3. Material modeling for crash energy absorption

Crash energy absorption is governed by how a material converts kinetic energy into plastic work, heat, and fracture surface energy. In LS-DYNA, this behavior is captured through a constitutive model (strength), a strain-rate formulation (rate sensitivity), and a failure definition (damage initiation and evolution). Getting these three layers consistent is the core of a trustworthy crashworthiness model. This section walks through the elastoplastic baseline, rate-dependent extensions, and the damage/failure criteria most commonly used for thin-walled absorbers.

3.1 Elastoplastic Baseline: MAT_PIECEWISE_LINEAR_PLASTICITY

The workhorse for metallic absorbers is *MAT_PIECEWISE_LINEAR_PLASTICITY (MAT_024). It defines an isotropic von Mises yield surface with an arbitrary hardening curve. The key inputs are density RO, Young's modulus E, Poisson's ratio PR, yield stress SIGY, and either a hardening tangent modulus ETAN or a true stress–plastic strain table (LCSS). For crash grades such as DP590 or AA6061-T6, a tabulated curve is strongly preferred over a single ETAN, because the slope changes significantly after yield.

A practical hardening table for a dual-phase steel (example values, not measured data) might be:

*MAT_PIECEWISE_LINEAR_PLASTICITY
$      MID        RO         E        PR      SIGY      ETAN      LCSS
         1   7.85e-9    210000       0.3       420       0.0         1
$ plastic strain vs. true stress
$   eps_p      sigma
      0.00       420.0
      0.02       560.0
      0.05       680.0
      0.10       790.0
      0.20       880.0
      0.40       950.0

Two modeling decisions dominate accuracy here. First, always feed true stress vs. plastic strain, not engineering stress–strain; LS-DYNA expects the plastic portion after subtracting elastic strain. Second, the element formulation matters: fully integrated shells (ELFORM=16) avoid hourglassing but lock in bending, while reduced integration (ELFORM=2) needs hourglass control. For axial crushing of square tubes, ELFORM=16 with five through-thickness integration points is a common, defensible starting point.

3.2 Strain-Rate Sensitivity

Steels and aluminum alloys strengthen under the high strain rates (10²–10³ s⁻¹) typical of crash events. LS-DYNA offers two standard routes. The Cowper–Symonds model scales the yield stress as

σ_y(ε̇) = σ_y0 [1 + (ε̇ / C)^1/p]

and is activated by setting SRFLAG or by supplying C and P in the material card. The Johnson–Cook model (*MAT_JOHNSON_COOK, MAT_015) instead uses a multiplicative form with a rate coefficient C and a thermal softening term. For room-temperature crash simulation without thermal coupling, Cowper–Symonds is usually sufficient and cheaper.

Rate sensitivity is not a cosmetic add-on. In a typical axial crush of a 1.5 mm DP590 tube at 10 m/s, the peak force can rise 15–25% when rate effects are included, and the fold pattern can shift from symmetric to mixed mode. Omitting rate sensitivity therefore biases both the peak deceleration and the mean crush force, which are exactly the objectives in a multiobjective study.

3.3 Damage Initiation and Failure Criteria

Elastoplasticity alone never deletes elements, so a crushed tube will keep carrying load through fully failed material. Crash models need an explicit failure definition. Three families are common:

• Effective plastic strain limit — the simplest: set FAIL in MAT_024 or use *MAT_ADD_EROSION with a plastic strain threshold. Fast, but mesh-dependent and unable to distinguish tension from shear.
• Stress/principal-strain criteria — *MAT_ADD_EROSION with MXEPS (max principal strain) or SIGVM. Better for ductile metals under multiaxial loading.
• Damage-mechanics models — GISSMO (*MAT_ADD_DAMAGE_GISSMO) or Johnson–Cook fracture. These accumulate damage D from a strain-to-failure surface that depends on stress triaxiality η and, optionally, the Lode parameter, then degrade stress through a softening curve.

GISSMO is the current best practice for crashworthiness because it separates initiation (when D reaches 1) from evolution (how stress fades to zero), and it regularizes the softening slope against element size. A minimal GISSMO setup couples a triaxiality-dependent failure curve with a damage-exponent DMGEXP and an instability curve. The failure strain typically falls sharply at high triaxiality (tension) and rises in shear, which is why a single plastic-strain limit cannot represent both a bending fold and a shear fracture.

3.4 Choosing and Calibrating the Model

The selection logic is straightforward: start from the alloy family, then match the failure mode you expect. Axial folding of ductile steel is dominated by plastic work and moderate triaxiality — MAT_024 with Cowper–Symonds plus a GISSMO or principal-strain failure works well. Cast aluminum or high-strength boron steel in bending may fracture at low strain, so a triaxiality-aware model is mandatory. Calibration should use at least one tensile test (for hardening and rate), one notched or shear test (for the triaxiality dependence), and, where possible, a component-level crush to validate the fold pattern.

3.5 Verification Checklist

Before running a design-of-experiments sweep, confirm the following on a single baseline model. The energy ratio (internal + kinetic + sliding) should stay near 1.0 in glstat; hourglass energy should remain below 5% of internal energy; and the simulated force–displacement curve should reproduce the experimental peak and mean crush force within about 10%. If the peak is too high, check rate constants and yield stress; if the mean force is too low, check the hardening tail and failure strain; if the fold pattern is asymmetric when it should be symmetric, check imperfection seeding and element formulation. Only after this baseline passes should material parameters be promoted to design variables in the multiobjective optimization.

The essential takeaway: strength, rate sensitivity, and failure are three coupled decisions, and the failure model must match the dominant fracture mode of the absorber. A well-calibrated MAT_024 + Cowper–Symonds + GISSMO stack gives a physically defensible energy-absorption response that optimization algorithms can then explore with confidence.