3. Material modeling for side impact

Side impact simulation is dominated by two physical realities that are easy to underestimate in a baseline model: the sheet metals in the door, B-pillar, rocker, and floor carry strain rates on the order of 10–1000 s⁻¹ during the intrusion phase, and the joints connecting those sheets (spot welds and structural adhesives) frequently govern the failure sequence before the base metal reaches its own limit. A model that uses quasi-static tensile data and rigid spot welds will typically over-predict energy absorption and under-predict separation, producing an intrusion profile that looks plausible but is wrong in the details that matter for occupant response. This chapter addresses how to build rate-dependent material definitions for steel and aluminum, how to represent spot-weld and adhesive failure, and how to validate the resulting parameter sets against coupon tests before they enter a full vehicle model.

Strain-rate dependence: what the solver actually needs

For crash codes using the Johnson–Cook or Cowper–Symonds formulations, rate sensitivity is expressed through a small number of parameters that must be identified from dynamic tests, not assumed. In LS-DYNA, the common choices are *MAT_PIECEWISE_LINEAR_PLASTICITY (MAT_024) with the LCSR load-curve field pointing to a table of effective stress–plastic strain curves at discrete strain rates, or *MAT_JOHNSON_COOK (MAT_015) with the C rate coefficient. For aluminum, MAT_024 with rate-dependent curves or MAT_098 (*MAT_SIMPLIFIED_JOHNSON_COOK) are both used; the latter is attractive because it needs only quasi-static yield, a hardening term, and a rate coefficient.

The practical distinction matters. A piecewise table interpolates between measured curves and preserves the actual hardening shape at each rate, which is preferable for dual-phase (DP) steels where the rate sensitivity is not uniform across strain. A single Cowper–Symonds coefficient compresses the entire rate response into one multiplier and is acceptable for mild steel or for early-stage concept models, but it will misrepresent DP600 and DP780 behavior at high strain. As a rule of thumb for side-impact grades, the flow-stress increase from quasi-static to 100 s⁻¹ is roughly 8–15% for mild steel, 15–25% for DP590/DP780, and 5–12% for 6xxx-series aluminum, with the aluminum showing a stronger difference between the 0° and 90° directions than between rates. These are order-of-magnitude expectations for checking test data, not substitute values.

Two modeling details are frequently missed. First, the rate used by the solver is the effective plastic strain rate, which in a shell element under bending can differ substantially from the nominal test rate; the coupon test rate must therefore be reported as the rate at a defined gauge location, and the material card should be built from that same definition. Second, the failure strain itself is rate-dependent. If the model uses an erosion strain or a damage initiation strain, that value must be tabulated against rate as well, otherwise the material will appear to become more ductile at high rate simply because the failure criterion was frozen at the quasi-static value.

Spot welds: from rigid connection to failure model

A spot weld in a side-impact model should be treated as a small structural component with its own stiffness and failure envelope, not as a node merge. The two workable approaches are a deformable solid or beam cluster representing the nugget and its heat-affected zone, or a spot-weld constraint with a failure criterion. For most body-in-white models, the practical choice is *MAT_SPOTWELD (MAT_100) applied to a short beam or solid element set, with normal and shear force resultants compared against a failure surface.

The failure surface is defined by the normal force N, the resultant shear force Q, and the moment resultants. A commonly used form is a quadratic interaction between normal and shear with separate tensile and shear limits:

(N / N_f)^2 + (Q / Q_f)^2 = 1        (tension–shear interaction)
N_f = 6–9 kN for 5 mm nugget in 1.2 mm DP590 (example range)
Q_f = 4–6 kN for the same joint (example range)

These numbers are illustrative starting points for a 5 mm nugget in 1.2 mm DP590; they must be replaced by values from the actual weld schedule and coupon tests. The important modeling decision is whether the weld fails in a force-based or displacement-based manner. Force-based criteria are easier to calibrate from lap-shear and cross-tension coupons, but they are mesh-sensitive when the surrounding shell mesh is coarse. Displacement-based or damage-based criteria (for example, MAT_100 with a defined plastic displacement to failure) behave better under the bending that dominates door and B-pillar joints during intrusion, because the joint is loaded in combined tension and peel rather than pure shear.

