Kink Radius

The Kink Radius tab answers the question a single kink radius cannot: what actually happens to this cross-section as the bend tightens, and which event comes first? One section is bent to a progressively tighter centerline radius and solved as a 2D finite-element cross-section at every step, so the ovalization, the collapse point, the lumen loss and the strain in each layer all come out of the real layup rather than a formula.

The tool is the Kink Radius tab, reachable from the tab bar or from Tools → Kink Radius. It requires a built model (the layer stack, materials and reinforcement it meshes come from those analysis results), and until there is one the tab shows a short "build the model first" state. The undeformed cross-section is drawn as soon as you open the tab and redraws as you change inputs.

When a run finishes, its headline events (first failure, collapse onset, 50 % lumen loss) are also written to that section's row on the Catheter Analysis tab, so the numbers sit alongside the rest of the section's properties.

Pullwires are geometric holes only

Pull-wire lumens are meshed as voids in the wall, which is how they weaken it. Tendon tension, actuated pre-curve, and pullwire stiffness contributions are not included: the section is bent as delivered, before any deflection is commanded.

Section

• Section: Which cross-section to bend. Every section is listed in order with its length and layer count, so the picker stays usable when several sections share a label. Sections the model cannot mesh remain in the list, greyed out with the reason: a manual-stiffness section has no layup, and a multi-lumen core defined by manual section properties has no outline to mesh.
• Section orientation: Rotates the cross-section in 90° steps before it is bent. 0° is the section as the setup wizard draws it: a single pull-wire lumen at the top, two left/right, four on the cross. The bend plane stays vertical, so this is how you put a lumen on the intrados, the extrados or the flank; 180° puts a single lumen on the intrados. On an asymmetric section this changes the answer, and it is the one thing no closed-form kink radius can see. A run bends the one orientation selected; to solve several at once, and to sweep them against a design variable, use the Design Sweep.

The layup index beside the plot lists every layer inner to outer (pull-wire liners and the core included) with its colour and thickness, the resolved OD and ID, and the pull-wire lumen count.

Mandrels and radii

The model bends to a centerline radius, so every radius on this page is measured to the catheter centerline. Nobody wraps a shaft around a radius, though, so each result also carries the mandrel diameter that produces it (mandrel = 2R − OD), and that is the number the page leads with.

The two are not interchangeable. The mandrel depends on the OD, so two designs of different diameter that kink at the same radius report different mandrels, and the mandrel collapses to zero at R = OD/2. Compare constructions on the centerline radius; take a pin off the shelf by the mandrel.

Running

• Run Section: Solves the ramp for the selected section, drawing each curvature increment as it lands. The progress bar covers the refinement pass too.
• Run All Sections: Runs every section that has no result yet and skips those that do, so pressing it after a single re-run fills only the gaps. Finished runs are kept, so the section picker then flips between them without re-solving. Cancel stops after the section it is on, and changing any input drops every result, since they were solved with it. Use Run Section to force a re-run of the one you are looking at.

While it runs

This is a tab, not a dialog, so a run does not tie up the application:

• Start it and walk away. Switch to another tab and the run keeps going. A dot on this tab pulses while it works and turns solid when it finishes, and the status bar posts a short note.
• Cancel stops the run cleanly and leaves the inputs as they were.
• Rebuilding the model clears every run, puts the page back to fresh, and cancels a run in flight. The results describe a cross-section that no longer exists, and leaving them on screen, one picker click from looking current, is worse than an empty card. The same rebuild clears the simulated rows on Catheter Analysis. Changing any input here does the same thing, for the same reason.
• Add the results to a report by ticking this tool's block in Report → Generate Report.... See Reports.

Reading the results

First failure is the headline: the largest mandrel this section can be wrapped on before it takes permanent damage, with the centerline radius and the mode that got there first (50 % lumen loss, or the first layer to crease) underneath it. It is the same number the Catheter Analysis tab and a Design Sweep report for this section, so the three can never disagree. None reached means nothing permanent happened down to the tightest bend solved.

A different Section orientation is a different load case and gives a different number. You are not left to remember which one you ran: any figure measured at other than the default orientation says so, in the Analysis row's tooltip and alongside the limit this run publishes to the rest of the app. At the default orientation nothing is flagged, because there is nothing to flag.

The views

• Deformed cross-section: The section at the selected step, each layer in its Catheter Setup colour, with pull-wire lumens as gaps and the compression side marked. On a multi-lumen core the core is drawn too, so you see the webs and septa deform with the wall. Scrub the Bend step slider, or use Play / Stop (with Loop) to animate. The last frame is the last bend actually solved.

  Per-layer strain is reported as numbers rather than a heat map: every layer's peak strain and how close it came to its own limit are on the results card and in the report's ramp sheet, and the crease rows name the layer that goes first and at what bend.

• Bend illustration: Beside the cross-section, the catheter drawn as a thick line at the step's bend, to scale against its own OD and in its outer layer's colour, captioned with the mandrel that bend wraps. When the bend is tight enough for the pin to fit the picture, that mandrel is drawn in as a grey circle tangent to the inner surface. It thins toward the apex by the solved flattening while the straight legs stay round, so a gentle bend reads as nearly straight and a kink as a hairpin: the picture the number alone does not give you.

