A molded-fiber tray that does not pass

A parametric fiber tray replaces EPS foam around a 1.5 kg laptop. The analysis says the tray fails two of three load cases. The tray also misses the mesh gate and swells out of its pocket spec. This page reports that.

Read these two limits before you read any number.

Every material property comes from published literature, and none of the properties is measured in a plant. Every value carries a citation in the recorded data sources.

The FEA is linear elastic and quasi-static. The model has no crush, no energy absorption, and no dynamic drop physics. This limit applies to every FEA number on this page.

The headline: the tray as specified does not pass

The frozen design fails two of three FEA load cases. The design also fails the mesh-convergence gate. The pocket swells past its dimensional spec in storage, and every coating scenario fails that spec.

These failures are findings. The project rule is that an expected failure is a finding, and not a bug to engineer away. The design review gives the fix: thicker walls, ribs, and humidity control.

FEA load cases2 of 3 failStacking and drop-corner fail. Side crush passes.

Mesh convergence18.9%Gate is under 5%. FAIL.

Pocket swelling1.92 mmSpec is 1.0 mm. FAIL for all three coatings.

Moisture fluxwax onlyThe wax blend alone clears the flux criterion. PASS.

The engineering problem

A 1.5 kg laptop ships in a corrugated box. EPS foam cushions the laptop today. A molded-fiber tray from recycled pulp can replace the foam and remove the petrochemical material.

But fiber is heavier than foam. Fiber also absorbs moisture, and fiber is harder to hold to a tolerance. The study asks one question, in three parts. The tray measures 385 x 285 x 20 mm. Can that tray hold the laptop in a 240.0 +/- 1.0 mm pocket? Can the tray carry the three design loads? Can the tray keep moisture away for 90 days?

The study evaluates the tray against an EPS foam benchmark. The study uses three methods: a GD&T tolerance stack-up, structural FEA, and a Fickian moisture model. Each method has an acceptance criterion that the plan froze before any analysis ran.

The tray has a volume of 555,279 mm3 and a mass of 222.1 g. Both values come from the parametric CAD model.

Tolerance stack-up

The pocket width is the headline characteristic. Three contributors add variation: the mold cavity, drying shrinkage, and warp. The study reports three methods, and the study never reports only the method that passes.

Method	Result	Spec	Verdict
Worst case	1.360 mm	1.00 mm	FAIL
RSS	0.793 mm	1.00 mm	PASS
Monte Carlo, nonconforming	0.0% of 100,000 draws	0 draws outside	PASS
Monte Carlo, total sigma	0.1984 mm	5.04 sigma to spec	CONTEXT

The three methods disagree, and they disagree by construction.

Worst case assumes that every tolerance stacks adversely at the same time. That assumption is deliberate. Worst case therefore gives the largest number, and worst case fails the spec here.

RSS assumes centred and capable processes at the Cpk 1.33 mapping. RSS predicts the real spread, and RSS passes. Monte Carlo draws 100,000 samples and quantifies the risk directly.

Each method is correct for the question it answers, but the three questions are different. Which method governs the pocket spec is a DFM decision with product design. This page does not make that decision silently.

All three stack-up methods against the 1.0 mm spec line. Only the worst-case bar crosses the line. The Monte Carlo bar shown is the 95th percentile, which is why it sits below the RSS total. RSS reports a spread, and the percentile reports a draw.

The Monte Carlo pocket-width distribution against the spec limits. The whole distribution sits inside the red limits, which is why the nonconforming rate is zero in 100,000 draws. The outer dotted lines mark the worst-case bound, and no draw reaches them.

Ten-tray stack height

Ten trays stack in the shipper. The stack must stay under the 210 mm threshold, because the box needs clearance above the stack.

Quantity	Value	Threshold	Verdict
Mean stack height	197.50 mm		CONTEXT
95th percentile	199.76 mm	210 mm	PASS
P(stack over threshold)	0.0	210 mm	PASS

Ten-tray stack height against the 210 mm threshold. The whole distribution sits far to the left of the red threshold line. The gap between the distribution and the threshold is the margin.

FEA results

CalculiX solves three load cases with second-order tetrahedra. The production mesh has 52,200 elements and 104,601 nodes. A cantilever fixture validates the solver first.

Validation fixture: a cantilever beam under a uniform load. The closed form gives 7.50 mm and CalculiX gives 7.61 mm, which is 1.50% apart against a 2% gate. The fixture passes, so the solver is set up correctly.

Load case	Deflection (mm)	Gate (mm)	Stress (MPa)	Safety factor	Verdict
Stacking, 300 N uniform	6.24	2	17.67	0.226	FAIL
Drop-corner, 150 N on the corner pad	1430.91	n/a	483.76	0.008	FAIL
Side crush, 50 N over a patch	0.73	5	1.39	2.883	PASS

The safety factor gate is 2 for all three load cases. The fiber compressive strength is 4 MPa, from the cited property table. The stress column reports the maximum von Mises stress.

