4. Material modeling for crashworthiness

Material modeling for crashworthiness 学习卡片

In a frontal impact simulation, the accuracy of the predicted deformation pattern, intrusion, and occupant loading depends far more on the constitutive and failure models than on mesh density or contact settings. A body-in-white (BIW) rail that folds correctly in the physical test but tears prematurely in the model usually points to a failure model that was never calibrated for the actual stress state and strain rate. This chapter covers the material modeling chain used in production crashworthiness work: elastoplasticity for the hardening response, strain-rate sensitivity for high-speed loading, and damage/failure models — GISSMO and Johnson-Cook — together with the calibration workflow that ties them to coupon test data.

Elastoplastic Metals: Hardening and the True Stress–Strain Curve

Crash-relevant metals (HSLA steels, DP590/DP780, 6xxx aluminum, press-hardened boron steel) are modeled with an elastoplastic formulation: linear elastic up to yield, then plastic flow with isotropic hardening. LS-DYNA's *MAT_PIECEWISE_LINEAR_PLASTICITY (*MAT_024) is the workhorse for this. The critical practical point is that the input curve must be true stress vs. plastic strain, not engineering stress–strain. Convert the tensile test data using:

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

For a DP780 coupon with E = 210 GPa, yield at 480 MPa engineering, and UTS of 820 MPa at 14% engineering strain, the true UTS is approximately 820 × 1.14 = 935 MPa at a true strain of ln(1.14) = 0.131, giving a plastic strain of about 0.127. Feeding engineering data directly into *MAT_024 underestimates the flow stress at large strain by 10–15% and produces rails that are too soft. Beyond necking, the curve must be extrapolated — a power-law or linear extension to the failure strain is standard, and the extrapolation choice should be documented because it directly affects energy absorption.

Strain-Rate Sensitivity

Frontal impact strains develop at 10²–10³ s⁻¹, where BCC steels show a pronounced yield-strength increase (commonly 30–60% at 1000 s⁻¹ for mild and HSLA grades), while FCC aluminum is far less sensitive. LS-DYNA offers two practical routes:

  • Rate-dependent plasticity via *MAT_024 with LCSS: supply a table of scale factors on the flow curve versus effective plastic strain rate. This is the most common approach for steels.
  • Cowper–Symonds / Johnson-Cook rate terms: a multiplicative factor on yield, e.g. 1 + C·ln(ε̇/ε̇₀) in Johnson-Cook, or 1 + (ε̇/D)^(1/p) in Cowper–Symonds.

Calibration requires split-Hopkinson pressure bar (SHPB) data at several rates (e.g. 0.001, 1, 100, 1000 s⁻¹). A common pitfall is applying a single rate factor uniformly across all plastic strains; in reality the rate sensitivity often decreases at large strain, so the scale-factor table should be built per plastic strain level if the data supports it.

Damage and Failure: GISSMO vs. Johnson-Cook

Ductile fracture in crash is stress-state dependent. The triaxiality η = σ_m / σ_vm controls void growth: shear-dominated states (η ≈ 0) and biaxial states (η ≈ 0.6–0.7) fail at very different equivalent plastic strains. Two models dominate:

ModelFormulationBest suited forKey inputs
Johnson-Cook damageε_f = (D1 + D2·exp(D3·η))·(1 + D4·ln ε̇*)·(1 + D5·T*)High-rate, thermal-coupled problems; aerospace and some aluminum crashD1–D5, rate and temperature terms
GISSMODamage accumulation D = (ε_p/ε_f(η))^n, with instability and regularizationSheet-metal BIW steels, shell models, mesh-size-sensitive fractureε_f vs. η curve, n, instability curve, regularization exponent

GISSMO (*MAT_ADD_EROSION with GISSMO or the dedicated keyword) is preferred for body structures because it separates damage from instability, allowing the model to capture the diffuse necking that precedes fracture — essential for predicting fold initiation in rails. Johnson-Cook damage is simpler but tends to over-predict failure under shear and does not handle mesh regularization natively.

Failure Calibration Workflow

Calibration is a coupon-driven process. The standard specimen set covers the triaxiality range:

  1. Uniaxial tension (η ≈ 0.33) — establishes the hardening curve and baseline ε_f.
  2. Notched tension (R = 2, 5, 10 mm; η ≈ 0.4–0.55) — intermediate triaxiality.
  3. Central hole / plane strain (η ≈ 0.6) — biaxial-dominant.
  4. Shear specimen (η ≈ 0–0.1) — critical for shear fracture in bending-dominated regions.
  5. Butterfly / biaxial (η up to 0.7) — completes the curve.

Each specimen is simulated with a fine, regular mesh (0.5–1.0 mm solid or shell with element size matching the intended BIW mesh). The failure strain is extracted by matching the simulated force–displacement curve to the test: the point where the simulated curve drops is tuned by adjusting ε_f at that η. The resulting ε_f(η) curve is then fitted and entered into GISSMO. The regularization exponent n is calibrated by running the same specimen at two or three mesh sizes (e.g. 0.5, 1.0, 2.0 mm) and adjusting n until the fracture displacement is mesh-insensitive.

Practical calibration tip: Always calibrate the hardening curve first, then the failure curve. A 5% error in flow stress propagates into a 10–20% error in the extracted failure strain because the specimen's force–displacement response shifts. Lock the hardening parameters before touching ε_f.
Common failure symptom: If a rail tears at the bend radius in simulation but folds in test, check (1) whether the shear branch of ε_f(η) is too low, (2) whether the instability curve triggers erosion too early, and (3) whether the element size in the bend matches the calibration mesh. Mismatched mesh size without regularization is the single most frequent cause of premature element deletion.

Verification and Result Interpretation

After calibration, verify on a component-level test — a three-point bend or axial crush of a closed-hat section — before applying to the full BIW. Compare the force–displacement curve, the peak load, the mean crush force, and the final deformation mode. A well-calibrated GISSMO model should reproduce the peak within 5–10% and the mean crush force within 5%. If the model is too stiff, revisit the rate-dependent scale factors; if it fractures too early, revisit the shear branch of the failure curve. Only after component verification should the material card be released for full-vehicle frontal impact runs.

Material Modeling & Failure Calibration Chain for Crashworthiness 1. Hardening Curve Tensile coupon σ_true vs ε_pl *MAT_024 / LCSS E, ν, yield, UTS 2. Strain-Rate Sensitivity SHPB: 0.001–1000 s⁻¹ Scale factor vs ε̇ Cowper-Symonds / JC C, p or D4 3. Failure Model GISSMO or JC damage ε_f(η) curve Instability + n Regularization 4. Verification Component crush test Force-displacement Deformation mode Peak & mean force Coupon Specimen Set for ε_f(η) Calibration Uniaxial η ≈ 0.33 baseline ε_f Notched R2/R5/R10 η ≈ 0.4–0.55 intermediate Central Hole η ≈ 0.6 plane strain Shear η ≈ 0–0.1 critical branch Butterfly η up to 0.7 biaxial Resulting Failure Locus ε_f(η) Stress Triaxiality η = σ_m / σ_vm Fracture Strain ε_f shear notched plane strain uniaxial butterfly Mesh Regularization Run at 0.5 / 1.0 / 2.0 mm Tune exponent n until fracture displacement is stable

The figure summarizes the full chain: hardening and rate data feed the constitutive model, the coupon set defines the failure locus, and mesh regularization ensures the calibrated ε_f(η) transfers across element sizes. Treating these as one integrated calibration — rather than four independent keyword entries — is what separates a model that predicts folding from one that predicts tearing.

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