4. Material model selection and calibration

In a crash simulation, the material card is where the physics of the structure meets the solver. A well-planned LS-DYNA model can still produce meaningless intrusion, force, or energy results if the constitutive model and its parameters do not represent the actual steel, aluminum, or polymer being deformed. This section covers how to choose among the common LS-DYNA material cards for crashworthiness work and how to fit their parameters from coupon tests.

4.1 Matching the Material Card to the Physical Behavior

The first decision is not "which card is most accurate" but "which deformation mechanisms dominate in this part." For thin-walled body-in-white components under axial crush, the dominant behavior is metal plasticity with strain hardening, strain-rate sensitivity, and eventual ductile failure. For a rubber-like bushing or a foam-filled rocker, the dominant behavior is hyperelasticity or cellular compression. The card must capture the mechanism that controls the crash metric you care about.

Three cards cover the majority of crash simulation needs:

• MAT_024 (*MAT_PIECEWISE_LINEAR_PLASTICITY) — the workhorse for ductile metals. It accepts a piecewise true stress–plastic strain curve, optional strain-rate scaling via a table, and optional failure strain. It is inexpensive and robust, which is why it remains the default for mild steel, HSLA, and many aluminum alloys.
• MAT_123 (*MAT_MODIFIED_PIECEWISE_LINEAR_PLASTICITY) — an extension of MAT_024 that adds a more flexible strain-rate formulation and improved failure handling. It is often preferred when the material shows pronounced rate sensitivity or when MAT_024's rate scaling becomes awkward to fit.
• MAT_187 (*MAT_SAMP-1) — a semi-analytical model for polymers and composites that separates deviatoric and volumetric behavior and supports pressure-dependent yield. It is the appropriate choice for glass-filled nylon brackets, PC/ABS interior trim, and similar materials where MAT_024 would be physically wrong.

Other cards appear when the mechanism demands them: MAT_003 for crushable foams, MAT_083 for honeycomb, MAT_224 for metals with temperature and rate coupling, and MAT_054/262 for laminated composites. The selection logic is summarized in the figure below.

4.2 From Coupon Data to Card Parameters

Coupon testing provides the raw data, but the card does not accept raw engineering curves directly. The conversion path is specific and must be followed carefully.

Step 1 — Convert engineering to true stress–strain. Tensile test output is engineering stress s and engineering strain e. LS-DYNA expects true stress σ and true plastic strain ε_p:

σ_true = s * (1 + e)
ε_true = ln(1 + e)
ε_plastic = ε_true - σ_true / E

For a typical DP590 coupon with E = 210 GPa, a measured engineering yield of 380 MPa at 0.002 strain converts to a true yield near 381 MPa and a plastic strain near 0.0002. The difference is small at yield but grows significantly near necking, where engineering strain of 0.18 becomes true strain of 0.166 and true stress of 620 MPa from an engineering 525 MPa.

Step 2 — Define the hardening curve. MAT_024 accepts up to eight pairs of plastic strain and true stress. The curve should start at zero plastic strain with the true yield stress and extend to the failure strain. Points should be denser in the region of high curvature (around yield and the onset of necking) and sparser in the linear hardening region. A common mistake is to use too few points, which causes the solver to linearly interpolate across a curved region and under-predict energy absorption.

Step 3 — Build the strain-rate table. If the material is rate-sensitive, define LCSS as a table of yield scaling factors versus plastic strain rate. For a mild steel tested at 0.001, 1, 100, and 500 s^-1, the scaling factors might be 1.00, 1.12, 1.28, and 1.35 respectively. These factors multiply the quasi-static curve. The table must cover the strain rates actually expected in the crash event; extrapolation beyond the tested range is unreliable.

Step 4 — Set failure criteria. MAT_024 uses FAIL as a plastic strain at failure, optionally with LCFAIL for rate-dependent failure. For MAT_123, the failure formulation is more flexible and can account for stress triaxiality. The failure strain should come from the coupon test at the relevant rate, not from a handbook value.

4.3 Calibration Example: DP590 B-Pillar

Consider a DP590 B-pillar inner panel. The coupon test matrix includes quasi-static tension, intermediate-rate tension, and high-rate tension using a split Hopkinson pressure bar. The following table summarizes the calibration inputs and the resulting MAT_024 parameters.

After running a single-element verification, the simulated force–displacement response should match the coupon test within 5% up to necking. If the simulated curve is too stiff, check whether the hardening curve was entered as engineering rather than true stress. If the failure occurs too early, verify that FAIL is plastic strain, not total strain.

4.4 Common Pitfalls and Verification

Three errors account for most material card problems in crash simulation. First, unit inconsistency: LS-DYNA is unit-agnostic, so mixing MPa with tonne–mm–s units produces stresses off by a factor of 10⁶. Second, using engineering stress–strain data directly in LCSS, which over-predicts stiffness and under-predicts failure strain. Third, neglecting strain-rate effects for materials that are rate-sensitive, which under-predicts crash force at high impact speeds.

Verification should be layered. At the coupon level, compare simulated and measured force–displacement curves. At the component level, compare a simple axial crush or three-point bend test. Only after both levels agree should the card be used in the full vehicle model. This staged approach isolates material errors from geometry, contact, and boundary condition errors.

For MAT_187, the calibration workflow differs because the model separates deviatoric and volumetric responses. The deviatoric response is fitted from tension and shear tests, while the volumetric response is fitted from compression or hydrostatic tests. The pressure-dependent yield surface requires at least three stress states to define. This makes MAT_187 more data-hungry than MAT_024, but it is the only physically defensible choice for polymers that show different behavior in tension and compression.

In summary, material card selection follows the dominant deformation mechanism, and calibration follows a disciplined path from coupon to single element to component. The card is not a tuning knob for matching a crash test; it is a physical representation that must be validated at the coupon level first.