agonize over does almost nothing here, which is exactly the kind of thing a sweep tells you and a single case never can.

Part 2 — where this started: How a Crumple Zone Absorbs a Crash

The design search above stands on a first study that asked the simpler question: what actually happens, fold by fold, when one crush tube takes a crash? That original study follows in full.

RESOURCES · SOLUTIONS BLOG

RS Rand Simulation · Applications Engineering AI · June 2026 · 6 min read

The most important part of your car is the part that's designed to be destroyed. In a crash, the front end of a modern vehicle isn't supposed to stay strong — it's supposed to fold up like an accordion, trading its own structure for your life. We pointed LS-DYNA at the single component that does most of that work: a thin-wall steel tube, hit head-on at 10 m/s, and watched it eat 8 kilojoules of kinetic energy one fold at a time.

Progressive folding of a 60×60×1.5 mm square steel tube struck by a 0.20 t rigid wall at 10 m/s. The plastic-strain fringe lights up at each fold hinge while the rest of the wall stays nearly elastic — the signature of a well-behaved energy absorber.

The physics: turning speed into folds

A crash is, at heart, a problem of getting rid of kinetic energy in a hurry. A 200 kg striker moving at 10 m/s carries 10 kJ. Stop it instantly against something rigid and that energy spikes back as a brutal deceleration — the kind that hurts people. The trick a crumple zone plays is to spend that energy slowly, over distance, by bending metal.

When you axially crush a thin-wall tube, it doesn't just squash uniformly. It buckles into a repeating train of folds — the classic accordion. Each fold is a set of plastic hinges where the steel yields and wraps over on itself, and every hinge soaks up a fixed quantum of energy. String enough folds together and you get something beautiful: a roughly constant resisting force over a long stroke. Constant force over distance is the textbook definition of an ideal energy absorber, and it's exactly why automakers build the front rails of a car to fold this way on purpose.

A good crumple zone isn't strong. It's predictably, controllably weak — and that's the whole point.

Inside the model

Geometry and mesh

The part is deliberately humble: a 60×60 mm square tube, 1.5 mm wall, 240 mm long — a stand-in for the kind of crush rail or bumper-beam crush can you'd find behind a fascia. We meshed it with roughly 3 mm Belytschko–Tsay shell elements, 6,400 of them, fine enough to resolve the individual folds and the global force history without drowning the explicit time step. Thin-wall folding is a shell problem through and through, so there are no solids here — fidelity where it matters, not where it doesn't.

The undeformed square tube and its shell mesh — roughly 3 mm Belytschko–Tsay elements (edges shown), 6,400 in all. This is the starting state, before the rigid wall touches it: a clean, uniform wall with no pre-set fold lines, so the accordion pattern that emerges is the structure's own buckling, not something we drew in.

Material, loads and solver

The tube is mild steel modeled with *MAT_PLASTIC_KINEMATIC: yield 300 MPa, tangent modulus 763 MPa, and — crucially — Cowper–Symonds strain-rate hardening with C = 40 s⁻¹ and p = 5. That rate term matters: steel hit fast is meaningfully stronger than steel pushed slowly, and leaving it out would underpredict the crush force. The "car" is idealized as a 0.20 t *RIGIDWALL_PLANAR_MOVING launched at 10 m/s, and self-contact during folding is handled by *CONTACT_AUTOMATIC_SINGLE_SURFACE so the tube walls don't pass through each other as they wrap up. The whole event runs in 15 ms of explicit LS-DYNA time.

A key decision worth calling out: the deck went through three iterations before it ran clean. LS-DYNA's comma-format multi-card keywords demand exact card counts — get the card count wrong and the deck reads as the wrong keyword blocks (we collected 29 errors that way). The fix was to lean on single-card-friendly keywords like MAT_PLASTIC_KINEMATIC and the moving planar rigid wall, which keep the deck simple and readable.

The result

The result: the tube absorbed 7.98 kJ of the striker's 10 kJ over a 107.5 mm crush (44.8% of its length), at a mean crush force of 74.2 kN with a first-fold peak of 249 kN — a specific energy absorption of 26.3 kJ/kg for the crushed material.

The same tube at the end of the 15 ms event: the front has collapsed into a stack of accordion folds while the rest of the wall is barely touched. That 107.5 mm of stroke — the distance the striker drove into the tube — is the run over which the tube spent the striker's kinetic energy — one fold-quantum at a time.

