Textile Structure
how cloth is put together
Concept

Poisson's ratio — where it appears

The ratio of the contraction across a sheet to the extension along it. For a woven cloth it is the slope of the constant-thread-length locus rather than a material constant, so it varies along the curve and is not the reciprocal of itself measured the other way round.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A ratio that will not hold still. The exchange rate between the two directions for 4 cloths, against how far each has been extended along the warp. Every curve is above one half everywhere it is drawn, and every curve rises — so a single number for a cloth's ratio has to name the state it was read at, which a material's ratio does not.

A cloth's Poisson ratio is not a material's

The ratio of a cloth's contraction to its extension has a name everywhere else in mechanics, and it breaks every rule the name comes with — above one half on all eight cloths measured, doubling across a four per cent span, and not reciprocal between the two directions.

mechanics · Tensile The poplin's two budgets as it is held stretched. What is left of a poplin's interchange in each direction as it is held at more and more warp strain. The warp's budget falls to nothing at 3.93%, which is the point of the curve; the weft's rises, because the crimp the warp gives up is crimp the weft takes on. There is one locus and one position on it, so the two are not two quantities that happen to be related — they are the two distances from one point to the two ends of one curve. The consequence is that a pre-tensioned cloth has almost no warp recovery left and more weft recovery than it started with. What the plot cannot show is that the exchange rate between them is not constant: the curve is not a straight line, and its slope is the Poisson ratio this site computes elsewhere.

A cloth has one budget for two directions

A woven cloth looks as though it carries two independent reserves of free extension, one along the warp and one across the weft. It carries one. There is a single curve of states and a single position on it, so every hundredth spent one way is refunded the other — which means a pre-tensioned cloth has not used its recovery up, it has moved it.

mechanics · Tensile A jersey gets taller before it gets shorter. How much a 20 tex cotton jersey shortens along its wales as it is pulled along its courses, with the course spacing at every extension chosen to minimise the loop's energy rather than assumed. Over the first 81% it is negative — the fabric gets 2.0% taller as it is pulled wider — and only then does it start to contract, reaching 88% at the geometric limit. A material with a negative Poisson ratio is a curiosity; a knit has one over part of its range for a reason with no material in it at all, which is that widening a wale at a fixed loop length first lets the loop's tightest bends open and only later starts taking height away from it.

A jersey gets taller before it gets shorter

Pull a knit along its courses and the first thing it does is grow along its wales — by two per cent, over the first eighty per cent of extension, before it turns round and contracts. The transverse response changes sign, and there is no material in the explanation at all.

knits · Knit

Named alongside it

The objects these essays reach for when they reach for this one.

AnisotropyCrimpCrimp interchangeJammingConstant length locusDimensional stabilityElastic recoveryElasticaExtensibilityInextensibleInterchange budgetKinematics

All concepts