2. Fundamentals of spot weld modeling in PAM-CRASH

Spot welds are the dominant joining method in stamped steel body-in-white (BIW) structures, and their numerical representation directly controls how a crash model absorbs, transfers, and redistributes energy. In PAM-CRASH, a spot weld is not a single entity but a modeling decision chain: which element type carries the connection, which connector formulation defines its stiffness and failure, and how the surrounding sheet mesh resolves the load path. Getting this chain wrong produces models that either tear prematurely at weld lines or hold together long after the physical joint would have failed.

Weld Element Types and Their Mechanical Roles

PAM-CRASH offers several ways to represent a spot weld, and each maps to a different physical assumption.

  • Solid weld elements (hexahedral or brick nuggets): A small cluster of solid elements spans the two sheets, sharing nodes with the shell mesh. This is the most physically faithful option because the nugget carries bending, shear, and peel simultaneously. It is also the most expensive and the most sensitive to mesh alignment, since the solid block must connect to shell nodes on both surfaces.
  • Beam or bar weld elements: A single beam element connects a node on the upper sheet to a node on the lower sheet. The beam transmits axial force, shear, bending, and torsion through its section properties. This is the classic "nugget beam" approach and remains the workhorse for full-vehicle models because it is cheap and stable.
  • Spot-weld connector elements (rigid or deformable): PAM-CRASH connector objects link two or more nodes without generating a mesh element. A rigid connector enforces kinematic constraint; a deformable connector applies a user-defined force–displacement or stress-based law. Connectors decouple the weld from the sheet mesh topology, which simplifies assembly but requires careful stiffness calibration.
  • Tied or glued contact interfaces: Used when the weld is treated as a bonded region rather than a discrete point. This is common for adhesive bonding or for weld lines modeled as continuous seams, but it cannot capture discrete nugget pull-out.

The choice is driven by the failure mode you need to predict. If the concern is nugget pull-out with sheet tearing, a solid or beam nugget with a calibrated failure criterion is required. If the concern is global load transfer and the weld is not expected to fail, a rigid connector is sufficient and far cheaper.

Connector Formulations and Failure Modeling

For beam and connector welds, the formulation defines how force builds up and when the joint releases. PAM-CRASH supports several approaches:

Formulation Behavior Typical Use
Rigid connector Infinite stiffness, no failure Non-critical welds, rigid links
Elastic–plastic beam Linear stiffness then yield, optional rupture General crash welds
Force-based failure connector Failure when resultant force exceeds limit Shear-dominated joints
Stress/plastic strain criterion Failure based on material state in nugget Detailed weld studies

A practical elastic–plastic beam weld is defined by its cross-sectional area, length, and a piecewise linear plastic curve. For a typical 6 mm nugget in 1.2 mm mild steel, an illustrative (not measured) calibration might use a beam diameter of 5 mm, an elastic modulus of 210 GPa, a yield force of about 8 kN, and a rupture displacement of 2–3 mm. These values are starting points for calibration against coupon tests, not validated constants.

Example connector definition (illustrative): 
WELD_BEAM id=1001
  node_a = 20451
  node_b = 31877
  area   = 19.6 mm^2
  length = 3.0 mm
  E      = 210000 MPa
  yield_force = 8000 N
  rupture_disp = 2.5 mm
  failure_mode = combined_shear_peel

The failure criterion matters as much as the stiffness. A pure force limit ignores the interaction between shear and peel; a combined criterion using a normalized interaction equation (for example, (F_shear/F_shear_max)² + (F_peel/F_peel_max)² ≥ 1) captures the mixed-mode behavior seen in real joints. PAM-CRASH allows this through user-defined failure functions or built-in interaction options.

Mesh Dependency Considerations

Spot weld results are notoriously mesh-sensitive. Three effects dominate:

  1. Weld spacing versus element size: If the average shell element edge length is 5 mm and welds are spaced 40 mm apart, each weld is surrounded by roughly eight elements. Refining to 2 mm changes the local stiffness and the strain field around the nugget, shifting failure timing. The weld model must be recalibrated when the mesh changes.
  2. Node alignment: Beam and connector welds require a node on each sheet at the weld location. If the upper and lower meshes are not aligned, the connector spans an offset, introducing artificial bending. PAM-CRASH can handle offsets, but the resulting moment arm must be intentional, not accidental.
  3. Nugget size versus element size: A solid nugget smaller than the surrounding shell elements creates a stiffness discontinuity. As a rule of thumb, the nugget footprint should be at least one element wide, and the transition from nugget to sheet should be gradual.
Common pitfall: Reusing a weld failure curve calibrated on a 5 mm mesh for a 2 mm mesh without revalidation. The finer mesh resolves higher local strains, so the weld may fail earlier in the simulation than in the physical test. Always document the mesh size associated with any calibrated weld parameter set.

Visual Overview of the Modeling Chain

The diagram below summarizes how element type, connector formulation, and mesh resolution interact to determine the simulated weld response.

Spot Weld Modeling Decision Chain in PAM-CRASH 1. Element Type Solid nugget (brick) Beam / bar element Connector object Tied contact 2. Connector Formulation Rigid (no failure) Elastic–plastic beam Force-based failure Stress / strain criterion 3. Mesh Dependency Element size vs weld pitch Node alignment / offset Nugget size vs element Recalibration on refine Simulated Weld Response Stiffness · Peak force · Failure timing · Energy absorption Validated against coupon test (tensile-shear / coach-peel) Iterate & recalibrate

Practical Calibration Workflow

A defensible weld model is built from the coupon upward, not from the full vehicle downward. The standard sequence is:

  1. Build a single-weld coupon model (tensile-shear and coach-peel) at the target mesh size.
  2. Assign an initial beam or connector formulation with estimated stiffness and failure parameters.
  3. Run the coupon simulation and extract the force–displacement curve.
  4. Compare peak force, initial stiffness, and failure displacement against the physical coupon test.
  5. Adjust section properties and failure limits until the curve matches within an acceptable tolerance (typically 10–15% on peak force).
  6. Freeze the parameter set, record the mesh size, and apply it to the full vehicle model.

If the full vehicle model uses a different mesh size than the coupon, the calibration must be repeated or the parameters scaled. This is the single most common source of weld-related correlation errors in BIW crash simulation.

Rule of thumb: Keep the weld pitch (spacing) at least four times the shell element edge length. If welds are closer than that, the local mesh cannot resolve the individual joints, and a seam or tied-contact representation may be more appropriate than discrete nuggets.

In summary, spot weld modeling in PAM-CRASH is a three-way coupling between element type, connector formulation, and mesh resolution. The element type sets the physical fidelity, the formulation sets the failure behavior, and the mesh sets the numerical resolution. All three must be consistent with the calibration data and the intended failure mode, or the simulation will produce weld behavior that looks plausible but does not match the physical structure.

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