Crush force vs displacement. The tall initial spike (249 kN) is the first fold forming; after that the force settles into a stable ~75 kN plateau as folds form one after another. That long flat plateau is the energy absorber doing its job.

Energy balance over the 15 ms event. The striker's kinetic energy converts cleanly into plastic internal energy as the tube folds; total energy stays conserved to 99.7%.

Is it right?

Three independent checks back up the number — and the most interesting one is deliberately not a one-to-one match.

The classic Abramowicz & Wierzbicki (1984) theory for a square box column gives a quasi-static mean crush force of roughly 35 kN for these dimensions. Our model predicts 74.2 kN — about 2.1× higher. That gap is the physics working as intended: at a 10 m/s collapse, the steel is straining fast enough that Cowper–Symonds rate hardening boosts the dynamic flow stress by roughly 2.2× (with inertial folding effects adding a little more on top). In other words, the FEA force is consistent with the static benchmark once you scale it by the rate enhancement — it is supposed to be larger, not equal.

The other two checks are housekeeping that earns trust in the number: total energy was conserved to 99.7%, so the 8 kJ of absorbed energy is real and not numerical drift; and hourglass energy stayed at 0.36% of internal energy — far below the 10% rule of thumb — so the reduced-integration shells aren't faking stiffness.

The real-world connection

This little tube is a microcosm of why surviving a head-on crash today is a completely different proposition than it was sixty years ago. The most visceral demonstration of that progress is the IIHS 50th-anniversary test, where a 1959 Chevrolet Bel Air — a slab of heavy, "solid" Detroit steel with essentially no managed crush structure — was run head-on into a 2009 Chevrolet Malibu. The old car, the heavier one, the one people remember as "built like a tank," is the one that loses. Its passenger compartment collapses; the modern car's crumple zone folds up out front exactly like our tube and keeps the cabin intact.

Engineers call the intentional weak points that trigger that fold pattern "crush initiators," and the goal is always the same one we measured here: a stable plateau of force over the longest possible stroke. (For a friendly primer, HowStuffWorks has a good walkthrough, and the IIHS YouTube channel is full of slow-motion crumple footage.) Get the geometry, the material, and the rate behavior right in simulation, and you can tune that plateau long before you ever bend a real piece of steel.

Revisions

v2 · Internal reviewThe mean crush force was corrected from 74.7 to 74.2 kN to reconcile with the solved 7.98 kJ over the 107.5 mm stroke; the stroke caption was clarified.

Honest scope. Explicit dynamic finite element in Ansys LS-DYNA: Belytschko-Tsay shells, piecewise-linear plasticity (AA6060-T4), segment-based single-surface self-contact for the folding, selective mass scaling. A 275 kg rigid mass at 15 m/s crushes each tube against a fixed base — a controlled axial-crush test, not a vehicle crash: no oblique impact, no real occupant, no strain-rate hardening or fracture in the material model, and a square section only. Specific energy absorption is taken over the stable folding stroke, before densification. The design search is optiSLang 26.1.0 driving LS-DYNA with a metamodel; the Pareto front’s corners are confirmed by real solves, but the interior is a surrogate prediction. The tube is a generic textbook crush element, not any production part. Part 2 (the original single-tube study): Honest scope. These are FEA / model-predicted values under the stated assumptions, not code-qualified safety ratings. The model includes no fracture or tearing criterion — the tube folds, it never splits — so the 26.3 kJ/kg SEA is best read as an upper estimate for a non-tearing absorber. The ~3 mm shell mesh resolves the fold pattern and global force well, but local peak strains are indicative only. The striker is an idealized rigid wall, and the mean crush force is benchmarked against the Abramowicz–Wierzbicki static formula scaled by Cowper–Symonds rate enhancement, not against a physical test. A production study would add a mesh-convergence sweep, a validated stress–strain curve with a failure model, and correlation to a real crush test.

Have a part whose job is a trade-off, not a single number? Crush structures, brackets, heat sinks, motors, antennas — the real question is usually “what is the lightest, cheapest version that still meets the limit,” and that is a front to be mapped, not a point to be solved. Pairing a validated Ansys solve with an optiSLang search turns a pile of solver runs into that map, and it is a few days of work. We do this across the Ansys structural, fluids and electromagnetics tools. Rand Simulation — innovation through insight.