Why a knit recovers and a woven does not

Pull a T-shirt sideways and it goes half as wide again and comes back. Pull a shirt sideways and almost nothing happens; pull hard enough for something to happen and it does not come back. Both are cotton, both are the same fibre and often the same yarn, and neither of them has any elastic in it.

The whole of that difference is structural, and it can be computed rather than asserted.

Four mechanisms #

Set them out, because the site has arrived at each of them separately and they belong on one page.

Crimp interchange. A woven thread is longer than the cloth it crosses, because it goes over and under rather than straight. Pull the cloth warpwise and the warp straightens, taking up its crimp; the cloth gets longer. Nothing stretches, and the extension available is exactly the warp crimp — a few per cent.

Bias shear. A woven cloth is a pin-jointed net, and a net has a degree of freedom nothing to do with material stiffness: the cells can change from squares to rhombuses while every side keeps its length. Pull on the diagonal and the trellis closes. The extension available along the diagonal is large — a third or more, against a few per cent along the threads — and it is limited by the angle at which the threads jam.

Rib unfolding. A ribbed knit is a plain knit folded, and the fold can be opened. The extension available is the secant of the fold angle, and at a normal fold that is around a hundred per cent.

Loop reconfiguration. A knitted loop is a closed curve of thread with a shape rather than a length. Pull the fabric and the loops become taller and narrower, or shorter and wider, and the yarn in them is redistributed without any of it changing length. This is the mechanism that operates in every knit, ribbed or not, and it is the largest of the four.

Where the extension stops #

The interesting question is not how much each mechanism gives but what happens at the end of it, because that is what decides recovery.

Crimp interchange stops when the crimp runs out. The warp is straight; there is nothing left to take up. Past that point any further extension is yarn extension, and a cotton yarn breaks at a few per cent — so a woven cloth pulled past its crimp goes suddenly, unforgivingly stiff and then fails.

Bias shear stops at the locking angle, where the threads jam against their neighbours and the trellis has no travel left. That limit is set by the sett: a densely set cloth locks at a small shear, an open one at a large.

Rib unfolding stops when the fabric is flat. The fold has been taken out, the section is planar, and the mechanism is exhausted.

Loop reconfiguration stops much later and less abruptly, because a loop has a great deal of shape available before its thread is straight. That is the reason a knit’s stress-strain curve is so long and so soft compared with a woven one’s.

Recovery is a different question #

Now the point of the essay, which is that extension and recovery are two questions and only the first of them is structural.

Every mechanism above is kinematic. A shape changed; nothing was strained. So in principle every one of them is completely reversible: put the shape back and the fabric is as it was.

In practice they are not equally reversible, and the reason is friction at the crossings.

A woven cloth’s crimp interchange is fought by friction between warp and weft at every intersection — and a woven cloth has a great many intersections, because that is what interlacing count means. The threads have to slide past one another for the crimp to move, and they resist, and when the load is removed the same friction holds them where they are. So a woven cloth extended by crimp interchange comes back slowly and incompletely: it has a permanent set, and it is why a shirt collar goes out of shape.

A knitted fabric’s loops slide against far fewer neighbours and are held far less tightly, so the reconfiguration is much freer. The loops return because the yarn’s own bending stiffness wants them to, and there is little to stop them.

Bias shear sits between the two, and it is friction-limited in an interesting way: a bias-cut garment recovers well while it is loose and sets permanently once it has been pressed, because pressing is exactly the operation that makes the threads stay where they were put.

The measurement that separates them #

The four mechanisms give numbers that differ by a factor of twenty-eight, and the numbers come from four different geometries rather than from one theory.

Crimp interchange gives whatever the warp crimp is — eight per cent in an ordinary cotton plain weave, and it is measured by unravelling the cloth and straightening a thread.

Bias shear gives thirty-eight per cent along the diagonal before locking in an openly set cloth, and twenty-seven in a dense one, computed from the trellis geometry and the angle at which the threads jam.

Rib unfolding gives around a hundred per cent, computed from the fold angle.

Loop reconfiguration gives more still, and it is the one the arithmetic here does not attempt: computing it needs a loop model with bending stiffness in it, and this site does not have one. What is quoted for it in the figure is the rib figure, which is a lower bound on the knitted case rather than an estimate of it — and saying so is more useful than producing a number nobody could check.

