The trend survived mesh refinement; the amplitude did not

Question

When eyelid thickness increased from 1.60 mm to 2.00 mm, a coarse finite-element model showed a decreasing pressure-related response. I wanted to separate two questions:

1. Does the ordering survive mesh refinement?
2. Is the absolute amplitude mesh independent under the registered 2% criterion?

They are not the same question.

Setup

The audit used three eyelid thicknesses, three global mesh sizes, and paired 0/20 mmHg pressure states. Probe advancement, corneal thickness, material scales, contact formulation, and the pressure-related observable were held fixed across each comparison.

The observable was computed from the pressure-paired probe-force difference:

$$q_{20}(h)=\frac{F(h,20,d)-F(h,0,d)}{A_{probe}}.$$

The study used completed MAPDL endpoints with zero solver errors, matched discretization inside each pressure pair, and a penetration quality-control threshold. Those checks reject incomplete runs and mismatched pairs; they do not establish convergence by themselves.

Result

All three levels preserve

$$q(1.60)>q(1.80)>q(2.00).$$

But the two finest levels still differ by as much as 12.31%, well above the pre-registered 2% threshold.

Interpretation

The direction of the thick-end response is robust inside the current model and tested meshes. The absolute values are not mesh independent. A stable ordering is useful evidence, but it is weaker than a converged quantitative prediction.

This means the audit does not support calling 1.60 mm a physical threshold, using the current amplitudes as hardware calibration, or extrapolating them to different materials, geometries, loading paths, or tissue.

Limitation

The refinement was global rather than targeted at the two contact interfaces. Solver ranks, I/O conditions, and campaign concurrency also differed, so recorded wall time is historical operational evidence rather than a controlled scaling benchmark.

Next question

A better next experiment is a pre-registered local-refinement study with consistent contact-surface topology, tighter force/contact tolerances, and one pressure pair used as a resource preflight before expanding the matrix. More global refinement would be expensive without directly resolving why the contact response is still moving.