• Curve plots: Both run left to right from a gentle bend to a tight one, against the mandrel diameter that bend wraps. The default view is centred on the first failure, with what leads up to it on the left and what follows on the right. That is deliberate: the ramp samples evenly in curvature, so on an evenly spaced mandrel axis the whole run piles into the tight end, with most of the solved steps and every event landing in the last tenth of the range. Nothing is discarded, so drag or scroll to see the gentle end.

  Every layer that creased gets a dashed line in its own colour on the moment plot. Only the first to fail is labelled; hover any other to name it and give its mandrel and radius. The plots stay empty while a run is in flight and arrive complete when it lands, because their window depends on where the first failure turns out to be. The cross-section and bend illustration carry the live feedback meanwhile.

The events

• Collapse onset: Where the moment-curvature curve peaks: the bend at which the section stops getting harder to bend and starts getting easier. Past it, less moment bends it further, which is what makes a kink run away once it starts. It is a criterion, not a mechanism: on a round tube it is classical Brazier collapse, the bore flattening until the wall loses its lever arm; on a multi-lumen core it is the same peak, but what softens the section is whatever gives first, the webs folding, a lumen flattening, the wall ovalizing around them. Scrub to that step to see which. Nothing has yielded at the onset itself, but bending past it concentrates the bend into a fold that may damage the section.

  If the moment was still rising where the ramp stopped, there is no peak and the tool says so ("not reached, still stiffening where the model stopped") rather than naming the stop radius as the onset. Any peak this section has lies at a tighter bend than the model could follow. Catheter Analysis and Design Sweep report that case as blank.

• Cross-section extents: OD major (how far the section spreads across the bend) and, on a round design, ID minor (how far the bore shuts in the bend plane), with lumen area on the right axis. A multi-lumen core plots only the OD major: it has no single round bore, so an ID minor or lumen area there would describe the wall's inner face against the core rather than a lumen anybody has.

• 50 % lumen loss: Where the lumen area falls to half, the kink definition used by ISO 25539-2 and EN 13868. It is typically a much tighter radius than the collapse onset: on a braided shaft the two can differ by 2×, which is precisely why one number cannot describe a kink.

• First crease (polymer layers): Where each polymer layer first reaches its crease strain, the onset of a visible crease. The strain is anchored on observed kinks rather than a coupon yield point, so it marks visible creasing rather than the gentler, invisible permanent set that comes first. That earlier set is not modelled: placing it would need a bend-strain-at-yield anchor per material that the library does not carry. A layer that does not crease reports how close it came, as a fraction of its own limit. Layers too soft for the model to place a limit on are named as such: a kink is not ruled out for them, it simply cannot be predicted this way. Braid and coil bands are not listed, since the crease limit they carry is their matrix polymer's, which the layers either side already report, unless the band is the first to go, in which case it appears as "(matrix)".

• Reinforcement wire buckling: A risk, never a prediction: Likely, Possible or Unlikely, with the bend it would start at when the model says likely. Braid or coil wires on the inside of a bend are squeezed along their own length and held only by the polymer around them; past a point they snake sideways out of the wall, which shows up on a bench as a wire standing proud, a bulge, or the braid opening, not as a lumen kink. That buckle is a wave running along the catheter, which a cross-section model cannot solve, so the tool measures how hard the wires are being squeezed and compares that with the load that triggers it. The trigger depends on how stiffly the polymer supports the wire, which published derivations put 2–3× apart, so treat the bend it names as something to check on a bench.

Housekeeping

• Solve time is how long the ramp took, and nothing else.
• about this run folds away the run's caveats, and only things you have to act on are in there: why the ramp stopped and what that means for the events it did not reach, a lumen that is absent and why, a reinforcement layer the model could not build (so the section reads softer than it is), a section EI that could not be reconciled with the analysis, the mesh the run used, and the self-overlap check being off. Solver bookkeeping goes to the log instead.
• Changing any input after a run clears the results. If the ramp stops before the end radius, a note says so: past that point the section deforms faster than an elastic model can follow, and events not listed may still occur at tighter radii.
• A run also stops if the walls pass through each other, the bore folding onto itself or into the outer wall. The model has no self-contact, so the shape past that point is not one it can hold. The note names the surfaces, and any event that would have landed at or inside that radius is reported as not reached rather than as a number. This is not the same as the lumen closing, which is an event the ramp is meant to reach and which fires earlier, at 5 % of the original ID.

Where these limits go

A finished run does not stay on this tab. Each section's measured bend limits become the capacity the rest of the app compares its demands against, so running a section here is what turns a bend radius elsewhere from a number into a verdict.

Run All Sections is the button that matters. Every consumer of these results wants every section: a section you never ran has no limits, and the other tabs say "not measured" rather than staying quiet, because silence would read as a pass. Run Section is still there for a single deep dive.