The bias has a ceiling, and the trade’s number is above it #

The second of those deserves its own section, because the figure at the top of this essay printed a different number until the geometry was asked directly.

The trade’s version is “half as long again”, and the trellis cannot give a half at any shear whatever. The cell is a rhombus of side $p$ with included angle $\theta$, so its long diagonal is $2p\cos(\theta/2)$ against $p\sqrt2$ unsheared, and the extension along it is $\sqrt2\cos(45° - \gamma/2) - 1$. That expression is largest when the cosine is one, which is $\gamma = 90°$ — a net closed flat, every cell collapsed onto a line — and its value there is $\sqrt2 - 1$, or 41.4 per cent. Fifty is not an optimistic reading of the mechanism; it is outside it. The ceiling is a property of squares, and no yarn, sett or finish moves it.

Real cloth stops a long way short of even that. The threads meet first, and where they meet is set by the cover: a cloth open enough to jam at sixty-six degrees reaches thirty-eight per cent and is already unusually loose, while a dense one locks at thirty-seven degrees with twenty-seven. So there are two limits stacked — an absolute one from the geometry of a square, a practical one from the diameter of the yarn — and the slogan clears both.

The failure is worth naming because it is not an arithmetic slip. The slogan quotes the mechanism and forgets the stop, which is the same shape as quoting a thread count without a weave or a maximum sett without a yarn: a quantity lifted out of the constraint that gives it a value. It survived here for the reason such numbers usually survive, which is that it sounds like a measurement, and it sat in a bar chart whose other three rows were computed from their own geometry while this one was typed in.

Why a woven cloth is not simply worse #

It would be easy to read all of this as a list of the knit’s advantages, and that is not what it says.

A woven cloth’s small extension is a feature for most of what woven cloth is used for. A shirt that stretched a hundred per cent would not hold its shape; a sail that stretched would spill wind; a webbing strap that stretched would be dangerous. The whole point of a woven structure is dimensional stability, and stability means precisely that the mechanisms are absent or small.

And the woven cloth has one mechanism the knit does not, which is the bias — available in one direction only, worth a great deal, and exploited by every dressmaker who cuts a panel at forty-five degrees so that it will follow a body it does not fit.

The knitted structure trades stability for conformity. That trade is the reason knitted fabric took over underwear and hosiery a century before it took over outerwear: the places where a fabric has to follow a shape are the places where the trade is worth making.

The one number this site will not compute #

An admission, because the figure at the top of this page has a bar in it that is a bound rather than a measurement.

Loop reconfiguration is the mechanism that gives a knit most of its extension, and computing how much it is worth needs something this site does not have: a model of a knitted loop with bending stiffness in it. The loop’s shape under load is a mechanical equilibrium, not a geometric construction, and every attempt to write one down involves a yarn’s flexural rigidity, the friction where loops bear on one another, and the tension the fabric was knitted at.

So what is quoted for it is the rib figure — the extension a folded section supplies — which the knitted mechanism certainly exceeds and by an amount that is not established here. A lower bound stated as a lower bound is worth more than an estimate nobody could check, and the alternative would be a number produced by choosing constants until it looked right.

That is the honest boundary of the whole comparison. Three of the four mechanisms are geometry and are computed; the fourth is mechanics and is bounded.

The fibre’s half of the answer #

Everything so far is structure, and structure supplies the extension. Recovery has a second half that structure cannot supply at all, and it is worth setting out because it is where most of the practical difference between two identical-looking fabrics lives.

A yarn strained and released returns in three parts. Some of the strain is elastic and comes back at once. Some is delayed elastic and comes back over minutes or hours. Some is plastic and does not come back at all. The proportions are a fibre property and they vary enormously.

Wool is the extreme good case. A wool fibre is a helical protein structure that can be extended a long way and returns almost completely, which is why a wool garment recovers from being sat on and why steaming restores it. Silk is good; nylon is good; polyester is good in the short term and creeps.

Cotton is the extreme bad case among common fibres. A cotton fibre is largely crystalline cellulose with very little available elastic strain, so almost everything past a per cent or two is permanent. That is why a cotton rib grows, a cotton T-shirt’s neck goes slack, and a pair of cotton jeans becomes a different size by the end of the day and returns after washing — the washing is not shrinking the fabric so much as letting the structure return to a shape the fibre would not bring it back to on its own.

