2. Diagnosing Hourglassing-Induced Chest Deflection Artifacts

Why Hourglassing Corrupts Chest Deflection in Belt-Loaded Models

In a seatbelt-loaded chest model, the belt webbing applies a concentrated, highly localized pressure over a narrow contact patch on the ribcage. Under this loading, reduced-integration solid and shell elements can develop zero-energy deformation modes — hourglass modes — in which the element distorts into an hourglass or bowtie shape without generating strain energy. Because these modes carry no stiffness, they grow unchecked and manifest as nonphysical deflection spikes in the chest deflection trace, often inflating peak deflection and corrupting injury-metric extraction. The diagnostic task is to distinguish genuine structural deflection from hourglass contamination, then apply hourglass control that suppresses the artifact without over-stiffening the response.

Diagnostic Signal: Energy Component Comparison

The most reliable first indicator is the energy balance. In a healthy explicit run, the total energy is conserved and the hourglass energy remains a small fraction of the internal energy. When hourglassing dominates, the hourglass energy grows rapidly and can approach or exceed the internal energy of the affected region. Extract the following from the LS-DYNA glstat and matsum files:

• Hourglass energy (glstat, "hourglass energy") — should stay below roughly 5–10% of peak internal energy for a well-controlled model.
• Internal energy and kinetic energy — confirm the run is not simply diverging.
• Added mass and sliding energy — rule out contact or mass-scaling artifacts that can mimic deflection spikes.

A chest deflection trace that spikes sharply while hourglass energy climbs in lockstep is the classic signature. If hourglass energy is flat but deflection still spikes, the cause is elsewhere (contact penetration, material instability, or a genuine rib fracture event) and hourglass control will not help.

Deformation Pattern Confirmation

Energy alone is suggestive but not conclusive. Confirm the mode visually by plotting the affected elements in the post-processor at the time of the spike. Hourglass modes show a characteristic alternating, checkerboard or bowtie distortion across adjacent elements, with element edges zig-zagging rather than following a smooth deformation gradient. In a belt-loaded chest, this typically appears in the flesh and rib shell elements directly beneath the belt path, where the contact pressure is highest and the mesh is coarsest relative to the local curvature.

Two practical checks sharpen the diagnosis:

1. Element-level hourglass energy: use *DATABASE_ASCII with GLSTAT and, where available, element energy output to localize which part contributes the hourglass energy. If the contribution concentrates in the chest flesh or rib shells under the belt, the diagnosis is confirmed.
2. Mesh sensitivity: refine the belt-contact region by one level and re-run. If the deflection spike shrinks markedly with refinement, the original mesh was under-resolved and prone to hourglassing — a mesh-quality contributor rather than a pure control-parameter issue.

Applying Hourglass Control

Once the diagnosis is confirmed, the corrective action is to activate or strengthen hourglass control on the affected parts. For solid elements, the standard approach is *CONTROL_HOURGLASS with an appropriate hourglass type and coefficient. For shell elements, the same keyword applies with shell-specific types. A practical starting configuration for a belt-loaded chest model is:

*CONTROL_HOURGLASS
         4       0.10

Here IHQ = 4 selects the Flanagan–Belytschko stiffness-based hourglass control, which is generally robust for solid elements under contact loading, and QM = 0.10 sets the hourglass coefficient. The coefficient controls the stiffness added to resist hourglass modes: too low and the artifact persists; too high and the model becomes artificially stiff, suppressing genuine deflection and biasing injury metrics low. A coefficient in the 0.05–0.10 range is a reasonable starting point for flesh and rib materials; validate by checking that hourglass energy stays below the 5–10% threshold while the chest deflection trace retains its physical shape.

For shell-dominated rib structures, IHQ = 4 or IHQ = 5 (Flanagan–Belytschko with different stabilization) are common; IHQ = 1 (viscous) is sometimes used but can add artificial damping that smears the deflection peak. Choose stiffness-based control when the goal is to preserve the deflection waveform, and confirm the choice by comparing the controlled run against the baseline.

Verification and Acceptance Criteria

After applying hourglass control, re-run the model and verify the following before accepting the result:

The controlled result should show a chest deflection trace that is smooth and physically plausible, with the peak deflection reduced from the artifact-inflated value to a level consistent with the belt loading and rib stiffness. If the spike persists after control is applied, revisit the mesh in the belt-contact region — hourglass control cannot compensate for an element that is too distorted or too coarse to represent the local bending.

Practical Troubleshooting Notes

• Spike without energy rise: suspect contact penetration or a material instability (e.g., negative volume onset) rather than hourglassing; hourglass control will not fix it.
• Hourglass energy high but deflection smooth: the control may be over-stiffening a region that is not driving the metric; check whether the energy is localized in a non-critical part.
• Spike shrinks with mesh refinement: the root cause is under-resolution, not control parameters; refine first, then tune control.
• Deflection under-predicted after control: QM is too high; reduce toward 0.05 and re-verify the energy balance.

Document the before/after hourglass energy fraction and the chest deflection peak in the case log so the correction is traceable and reproducible for subsequent validation cases.