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.
Pull-wire lumens are meshed as voids in the wall, which is how they weaken it. Tendon tension, actuated pre-curve, and pull-wire stiffness contributions are not included: the section is bent as delivered, before any deflection is commanded.
A lumen liner is meshed as its own ring of tiles around the void. A polymer liner is its material; a closed-coil liner is a metal ring in the section plane (each turn is a wire hoop) and a helical spring along the axis, with any polymer jacket as a second ring outside it. A coil-lined lumen therefore holds its shape while the wall around it ovalizes, which is what you see in the deformed cross-section.
Section
- Section: Which cross-section to bend, listed by position and label so the numbers match the color bar. Sections with nothing to mesh are left out: the Pullring, a manual-stiffness section (no layup), and a multi-lumen core defined by manual section properties (no outline).
- 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 color 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. Stop ends the sequence at 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.
- Stop ends the run and shows the bends solved so far, marked as a stopped run; the inputs are left 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
Kink is the headline: the largest mandrel this section can be wrapped on before it kinks, with the centerline radius and the event that got there first underneath it: the collapse onset (the section stops resisting the bend and starts to flatten) or 50 % lumen loss (the ISO kink). It is the same number the Catheter Analysis tab and a Design Sweep report for this section. When the run stops before the kink but the moment curve has flattened enough to place it, the headline gives that estimate, marked (est.). Not reached means the section was still holding its shape where the run stopped and the curve had not flattened enough to estimate the kink: it kinks at a tighter bend than the model could follow. None reached means no kink down to the tightest bend solved. Each layer's permanent set is listed below the headline rather than in it: it usually starts at a gentler bend than the kink, and for some materials the limit behind it is estimated.
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
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Deformed cross-section: The section at the selected step, each layer in its Catheter Setup color, 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 permanent-set rows name the layer that goes first and at what bend.
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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 color, 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 gray 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.
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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 centered on the first event, usually the first permanent set, with what leads up to it on the left and what follows on the right, and it never opens past the collapse onset: on a thin wall the moment peak sits well gentler than the first permanent set, so the window widens until the rise to the peak is in view. 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 takes a set gets a dashed line in its own color on the moment plot. Only the first to fail is labeled; 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 event turns out to be. The cross-section and bend illustration carry the live feedback meanwhile.
The events
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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 ("The simulation stopped before reaching collapse onset.") rather than naming the stop radius as the onset. Any collapse this section has lies at a tighter bend than the model could follow: the Kink headline reads Not reached, and the permanent-set rows still say where the section starts to take a set. Once the moment curve has flattened to 60 % of its initial slope, the row also gives an estimate of the collapse ("From the moment curve it is estimated at a 7.1 mm mandrel."), from Brazier's form fitted to the last solved points: on the bundled sections that do reach a collapse it lands within 5 % (median) and 16 % (worst) of the computed onset, in curvature. It assumes a smooth collapse and can read low on a section that folds locally beside its lumens. The opposite miss, a moment already falling at the first solved bend, is reported the same way ("not resolved, already softening at the first solved bend"): the peak is at or gentler than where the ramp started. Catheter Analysis and Design Sweep report both cases as blank.
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Cross-section extents: All four extents, paired by color: the OD pair in one color, the ID pair in the other. In each pair the solid line is the one that carries the story (OD major, how far the section spreads across the bend; ID minor, how far the bore shuts in the bend plane) and the dashed line is its mirror image across the other axis. The gap between a color's two lines is that circle's ovalization. Lumen area runs on the right axis. A multi-lumen core plots only the OD pair: it has no single round bore, so an ID extent or lumen area there would describe the wall's inner face against the core rather than a lumen anybody has.
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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.
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Permanent set (by layer): Where each layer reaches the strain past which it stays deformed: a lasting set, not the small residual most polymers show at gentler bends and recover from with time. Each limit comes from the material's published or derived data; elastomers keep a stiffness-based estimate until they are measured. Hover a layer's row to see which:
- published: the material's own set-onset strain (Nitinol 6 %), or for a metal its 0.2 % yield strength divided by its modulus.
- derived: a polymer with a published yield strength. A yield published as a 0.2 % offset or a proportional limit is used as it is, yield strength over modulus. A yield published as the stress maximum sets the limit at the yield strain for semicrystalline polymers and PEBA, such as PE, PA11, PA12 and Pebax 5533 to 7433 (Pebax 7233: 18 %), and at 0.7 of it for glassy polymers such as PEEK, PET, polyimide and clear polyamides, and for any other polymer. PTFE and FEP layers, liners included, use yield strength over modulus (a Sub-Lite-Wall liner: 7 %). A brittle material, such as glass-filled PTFE, is limited where it fractures, marked fractures (no plastic reserve).
- estimated (stiffness law): elastomers (TPU, silicone, PVC, Pebax 4533 and softer) and the few polymers with no published yield. Their limit is estimated from stiffness and two observed kinks.
On a braided or reinforced shaft the section often collapses before any layer reaches its lasting set. Treat the result as a guide rather than a number to design a margin against. A layer that does not take a set reports how close it came, as a fraction of its own limit. A fibre layer reads fibre: no permanent set (kink bands only), a layer too soft for the stiffness law reads too soft to place one, and a material with no published limit says so. Braid and coil bands are not listed unless the band is the first to go, in which case it appears as "(matrix)": their limit is the matrix polymer's, and the wires' own set is not checked.
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Braid or coil wires lifting out of the wall is not a result row. When the model rates it likely, a note under About this run says so: it is a three-dimensional effect this cross-section model can only flag.
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 when the bore walls close onto each other, or if a wall passes through another (the bore folding into the outer wall). The shape past that point is not one the model 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 simulated 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 simulated" 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. Steer a section past a limit and its Bend Radius row turns orange (permanent set) or red (collapse, lumen closure or self-intersection) until you straighten it.
- Pushability: the tightest bend each section reaches in the push, beside the limit it has to clear.
- Reports: the record. Every section, its simulated 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 ovalized 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.
Occasionally the solver stops while the section is still round and still stiffening. That is a limit of the model, not a collapse: the snap row reads "Not reached", the collapse onset row says the simulation stopped before reaching it, and it is never reported as a snap or a kink. Sections with pull-wire lumens run through the local folds beside their lumens to the collapse. A braid band in a soft matrix is stiffened through its thickness in this simulation (to at least 1/15 of its stiffness around the tube, its ring stiffness unchanged) so that the solver can follow it where it is squeezed beside a lumen; the run notes say when that applies.
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
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 fiber) 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. A thin wall collapses at a gentler bend than a thick one (Brazier's estimate scales as radius² / wall), so for a wall thinner than about 5 % of its OD the ramp starts gentler still, at four times that estimate, and takes smaller steps so that at least four land before the expected peak. On the bundled examples this changes nothing; on a thin-walled 28 Fr it is the difference between resolving the moment peak and reporting a collapse the first step had already passed. The mesh is at least 96 elements around with three rings through every layer, and at least 192 around on a section with pull-wire lumens (a deliberate balance: a finer mesh moves the collapse onset of those sections by up to 10 % but takes two to five times as long). A run takes roughly a minute a section without lumens and one to two minutes with them, and bends one orientation with no guidewire in the bore. One number the mesh cannot pin down is a snap-through radius, which is quantized 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 fiber 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 localization 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 permanent-set rows report where a material reaches its permanent-set strain, but the wall is not modeled as yielding afterwards. Thick-walled designs, which take a set 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 generalization, 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.