Where they surface:

• Steering Simulation: a note above the readouts while any section is unmeasured, and a live warning if you steer a section past a limit.
• Pushability: the tightest bend each section reaches in the push, beside the limit it has to clear.
• Reports: the record. Every section, its measured limits, and the tightest bend it actually reached.

How a section ends

Bent tighter and tighter, a section can finish three ways, and which one it does is as useful as the radius:

Outcome	What happened
Collapse	The moment peaked (the limit point that leads to Brazier collapse), or the section snapped. The deal-breaker.
Lumen closure	No peak, no snap: the bore just ovalised until its walls were almost touching. Common in soft sections with a thick wall, and a real answer: this section does not kink, it closes.
Self-intersection	The bore or a core's channels deformed far enough to pass through each other. Nothing past that radius is physical, but the radius itself is a genuine endpoint.

A fourth reading, not determined, means the ramp ended before any of the above: the only one that means "we did not measure it", and it is reported differently on purpose.

Where a section snapped without ever showing a moment peak, the snap becomes the collapse onset, and the app says where the number came from. A peak, when there is one, always wins: it is the earlier event and it converges an order of magnitude better.

Severity, and why it is ordered this way

Warnings escalate permanent set → lumen closure → self-intersection → collapse. That is an engineering judgement, not an alphabetical one: an engineer may knowingly accept some permanent set in a single-use device, a closed lumen stops it working, and an aggressive kink is a deal-breaker.

Wire micro-buckling is deliberately not part of that ladder. It is a three-dimensional mode this 2D model cannot carry, and its trigger load is only known to within 2–3×, so it stays on this tab as information rather than driving a warning elsewhere.

Exporting

This tool has no export buttons of its own. Tick its block in Report → Generate Report... and the report carries the run: inputs and events side by side, the cross-section at the collapse onset and at the end of the ramp, and the moment and geometry curves. Choosing Excel also writes the full bend ramp as its own sheet, one row per curvature step, with centerline radius and equivalent mandrel diameter, moment, OD and ID major/minor, lumen area, and per-layer strains.

A few columns that would come from an element-by-element strain map (max_strain_utilisation and the ..._area_pct_past_strain_limit family) are left empty rather than zero: they are not computed, and "not computed" must not read as "nothing over the limit". The per-layer strain columns beside them are real and filled. See Reports.

Model notes and limits

What the tool sets for you

There is nothing to tune before a run. The section is bent in uniform curvature steps, starting at a mandrel 100 × its OD (about 1 % strain at the outer fibre) and tightening until it fails or folds double: twenty steps, plus five more inside every bracket where an event lands, so the reported radii are independent of the step count. The mesh is at least 96 elements around with three rings through every layer, refined around each pull-wire lumen. A run takes roughly a minute a section, and bends one orientation with no guidewire in the bore. One number the mesh cannot pin down is a snap-through radius, which is quantised by the ramp rather than resolved by the mesh: read it as about here.

The cross-section is meshed with quadratic elements (one band per layer in the wall, ring elements around every lumen, quadratic triangles inside a multi-lumen core) and bent under the tube-bending kinematics used for this problem in the literature: plane sections stay plane, and the axial fibre strain follows the deformed position of the wall. That last point is the physics: as the section flattens, its own axial stresses pull the wall toward the neutral axis, which is what produces the collapse. Polymer layers are isotropic and follow a finite-strain (neo-Hookean) law, so the wall stays well-behaved at the 20–30 % strains a thick section reaches near its fold; braid and coil layers are smeared from the same plies the Catheter Analysis stiffness is built from.

• 2D: the model is one cross-section. The fold itself, the localisation along the catheter, and wire buckling are all three-dimensional and out of scope: the tool stops at the collapse and flags what it cannot solve.
• Elastic: the crease events report where a material reaches its permanent-set strain, but the wall is not modelled as yielding afterwards. Thick-walled designs, which crease long before they ovalize, are where this matters most.
• Reinforcement is smeared, so the wall is treated as a continuous orthotropic layer rather than discrete wires. The hoop stiffness of a braid is the least anchored input in the model.
• A multi-lumen core is one isotropic polymer with its lumens as voids, bonded to the wall. The extrusion does not collapse the way a hollow tube does, so for core designs the useful outputs are the per-layer crease results and the cross-section view of the webs and septa deforming, rather than the lumen-loss events, which track the bore at the wall.

The literature the model reproduces (the classical thin-tube limit point, its orthotropic generalisation, and the strain-limited-to-collapse-limited crossover seen in industrial pipe and tubing bend tables) is documented on the Model Accuracy page, on its terms: relative comparisons between designs and bend directions are the reliable use.

Related pages

• Catheter Setup Tab: where the sections, layers, and materials being bent are defined.
• Catheter Analysis: the per-section stiffness this tool's EI is checked against, and where its headline events are published.
• Design Sweep: runs this model across a design space, and across more than one bend direction at a time.
• Pushability: the companion tool for the axial direction.
• Model Accuracy: how far to trust the underlying predictions.