4. Ply-by-ply shell modeling in PAM-CRASH

Ply-by-ply shell modeling is the workhorse approach for composite crashworthiness in PAM-CRASH. Instead of smearing a laminate into equivalent orthotropic properties, each physical ply is represented explicitly, so intralaminar failure, delamination onset, and stacking-sequence effects can be captured during progressive crushing. This chapter covers the three decisions that dominate accuracy and cost: which shell element formulation to use, how to define the layup and material orientation, and how many through-thickness integration points are required.

Element Types for Composite Shells

PAM-CRASH offers several shell element families. For composite crash work, the relevant choices are the four-node quadrilateral (Q4) and the three-node triangle (T3), both available in fully integrated and reduced-integration forms. The recommended default for ply-by-ply laminates is the fully integrated Q4 shell with assumed strain (Type 1 / Type 2 family), because it avoids hourglassing without artificial stabilization and handles bending-dominated delamination buckling more reliably. Reduced-integration Q4 shells (Type 0 / Type 1 with hourglass control) are cheaper but can leak energy through the hourglass modes when plies buckle locally; if you use them, monitor the hourglass energy and keep it below roughly 5% of internal energy.

Triangular shells should be used sparingly. They are useful for transition zones and complex geometry, but a mesh dominated by T3 elements tends to be overly stiff in bending. A practical rule: keep the triangle fraction below 5–10% of the composite panel, and never place triangles in the expected crush front where folding and fragmentation occur.

Element size matters as much as formulation. For a typical carbon/epoxy laminate with ply thickness around 0.125–0.25 mm, an in-plane element size of 2–5 mm gives a reasonable balance. The element aspect ratio should stay below 3:1, and warping should be minimized. A useful sanity check is that at least 4–6 elements span the expected fold half-wavelength; otherwise the folding pattern is artificially constrained.

Layup Definition and Material Orientation

In PAM-CRASH, the layup is defined through the composite shell property card, typically /PROP/SHELL/COMP or the equivalent /MAT/COMP block depending on the solver version. Each ply is entered with its thickness, material ID, and orientation angle. The orientation angle is measured relative to a reference direction defined by the element coordinate system or a user-specified vector field.

The critical practical point is that the ply angle is not global — it is local to each element. If the mesh is not aligned with the intended 0° direction, the layup will be wrong even if the numbers look correct. Two robust approaches exist:

• Mesh-aligned definition: generate the mesh so that element edges follow the principal fiber direction, then define ply angles relative to the element local axis. This is the cleanest method for flat or gently curved panels.
• Vector-field definition: define a reference direction field (for example, along the crush axis) and let the solver project ply angles onto each element. This is preferred for curved or doubly-curved geometries where mesh alignment is impractical.

A typical layup for a crashworthy carbon/epoxy tube might be [0/±45/90]s with ply thickness 0.125 mm, giving a 2 mm laminate. In the property card this becomes eight ply entries with angles 0, +45, −45, 90, 90, −45, +45, 0. Note that the sign convention for ply angle must be consistent: a positive angle is a counterclockwise rotation about the element normal, viewed from the positive normal direction. If you flip the normal direction, the sign of every angle reverses.

Integration Points Through the Thickness

Through-thickness integration points (IPs) determine how the stress state is resolved across the laminate. For ply-by-ply modeling, the minimum requirement is one integration point per ply. With one IP per ply, the solver samples the stress at the ply mid-surface, which is adequate for in-plane failure criteria such as Hashin or Puck.

However, for crashworthiness, bending and delamination matter. A single IP per ply cannot capture the through-thickness stress gradient that drives delamination. The practical recommendation is:

Increasing IPs raises cost roughly linearly. A 16-ply laminate with 3 IPs per ply means 48 through-thickness sampling points per element — this is expensive but often necessary for accurate energy absorption prediction. A useful compromise is 2 IPs per ply for the plies near the free surfaces and 1 IP per ply for the interior plies, though PAM-CRASH requires a uniform definition per property card in most versions.

The integration point locations are equally important. PAM-CRASH places IPs at the ply mid-surface by default when one IP per ply is used. With multiple IPs per ply, they are distributed within the ply thickness. You should verify the actual IP coordinates in the output file (.out or .res) to confirm the distribution matches your intent.

Practical Workflow and Verification

A reproducible ply-by-ply setup follows this sequence:

1. Mesh the panel with Q4 elements, target size 3 mm, triangle fraction below 5%.
2. Check and enforce consistent element normals.
3. Define the composite shell property with ply thickness, material ID, and angle for each ply.
4. Set the number of integration points per ply based on the analysis goal.
5. Assign the property to the part and verify the layup in the pre-processor's ply viewer.
6. Run a short eigenvalue or static check to confirm the laminate stiffness before the full crash run.

Verification criteria: the first eigenvalue should match a hand calculation within 5–10%; the hourglass energy should stay below 5% of internal energy; and the ply viewer should show the intended stacking sequence. If the eigenvalue is off by more than 10%, the most likely causes are wrong ply angles, inconsistent normals, or an incorrect number of integration points.

The figure summarizes the three coupled decisions: the stacking sequence defines the ply angles, the element local axes define the reference for those angles, and the integration point count defines how finely the through-thickness response is resolved. Getting all three consistent is what separates a predictive composite crash model from a decorative one.