The EPS benchmark

The same three load cases run on EPS foam. The EPS numbers are a stiffness benchmark only, and no acceptance criterion applies to them.

Load case	Fiber deflection (mm)	EPS deflection (mm)	Fiber stress (MPa)	EPS stress (MPa)
Stacking, 300 N uniform	6.24	1763.26	17.67	19.27
Drop-corner, 150 N on the corner pad	1430.91	443979.13	483.76	455.69
Side crush, 50 N over a patch	0.73	204.04	1.39	1.34

The EPS benchmark is also outside linear validity.

Linear elastic EPS deflects 1763 mm under the stacking load. Real EPS does not do this. Real EPS crushes, and crushing is a non-linear response that this model excludes.

So the benchmark shows that fiber is stiffer than foam in a linear comparison. The benchmark does not show that the fiber tray is acceptable, because the fiber tray fails its own gates.

Vertical deflection on the tray top surface under the stacking load. The dark band along the middle of each long wall is the deepest deflection. The corners stay near zero, so the long unsupported wall spans are what deflect.

Vertical deflection under the side-crush load. Read the colour scale before you compare this figure to the stacking figure. This scale spans about 0.3 mm, and the stacking scale spans about 6 mm. The two heatmaps look similar and are two orders apart.

How to read the drop-corner safety factor

A safety factor of 0.008 does not mean that the tray breaks 125 times over.

The arithmetic invites that reading. Divide 1 by the rounded safety factor of 0.008 and you get 125. Divide 1 by the full-precision value and you get 121. A reader can take either number literally, and a reader who does so has been misled.

Here is what the number means. Linear-elastic theory stops being valid long before the tray reaches this load. The model assumes that stress stays proportional to strain, and that the part keeps its shape.

Real molded fiber does not behave that way at this load. The material creases, it crushes, and it absorbs energy as it deforms, but this model contains none of that behaviour.

The computed deflection is 1431 mm. The tray is only 20 mm tall. A deflection far larger than the part itself is the clearest signal that the model has left its valid range.

So read the drop-corner result as a direction, and not as a prediction. The direction is clear: the 3 mm floor is too thin to carry a concentrated corner load. The magnitude is not a physical quantity. A real drop assessment needs a non-linear dynamic model, and this study does not have one.

Mesh convergence

The mesh-convergence gate is not met.

The study runs three uniform meshes at 9 mm, 6 mm, and 3 mm. Between the two finest meshes the deflection changes 18.9%. The gate is a change below 5%, so the gate fails.

This result is reported openly, per change record PC-003. The cause is a budget. The target mesh needed 96,781 elements, and the element budget is 60,000. The study reports the largest converged mesh and states the change, and the study never hides the change.

One consequence follows, and the consequence is important. Every FEA number on this page carries mesh uncertainty. The deflections are the stable quantity, but the deflections are not converged to the 5% gate.

The maximum stress is a separate matter. The load is applied at a point, so the stress there is a singularity. A point singularity does not converge under mesh refinement at all, and no mesh makes that stress converge.

Stacking deflection against uniform mesh size, with the element count on the right axis. The deflection does not settle as the mesh refines. It rises from the 9 mm mesh to the 6 mm mesh, then drops at the 3 mm mesh. A converged result would flatten instead.

Uniform mesh	Elements	Deflection (mm)	Stress (MPa)
9 mm uniform	15,072	6.139	18.02
6 mm uniform	31,928	6.363	16.78
3 mm uniform	134,572	5.163	20.14

Anisotropy sensitivity

Molded fiber is anisotropic. The through-thickness modulus is lower than the in-plane modulus. The study varies the through-thickness modulus across its cited range and records the stacking deflection.

Through-thickness modulus	Deflection (mm)	Stress (MPa)
in-plane / 2	5.89	17.42
in-plane / 3 (nominal)	6.24	17.67
in-plane / 4	6.48	17.77

The deflection band runs from 5.89 mm to 6.48 mm. Every value in the band fails the 2 mm gate, so the anisotropy range does not change the verdict.

Stacking deflection across the cited through-thickness modulus range. The black bar is the nominal case. The three bars span a narrow band, so this uncertainty moves the deflection much less than the mesh does.

Moisture flux through the wall

A Fickian model moves moisture through the 3.0 mm wall for 90 days at 38 C and 90% RH. Coatings act as series resistances. The criterion is a flux at or below 5.0 g per day into the box.

Scenario	Flux (g/day)	Criterion (g/day)	Verdict
Uncoated	200.00	5.0	FAIL
PLA coating, 20 um	7.23	5.0	FAIL
Wax blend	1.98	5.0	PASS

The wax blend clears the moisture-flux criterion. The wax blend is the only scenario that clears it.

