RESOURCES · SOLUTIONS BLOG

When a Bullet Meets Armor — and the Bullet Is What Shatters

RS Rand Simulation · Applications Engineering AI · June 2026 · 14 min read

High-speed footage of a bullet striking a steel plate shows something that feels backwards: the bullet, not the plate, is what comes apart. The reason is simple once you look at the materials — a rifle bullet is mostly lead, one of the softest metals there is, and armor plate is hardened steel several times stronger. At supersonic speed the soft projectile has nowhere to go, so it does what anything soft does against something hard and immovable: it splashes. We rebuilt that instant in LS-DYNA explicit dynamics — and then modeled it four different ways, to show how much the choice of numerical method changes the picture.

The marketing-grade hero render of the impact: a brushed-steel plate reflecting an industrial-shop HDRI, a physically-based lead-gray core and warm-brass jacket, and the freed material thrown off as a metallic debris spray colored by speed. Eroded elements simply vanish, so the spray reads like real high-speed footage. (Physically-based render over the LS-DYNA result.)

A ~.30-calibre lead-core / brass-jacket bullet striking a 12 mm Armox-class plate at 850 m/s. Within ~20 µs the projectile mushrooms flat; by ~40 µs the most-strained material is shed as a debris spray — drawn as a point cloud colored by speed, so failed material flies off as discrete fragments while the intact bullet stays a solid mesh. (Lagrangian + erosion.)

The physics of a splash

The brass nose touches first, and the lead behind it — under pressures of tens of thousands of atmospheres — starts to flow sideways like a fluid. The projectile is a two-material idealization of a real jacketed round: a soft lead-antimony core wrapped in a thin brass / gilding-metal jacket, both carried with Johnson-Cook strength and a Mie-Grüneisen equation of state from the open ballistics literature (Peroni et al., DYMAT 2012; Iqbal et al. for the Armox plate). The plate soaks up the energy as a permanent crater — its own fracture is deliberately switched off, so it dishes rather than perforates. This is a study of the projectile, not a penetration prediction.

The headline number: the bullet arrives with ~3.9 kJ of kinetic energy and leaves with ~0.4 kJ — about 90% of the impact energy is dumped into deformation and debris, and roughly 72% of the bullet's mass erodes away as fragments.

The same impact, four ways

A debris cloud is exactly the kind of event where the numerical formulation stops being a footnote. We ran the same shot through four LS-DYNA methods, each with a different way of handling material that has torn itself apart:

Lagrangian + element erosion — the classic. Failed elements are deleted; ~90% of the KE goes to deformation, a 6.7 mm crater. Fast, but the deleted mass under-counts late debris and the single-point elements carry elevated hourglass energy.
SPH (smoothed-particle hydrodynamics) — the bullet becomes particles that can't be deleted, so it conserves mass (100% retained) and runs clean (hourglass ~3%), but transfers a different share of its energy because nothing erodes.
EFG (element-free Galerkin) and S-ALE (structured ALE) — two more routes to the same fragmentation, each trading robustness against cost.

The SPH run: the projectile splatters as a particle cloud that conserves mass, where the Lagrangian run erodes it. Same physics, different numerical bookkeeping — and different residual numbers.

Reading the residuals

The headline numbers above are easy to assert and hard to feel. So here we pull the actual fields straight out of the solve — no re-running, just richer post-processing of the existing LS-DYNA results — and let the residuals show why the method choice moves them. Three pictures carry most of the argument.

1 — the lead flows like a fluid, so look at strain, not displacement

At impact the contact pressure is on the order of tens of GPa — thousands of times the lead core's ~1 MPa yield strength. When the driving pressure dwarfs the material strength, the metal stops behaving like a structure and starts behaving like a fluid: it doesn't deflect, it flows. That is why a displacement plot of the bullet is almost meaningless (every point is moving) while the effective plastic strain field is exactly the right diagnostic — it marks the material that has flowed past its failure strain and is about to be shed.

Effective plastic strain on the bullet at 20 and 40 microseconds — **Effective plastic strain on the bullet, splash crown.** Left: the mushroom at ~20 µs — the intact core (dark) still rides on a flaring crown of heavily-strained lead and brass (orange/cyan, peak eff. plastic strain ≈ 1.24) that is flowing radially outward. Right: by ~40 µs (peak ≈ 1.25) that crown material has passed its failure strain and left the model as debris, so only the lower-strain remnant survives as solid elements. The strain field, not displacement, is what tells you where the projectile is coming apart. (Hi-res Lagrangian run; eroded elements removed; the few failed-but-not-yet-deleted "needle" cells are gated out so the core reads cleanly.)

The plate sees the other side of that same flow. As the lead splashes, it drives a stress wave out across the armor face — and because the plate is strong enough to stay a structure, von-Mises stress is the right thing to watch there.