The consequence for this essay’s framing is sharp. The mechanisms are all reversible in principle. The fibre decides whether the fabric actually goes back, and a structure with an enormous extension available in a fibre with no recovery is a structure that will end up permanently the wrong size. That is precisely the case of the cotton rib, and it is why elastane exists — not to provide extension, which the geometry already supplies in abundance, but to supply a restoring force the cotton does not have.

Two more mechanisms this site has met #

Completeness, because the list of four is not the whole list.

Thread extension is the obvious one and the one everything above is defined against: yarn actually getting longer. A few per cent in cotton, more in wool, a great deal in elastane. Every fabric has it, and it is the last mechanism to engage in almost every case, which is why fabrics feel soft and then suddenly stiff.

Structural jamming release is the odd one out. A cloth that has been compressed — beaten up hard on the loom, or fulled in finishing — can extend by the threads simply moving apart, without any crimp exchange or shear. It is small, it is entirely irreversible, and it is the reason a new cloth’s first wash changes its dimensions more than any subsequent one.

Neither of those is a mechanism in the sense the other four are, because neither is a shape with a computable travel. They are included here so that a reader adding up the four bars and comparing them with a real fabric’s stress-strain curve is not surprised by the difference.

What the comparison leaves out #

Three things, and the third undermines the whole framing in a way worth admitting.

Time. Every number here is a limit, not a behaviour. How fast a fabric extends and how fast it returns are viscoelastic questions, and a fabric that recovers fully in an hour behaves quite differently from one that recovers fully in a second.

Load. Nothing here says how hard any of these mechanisms is to operate. A bias-cut cloth shears under its own weight; a crimped one does not extend measurably until it is pulled hard. The extension available and the force needed are independent, and only the first is geometric.

And the mechanisms are not exclusive. A real knitted fabric pulled sideways is unfolding its ribs, reconfiguring its loops, and extending its yarn, all at once and in a proportion that changes with the load. Treating them as four separate mechanisms with four separate limits is a useful decomposition and it is not what the fabric is doing.

How the difference is actually measured #

The laboratory version of this essay is a cyclic test, and its shape is worth knowing because it separates the two questions cleanly.

A specimen is extended to a fixed strain, held, released, and left for a stated recovery time; then the process is repeated. Three numbers come out. The extension at a given load is how far it went. The immediate recovery is how much came back at once. The delayed recovery is how much came back after the rest period, and what is left is the permanent set.

Run it on a woven and on a knitted fabric of the same fibre and the pattern is exactly what the mechanisms predict. The woven extends very little and recovers most of that little; the knit extends enormously and recovers nearly all of it. And run it repeatedly, which is the test that matters for a garment, and the knit accumulates set slowly while the woven, which had little to give, reaches its limit and stops changing.

The interesting failure of the framing shows up in the second cycle. A fabric extended once and released does not return to where it started, and the second extension is easier than the first — the structure has been rearranged and some of the friction has been overcome. That is why textile testing standards specify a conditioning cycle before the measured one, and it is a reminder that the mechanisms in this essay are described as though they were reversible and are only nearly so.

One sentence that summarises it #

Everything above compresses into a statement worth keeping.

Extension is geometry; recovery is material.

The four mechanisms are shapes with travel in them, and how much travel each has can be computed from the structure with no reference to what the fabric is made of. Whether the shape comes back is decided by the yarn’s own elasticity and by the friction at the crossings, and neither of those is in any structure at all.

That is why two fabrics with identical constructions in different fibres behave completely differently after a month, and why a designer choosing a structure and a designer choosing a fibre are solving two problems that look like one.

Where the ladder goes next #

This is the top of the knits ladder as it stands. Below it are rib and interlock, where the folding mechanism is built; why stockinette curls, which is the same asymmetry seen at an edge; and the loop at the base.

Across the fields, the two mechanisms it has been comparing against have their own ladders: crimp and interchange in setting, and the bias in mechanics. All three ladders are about the same idea — that a fabric’s most striking mechanical behaviour is usually a shape changing rather than a material yielding — and they arrive at it from three different structures.