4. Material modeling for crashworthiness

Crashworthiness simulation lives or dies by the material model. A perfectly meshed BIW with a converged explicit time step will still produce meaningless intrusion and energy curves if the constitutive response, strain-rate sensitivity, and failure definition do not match the physical steel, aluminum, or composite being crushed. In PAM-CRASH this means selecting the correct material law (the /MAT card family), supplying calibrated parameters, and pairing the model with a failure criterion that triggers at the right strain under the right stress state. This section covers the four decisions that dominate crash material modeling: elastic-plastic flow, rate dependence, failure, and card selection.

Elastic-Plastic Metals: The Baseline Constitutive Law

For ductile metals under crash loading, the standard choice is an isotropic elastic-plastic model with von Mises yield and isotropic hardening. In PAM-CRASH the workhorse cards are /MAT/PLASTIC (rate-independent, tabulated or power-law hardening) and /MAT/ELAST/PLAST for the simplest bilinear form. The input is a stress–plastic-strain curve, not an engineering stress–strain curve. This distinction is the single most common source of error: crash codes require true stress and true (logarithmic) plastic strain, converted from the tensile test using

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

For a typical DP780 advanced high-strength steel, a tensile test might give an ultimate engineering stress of 800 MPa at 15% engineering strain with E = 210 GPa. Converting yields a true stress near 920 MPa and a true plastic strain near 0.146. Feeding the raw engineering curve into /MAT/PLASTIC underestimates the flow stress at large strain by 10–15%, which directly softens the simulated crash force. Always extend the hardening curve beyond the uniform elongation point using a power-law or Hockett–Sherby extrapolation, because crash folds routinely exceed 30–50% local plastic strain.

The hardening curve must be monotonic and defined to the largest strain the element will experience. A curve that terminates at 0.15 plastic strain will cause PAM-CRASH to clamp the flow stress, producing artificially stiff response in the fold region.

Strain-Rate Dependence

Mild and high-strength steels exhibit a positive strain-rate sensitivity: flow stress rises with loading rate. In a 50 km/h frontal impact, local strain rates in the crush zone reach 10²–10³ s⁻¹, well above the quasi-static 10⁻³ s⁻¹ of a tensile test. Ignoring this makes the model too soft and under-predicts peak force.

PAM-CRASH offers two practical routes. The first is the Cowper–Symonds scaling used by /MAT/PLASTIC with rate flag, where the dynamic yield stress is

sigma_d = sigma_s * (1 + (eps_dot / D)^(1/p))

with D and p calibrated per material. For mild steel, D ≈ 40 s⁻¹ and p ≈ 5 are common starting values; for DP780, D ≈ 8000 s⁻¹ and p ≈ 4.5 are more representative. The second route is a tabulated rate-dependent model such as /MAT/PLASTIC/RATE or /MAT/JP, where you supply separate stress–plastic-strain curves at 0.001, 1, 100, and 1000 s⁻¹ and the solver interpolates. Tabulated curves are preferred when split-Hopkinson bar data are available, because the Cowper–Symonds fit can deviate at the highest rates.

Aluminum behaves differently: 6xxx and 7xxx alloys show weak or even negative rate sensitivity, so applying steel-like rate parameters over-stiffens the model. For aluminum, use rate-independent plasticity unless test data justify otherwise.

Failure Criteria

Element deletion without a physically grounded failure criterion is guesswork. PAM-CRASH provides several families:

  • Equivalent plastic strain (/FAIL/PLASTIC or the failure strain on the material card): simple, but mesh-size dependent and stress-state blind. Use only for calibration studies.
  • Johnson–Cook (/FAIL/JOHNSON): failure strain depends on stress triaxiality, strain rate, and temperature. Well suited to steels and aluminum where triaxiality data exist.
  • GISSMO (/FAIL/GISSMO): the current industry standard for crash. It defines a stress-state-dependent failure curve (equivalent plastic strain vs. triaxiality) plus a damage accumulation exponent and optional instability (necking) trigger. GISSMO handles the shift from shear-dominated to biaxial stress states across a folding component.
  • Forming limit diagram (FLD) (/FAIL/FLD): used when the part carries forming history; failure is judged against major/minor strain.

For a DP780 B-pillar, a representative GISSMO setup uses a failure curve with equivalent plastic strain of 0.55 at triaxiality −0.33 (shear), 0.35 at 0.33 (uniaxial), and 0.20 at 0.67 (plane strain), a damage exponent of 3, and an instability curve triggering necking at 0.8 of the failure strain. These are illustrative values; they must be calibrated against coupon tests.

Mesh-size regularization is mandatory with strain-based failure. A 5 mm shell and a 2 mm shell will localize differently. PAM-CRASH supports non-local or GISSMO length-scale regularization; without it, refining the mesh artificially delays failure.

Material Card Selection in PAM-CRASH

The selection logic follows the physics, not convenience. The diagram below maps the decision from material class and available test data to the recommended card and failure pairing.

PAM-CRASH Material Card Selection for Crashworthiness Material Class Constitutive Card Rate Treatment Failure Card Mild / HSLA Steel DC04, HSLA340 /MAT/PLASTIC tabulated hardening Cowper–Symonds D≈40, p≈5 /FAIL/GISSMO triaxiality curve AHSS / UHSS DP780, MS1500, 22MnB5 /MAT/PLASTIC/RATE or /MAT/JP Tabulated curves 0.001–1000 s⁻¹ /FAIL/GISSMO + instability trigger Aluminum 6xxx, 7xxx extrusion /MAT/PLASTIC Voce / power law Rate-independent weak sensitivity /FAIL/JOHNSON or GISSMO Cast Al / Mg low ductility /MAT/PLASTIC + damage coupling Rate-dependent if data available /FAIL/PLASTIC low eps_f Calibration rule: Coupon test → true stress–plastic strain → rate curves → failure curve vs. triaxiality → mesh regularization → component validation.

Calibration Workflow and Verification

Card selection is only half the task; the parameters must be calibrated and verified. A defensible workflow for a new AHSS grade proceeds as follows. First, run quasi-static tensile tests at 0.001 s⁻¹ and dynamic tests at 1, 100, and 1000 s⁻¹, extracting true stress–plastic strain curves at each rate. Second, fit the hardening law (Swift or Hockett–Sherby) and the rate parameters. Third, run notched and shear coupon tests to populate the GISSMO failure curve across triaxialities from −0.33 to +0.67. Fourth, build a single-element or small coupon model in PAM-CRASH, apply the same boundary conditions as the test, and compare force–displacement and failure location.

Verification criteria are concrete: the simulated peak force should fall within 5% of the measured coupon peak, the failure displacement within 10%, and the failure location must match the test. If the model fails early, check whether the failure curve was entered as plastic strain (correct) or total strain (wrong), and whether regularization length matches the coupon mesh. If the model is too stiff at high rate, the Cowper–Symonds p exponent is likely too low; increase p or switch to tabulated curves. If elements delete in a scattered pattern rather than along a localized band, the damage exponent in GISSMO is too high or the instability trigger is missing.

Finally, remember that material cards interact with element formulation and mesh size. A shell with five through-thickness integration points and a 5 mm characteristic length will behave differently from a 2 mm mesh with three points. Document the mesh size alongside the material card in the model database, and re-verify whenever the mesh changes. This discipline is what separates a crash model that predicts from one that merely runs.

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