Steady-state moisture flux for each coating against the 5 g/day criterion. The uncoated line sits far above the criterion. The PLA and wax lines crowd together near the bottom. Only the wax line falls below the red criterion line.

Pocket swelling

The pocket swells past its spec in all three coating scenarios.

At equilibrium the pocket grows 1.92 mm. The spec allows 1.0 mm. So every scenario fails, and that includes the wax blend.

Here is the engineering point. A coating slows how fast moisture enters the fiber, but a coating does not change where the moisture stops. The storage humidity sets the equilibrium moisture content, and the equilibrium moisture content sets the swelling.

So the coating buys time and nothing else. The uncoated tray fails in 0.8 days. The wax blend delays the same failure to 11.3 days. Storage runs for 90 days, so every scenario reaches equilibrium well inside the storage window.

Two fixes work. Control the storage humidity with desiccant, or change the pocket spec with product design. Cavity pre-compensation to 238.1 mm helps only if the humidity is controlled. One cavity setting cannot serve both humid and dry storage.

Do not read the wax flux PASS as an overall pass.

The wax blend passes one criterion, which is the moisture flux to the product. The wax blend fails the dimensional criterion, exactly as the other two scenarios do. The two criteria are independent, and the wax blend meets one of them.

Scenario	Growth (mm)	Spec (mm)	Days to failure	Verdict
Uncoated	1.92	1.0	0.8	FAIL
PLA coating, 20 um	1.92	1.0	3.8	FAIL
Wax blend	1.90	1.0	11.3	FAIL

Tray moisture content against storage time. All three curves climb to the same equilibrium at the top. The coating changes how fast each curve rises, and the coating does not change where any curve ends. Each curve crosses the red growth limit within days.

Recommendations

These recommendations come from the design review. Each recommendation follows from a number above, and not from the plan.

Thicken the structure. The wall and the floor are 3 mm. That is too thin for the stacking load and the drop load. Increase the thickness to 4 mm or 5 mm, or add ribs under the corner pads and across the floor.
Re-run the analysis after the change. A thickness change alters the geometry, so the mesh changes too. Re-run the stacking case and the drop-corner case, and revisit the mesh convergence with the new geometry.
Bind the pocket spec to storage humidity. Keep the pocket spec, but tie the spec to a controlled storage condition. The pre-compensation target of 238.1 mm works only under humidity control.
Choose the wax blend if flux governs. The wax blend is the only coating that meets the flux criterion. The wax blend still does not fix the swelling.
State the mass cost. Fiber is denser than EPS foam by a factor of about 25. That ratio is a density ratio, and the ratio does not change with the design.

Verification

Three independent checks cover this work. Each check runs from the committed sources.

Test suite. 38 tests pass. The tests cover the geometry, the property table, the stack-up engine, the FEA parsing, and the permeation solver.
Self-re-derivation. A separate pass re-derives 30 headline numbers from the raw outputs. The pass confirms every number against the machine-readable results file.
Plan-consistency audit. A recorded audit checks the plan documents against each other. All 51 of 51 checks pass. This audit checks the plan text, and the self-re-derivation checks the executed results.

Each numerical engine also has a published reference. The stack-up engine matches a published worked example. The FEA matches a closed-form cantilever within 1.50%. The permeation solver matches the analytic slab series within 1%.

Toolchain pinned in the project record: CalculiX 2.23, gmsh 4.15.2, FreeCAD 1.1.3, Python 3.14.5. Monte Carlo work uses a fixed seed, so the draws reproduce exactly.

Limitations

These limits shape every number on this page. They are stated here, and not in a footer.

Literature properties. Every material property comes from published literature or a standard. None of the properties is measured on this tray or in a plant. The cited ranges are wide, and the study uses the nominal values for the headline numbers.
Linear-elastic quasi-static FEA. The model has no crush and no energy absorption. The model has no dynamic drop physics either. The drop-corner case is the clearest place where this limit bites, and the interpretation note above explains it.
The mesh gate is unmet. The deflection changes 18.9% between the two finest meshes, against a 5% gate. So every FEA number carries mesh uncertainty.
One-dimensional stack-ups. The stack-ups are one-dimensional, as the frozen plan requires. Real parts vary in more than one direction.
One-dimensional moisture transport. The moisture model moves water through a flat slab in one direction. The model uses the first mode of the analytic series, so the early transient is approximate.
Coatings were never applied. The coating data is a set of published typical ranges. The study applied no coating to a physical tray, and the study measured no coating.
Lifecycle impact is out of scope. The study compares fiber and foam on structure, dimensions, and moisture. The study does not compare the two materials on lifecycle impact.
The drying-shrinkage input is an assumption. The shrinkage contributor comes from the frozen plan, and no molding campaign measured it.