Von-Mises stress on the steel plate at peak load — **Von-Mises stress in the plate at peak load (~8 µs).** Concentric rings of stress spread outward from the impact point like ripples, with a hot core that pins at the Armox-class flow stress (≈ 1810 MPa — consistent with the Johnson-Cook fit used for the plate). This is the load path the bullet's kinetic energy takes into the steel: a fast pressure pulse that the plate absorbs as plastic work rather than passing through. (Lagrangian baseline run, nodal von-Mises on the deformed mesh.)

2 — where the energy goes: a permanent crater, not a hole

The plate doesn't perforate — its fracture is deliberately switched off — so all that absorbed work has to go somewhere visible. It goes into a permanent dish. Reading the final-state z-displacement over the plate nodes only (excluding bullet debris) gives the crater depth directly, and it lands on 6.7 mm — the same number quoted up top, now measured off the field instead of asserted.

Permanent plate crater depth contour, peak 6.7 mm — **Permanent plate crater — z-displacement depth field at 80 µs.** The struck face dishes into a clean bowl that bottoms out at **6.7 mm** below the original surface; the rest of the 100 mm plate barely moves. With target fracture OFF the plate *dishes rather than perforates*, so this is a deformation study, not a penetration prediction — but it is exactly the right picture for "how much energy did the armor eat." (Plate nodes only; depth measured directly from the displacement field.)

Tracking that energy globally closes the books. The bullet arrives with 3.85 kJ of kinetic energy; the curve below shows it draining almost entirely into internal (plastic-deformation) energy — the crater and the splash — while two smaller terms quietly tell the Lagrangian story: an eroded-KE term that carries energy out of the model with each deleted fragment, and a hourglass term that climbs to ~21.5% of the internal energy (the numerical tax of single-point solid elements under this much distortion).

Energy time-history: kinetic, internal, eroded, hourglass — **Global energy bookkeeping vs. time (Lagrangian + erosion).** Kinetic energy (orange) collapses from 3.85 kJ as internal/plastic energy (blue) rises to ~2.1 kJ — the deformation that makes the crater and the mushroom. The purple **eroded-KE** curve is energy leaving with deleted debris; the yellow **hourglass** curve (peaking ~0.45 kJ, ~21.5% of internal) is the numerical cost of these single-point elements. Read the bookkeeping and the erosion model's two tell-tales — lost mass and elevated hourglass — are both right there on the plot. (Note: this is the *whole-model* kinetic energy; the ~0.4 kJ residual quoted earlier is the *bullet-only* KE from the per-part history.)

3 — the method-to-method difference, made visible

That hourglass-and-erosion signature is precisely what changes when you change the formulation. The Lagrangian model represents failed lead by deleting the element — the mass and its kinetic energy simply leave the simulation. SPH represents the same lead as particles that cannot be deleted: the bullet conserves 100% of its modeled mass and persists as a spray. Put the same instant from both runs side by side and the bookkeeping difference stops being a sentence and becomes a picture.

Lagrangian vs SPH at the same time, 30 microseconds — **Same shot, same instant (~30 µs): Lagrangian (left) vs. SPH (right).** Left, the Lagrangian bullet has eroded — the most-strained cells are *gone* (deleted), and with them their mass and kinetic energy; what survives is colored by effective plastic strain. Right, the SPH bullet has lost nothing: ~4,500 particles persist as a conserved spray (here colored by speed, since the SPH particles in this result carry kinematics but no per-particle plastic-strain output). That single visual difference — deleted material vs. retained spray — is the whole reason the two runs report different residual KE, different crater depth (6.7 mm vs. 4.1 mm), and wildly different hourglass energy (21.5% vs. 2.7%). Neither is "right"; they are different, honest trade-offs.

Why this one matters

Impact and fragmentation problems live or die on the formulation. A Lagrangian erosion model gives you a fast, intuitive answer and quietly loses mass; SPH keeps the mass and changes the energy split; the meshfree methods sit in between. The engineering value isn't a single hero number — it's knowing which method to reach for, what each one is honest about, and what each one hides.

Honest scope. This is a qualitative engineering demonstration and formulation comparison, not a validated terminal-ballistics prediction. Target fracture and erosion are intentionally disabled, so the model says nothing about plate perforation or a ballistic limit. Material constants are from the open literature; the bullet is a simplified two-material idealization. Element erosion under-counts late-time debris, and the single-point solids carry elevated hourglass energy — so the baseline fragmentation, force and crater numbers are qualitative, and the value of the study is the method-to-method comparison, not any single absolute figure. Every figure in the "reading the residuals" section above is post-processed directly from the existing LS-DYNA results (no re-solve); the EFG run is omitted from these plots because its meshfree initialization needs further setup work in our deck, so it produced no state data to read.

When your hardware has to survive an impact that tears material apart, which solver formulation would you stake the answer on? Running one 850 m/s shot through LS-DYNA explicit dynamics four ways — Lagrangian erosion against SPH, EFG and S-ALE — with the energy books held open (erosion's deleted mass and 21.5% hourglass tax versus SPH's 100% mass retention at 2.7%) and the 6.7 mm crater read off the displacement field instead of asserted — is how simulation shows you what each method is honest about, and what it hides, before anyone fires a live round to find out. That's innovation through insight.