Calibration follows a three-coupon logic: lap-shear for the shear limit, cross-tension for the normal limit, and a peel or coach-peel specimen for the mixed-mode interaction. Each coupon is modeled with the same element formulation and mesh size that will be used in the full vehicle, and the failure parameters are adjusted until the force–displacement curve matches in peak force and in the displacement at which the force drops. Matching only the peak force is insufficient; the post-peak drop defines how much energy the joint absorbs before separation, and that energy directly affects the intrusion history.

Structural adhesives: cohesive zones and their traps

Adhesive joints in modern bodies (flange bonds along the B-pillar, roof, and door inner) are best represented with cohesive elements or a cohesive contact. The traction–separation law requires three groups of parameters: stiffness (K_n, K_t), strength (t_n, t_s), and fracture energy (G_Ic, G_IIc). A typical toughened structural adhesive might show t_n ≈ 25–40 MPa, t_s ≈ 15–25 MPa, G_Ic ≈ 1.5–3.0 kJ/m², and G_IIc ≈ 4–8 kJ/m²; again, these are example ranges for orientation, not validated values.

The most common error is an excessively high cohesive stiffness chosen to "keep the joint stiff." Very high K values force the explicit time step down and can trigger numerical instability at the cohesive interface, while providing no physical benefit once the stiffness exceeds the surrounding sheet stiffness by more than about two orders of magnitude. A second common error is calibrating only mode I from a double-cantilever beam test and then applying the same fracture energy in shear; side-impact flange bonds are loaded predominantly in mode II, and the mode II fracture energy is typically two to three times the mode I value. Calibrate mode II from an end-notched flexure or a lap-shear specimen with a known bondline, and use a mixed-mode criterion such as a power law or a Benzeggagh–Kenane form to blend the two.

Validation against coupon tests: the gate before full vehicle

Before any material or joint card enters the full vehicle model, it should reproduce its own coupon test in a single-element or small-panel simulation. The validation is not a formality; it is where rate-table interpolation errors, unit inconsistencies, and failure-criterion mismatches are caught cheaply. A workable validation matrix for this chapter's scope is shown below.

The acceptance bands above are example tolerances appropriate for a first-pass correlation; a production program would tighten them after the test scatter is characterized. The key procedural point is that the coupon simulation must use the same element type, mesh size, and hourglass control as the target model. A material card validated on a 1 mm mesh and then applied to a 5 mm mesh in the vehicle will show different failure initiation because the element's characteristic length enters the damage evolution.

Typical failure symptoms and their causes are worth recording in the validation log. If the coupon simulation is too stiff at small displacement, check the elastic modulus and the shell formulation (fully integrated versus reduced with hourglass control). If the peak force matches but the drop is too abrupt, the damage evolution or post-failure displacement is too short. If the simulated weld fails in tension when the test shows pull-out, the normal-to-shear strength ratio is wrong, not the absolute values. If the adhesive debonds prematurely at the load introduction point, the cohesive stiffness is too high relative to the adjacent shell and the load is being transferred through a numerical stress concentration rather than the bondline.

The validation chain above is deliberately ordered so that each stage produces a traceable artifact: the raw coupon curves, the identified parameter set with its source test, the coupon simulation deck, and the acceptance record. When a full vehicle side-impact model later shows an unexpected weld separation or an adhesive debond that does not match physical teardown, the validation log is what allows the analyst to determine whether the joint model was mis-calibrated or whether the vehicle-level loading simply differs from the coupon assumption. Without that record, every discrepancy becomes an unproductive debate about mesh and contact settings.

One final practice deserves emphasis: keep the rate-dependent material tables and the joint failure parameters under version control together with the coupon test identifiers. A parameter set without its test provenance is not a validated model; it is a number that happens to produce a plausible curve. In side impact, where the difference between a bonded flange that holds and one that peels can change the occupant's chest loading by a meaningful margin, that provenance is the difference between a simulation that informs a design decision and one that merely illustrates it.