2. Finite element modeling for side impact

Side impact is a stiffness- and inertia-dominated event with a very short loading window. In a typical pole or barrier impact, the struck door and B-pillar must absorb energy within 30–60 ms, and the occupant's pelvis and thorax interact with the door trim within roughly 20–40 ms of contact. Because the explicit solver's stable time step is governed by the smallest element in the model, every meshing decision has a direct cost in wall-clock time. This chapter treats the BIW, closures, and trim as three distinct meshing problems, then addresses element formulation, hourglass control, and mass scaling as coupled trade-offs rather than independent settings.

Meshing the body-in-white

The BIW carries the primary load path: barrier or pole → outer door skin → door intrusion beam → hinge and latch → B-pillar → rocker → floor and tunnel → opposite side. Mesh density should follow this path. A practical baseline for a passenger car BIW in side impact is a nominal shell size of 6–8 mm on the struck side, refined to 4–5 mm on the B-pillar, door beams, rocker, and sill, and coarsened to 10–12 mm on the non-struck side and roof where bending dominates and gradients are mild. The target is at least three elements across any section expected to form a plastic hinge; a B-pillar section 60 mm deep therefore needs roughly 5 mm elements to capture the hinge line without locking the deformation into a single row of elements.

Geometry preparation matters more than nominal size. Flanges, beads, and spot-weld footprints must be represented explicitly, because a side impact load path is a chain of connections. Weld flanges should be meshed with at least two element rows so that a spot weld does not sit on a single row that can rotate freely. Use a transition zone of one to two element rows when changing size, and keep aspect ratios below about 3:1 in energy-absorbing regions. Avoid triangular shells in the hinge zones; they are overly stiff in bending and will suppress the plastic hinge you are trying to predict.

Closures and trim

Doors are the first structure to be loaded and the last to be trusted. The outer panel is thin (0.6–0.8 mm) and buckles early; the intrusion beam and belt-line reinforcement carry the load. Mesh the beam at 4–5 mm with its closed section represented by shells plus offset, and model the hinge and latch with rigid or deformable connections that transmit moment, not just force. A common error is to tie the door to the body with nodal constraints at the hinge, which creates an unrealistically stiff rotational path; use a joint element or a short deformable bracket instead.

Trim and occupant-facing components are where side impact models most often lose fidelity. Door trim, armrest, and bolster are typically modeled as crushable foam or honeycomb with a measured or assumed pressure–displacement curve. Use solid or thick-shell elements with at least two elements through the thickness of the energy-absorbing pad, and define contact between the trim and the occupant's pelvis and thorax. If the trim is represented as a rigid surface, the occupant will load too early and too hard; if it is omitted, the occupant will load too late. The trim's force–deflection behavior should be calibrated against a component test or a material card, and the calibration should be documented as an assumption, not presented as validated data.

Element types and formulation

Shells dominate the BIW and closures. Use reduced-integration shell elements (type 2 in LS-DYNA, or the equivalent in Radioss/Abaqus Explicit) with five through-thickness integration points for bending accuracy. Fully integrated shells avoid hourglassing but are stiffer in bending and roughly 2–3× more expensive; reserve them for small, critical regions such as hinge brackets. Solids are appropriate for thick castings, extrusions, and foam pads; use one-point reduced-integration solids with hourglass control, or fully integrated solids where shear locking is not a concern. Rigid bodies are appropriate for the barrier, pole, and any component whose deformation is not of interest, but their mass and inertia must be assigned correctly.

Connection modeling is part of element selection. Spot welds should be represented by beam or solid elements with a failure criterion, not by rigid ties, if weld rupture is a possible outcome. Adhesive bonds need cohesive elements or a tied contact with a defined failure envelope. The choice changes the load path after the first weld fails, which is often the difference between a door that stays attached and one that separates.

Hourglass control

Reduced-integration elements can develop zero-energy modes—hourglassing—that produce mesh-shaped, non-physical deformation. In side impact, hourglassing most often appears in the door outer panel, the floor, and thin trim pads. Use stiffness-based hourglass control (type 4 or 5 in LS-DYNA) with a coefficient of 0.05–0.10 for shells, and monitor the hourglass energy reported in the energy summary. A practical acceptance criterion is that hourglass energy stays below 5% of internal energy, and below 2% in regions that drive occupant response. If it exceeds that, refine the mesh locally, switch to fully integrated elements in the affected region, or adjust the coefficient—but do not simply raise the coefficient to hide a meshing problem, because excessive stiffness-based control adds artificial stiffness and can suppress real buckling.

Mass scaling trade-offs

Explicit time step is Δt ≈ L/c, where L is the characteristic element length and c is the wave speed. A single 2 mm element in a 6 mm model can cut the time step by a factor of three and triple the run time. Mass scaling adds non-physical mass to small elements to raise their stable time step. The trade-off is inertia: added mass changes the momentum of the struck structure and can slow its response, which is exactly the quantity of interest in side impact.

Use selective mass scaling targeted at elements below a threshold, not global scaling. A workable procedure is: (1) run a mass-scaling check and list the smallest elements; (2) set a target time step, for example 0.8–1.0 μs for a 6 mm nominal mesh; (3) apply scaling only to elements below the threshold, and cap the added mass per element; (4) verify that total added mass stays below 1–2% of the model mass and that the kinetic energy of the added mass is negligible; (5) confirm that the struck-side door and B-pillar velocities at 20 ms match the unscaled or coarser-mesh reference within a few percent. If added mass exceeds the cap, fix the mesh instead of scaling further.

Putting the trade-offs together

The three decisions are coupled. Refining the B-pillar to 4 mm improves hinge resolution but lowers the time step; selective mass scaling can recover the run time, but only if the added mass stays small. Switching a problematic door panel to fully integrated shells removes hourglassing but increases cost, which may then require a coarser mesh elsewhere. A defensible workflow is to fix the load-path mesh first, choose formulations second, then tune hourglass control and mass scaling against the energy and velocity checks above. Document the nominal sizes, the scaling threshold, the added-mass percentage, and the hourglass energy fraction as part of the model's assumptions, so that later occupant-response differences can be traced back to modeling choices rather than attributed to the restraint system.

With the structural model verified against these checks, the occupant and restraint models can be added without the mesh itself dominating the response. The next step is to define the occupant positioning and contact interfaces that sit on top of this verified structure.