3. Material modeling for bumper and crash box steels and aluminum alloys

Bumper beams and crash boxes absorb energy through controlled plastic deformation, so the accuracy of a CAE model depends far more on the constitutive law than on mesh density. In LS-DYNA, two material cards dominate this application space: *MAT_PIECEWISE_LINEAR_PLASTICITY (MAT_024) and *MAT_PLASTIC_KINEMATIC (MAT_003). Both are von Mises metal plasticity models with isotropic hardening by default, but they differ in how the flow curve is defined and how kinematic hardening and strain-rate sensitivity are handled. Choosing the wrong card, or feeding it an unconverted tensile curve, is one of the most common sources of non-physical crash results.

MAT_024: Piecewise Linear Plasticity

MAT_024 defines the hardening curve as a true stress–true plastic strain table, which makes it the natural target for coupon test data. The essential parameters are:

• RO — mass density (e.g., 7.85e-9 tonne/mm³ for steel, 2.70e-9 tonne/mm³ for aluminum).
• E — Young's modulus (210 GPa steel, 70 GPa aluminum).
• PR — Poisson's ratio (0.30 steel, 0.33 aluminum).
• SIGY — initial yield stress; used only if LCSS is left at zero.
• LCSS — load curve ID giving effective stress versus effective plastic strain.
• ETAN — plastic hardening modulus for the bilinear fallback.
• FAIL — effective plastic strain at element deletion (optional).
• VP — strain-rate formulation flag (0 = yield scale factor from LCSS curve, 1 = Cowper–Symonds).

The critical modeling step is converting the engineering stress–strain curve from a tensile test into true stress–true plastic strain. Up to necking, use:

sigma_true = sigma_eng * (1 + eps_eng)
eps_true   = ln(1 + eps_eng)
eps_pl     = eps_true - sigma_true / E

Beyond necking the conversion is invalid because the gauge section is no longer uniform. The standard practice is to extrapolate the true curve to the failure strain using a power law (Swift or Voce) fitted to the pre-necking data, then truncate at the failure strain measured by DIC or thickness reduction. Feeding raw engineering data directly into LCSS over-predicts stiffness and under-predicts absorbed energy.

MAT_003: Plastic Kinematic

MAT_003 uses a bilinear approximation defined by SIGY, ETAN, and a hardening parameter BETA that blends isotropic (BETA = 1) and kinematic (BETA = 0) hardening. It also carries the Cowper–Symonds rate parameters C and P directly on the card. Its advantages are speed and robustness; its limitation is that a single tangent modulus cannot capture the multi-stage hardening of modern AHSS. For mild steel crash boxes and for aluminum extrusions where a bilinear fit is acceptable, MAT_003 is often sufficient and computationally cheaper. For DP590, DP780, or 6xxx-series extrusions with pronounced hardening, MAT_024 with a measured curve is preferred.

Strain-Rate Effects

Bumper and crash box steels are strain-rate sensitive: yield strength rises with strain rate, and the effect is stronger for BCC steels than for FCC aluminum. Two formulations are common:

• Cowper–Symonds (MAT_003, or MAT_024 with VP=1): the dynamic yield stress is scaled by 1 + (eps_dot/C)^(1/P). Typical values for mild steel are C ≈ 40 s⁻¹ and P ≈ 5; for DP780, C ≈ 800 s⁻¹ and P ≈ 4.5.
• Tabulated rate scaling (MAT_024 with VP=0): a load curve of yield scale factor versus effective strain rate, derived from split-Hopkinson bar tests at 10²–10³ s⁻¹.

Aluminum 6xxx extrusions show much weaker rate sensitivity; a scale factor of 1.05–1.15 at 1000 s⁻¹ is typical, versus 1.4–1.6 for mild steel. Ignoring rate effects under-predicts peak force and can flip a pass/fail decision on the bumper intrusion criterion.

Practical Parameter Set and Verification

The table below summarizes a representative starting point for a DP780 crash box and an AA6063 extrusion. Values are illustrative and must be replaced with measured data for production work.

After building the card, verify it before running the full model. A single-element uniaxial tension simulation at a prescribed velocity should reproduce the input flow curve within a few percent. Then run a three-point bend or axial crush of the crash box and compare the force–displacement curve against a physical test or a validated reference. Key checks: initial peak force (rate and yield), plateau force (hardening slope), and the point of densification (failure strain). If the plateau is too high, the true curve was over-extrapolated; if the peak is too low, the rate parameters are missing or too weak.

In summary, MAT_024 with a properly converted and extrapolated true stress–plastic strain curve is the default for AHSS and aluminum crash components; MAT_003 remains useful for mild steel and rapid concept screening. Strain-rate sensitivity must be included for any high-speed event, and the choice between Cowper–Symonds and tabulated scaling should follow the available test data and the solver version's implementation.