Textile Structure
how cloth is put together
Concept

Trellis — where it appears

Cloth modelled as inextensible threads free to rotate where they cross, which says what is possible and never what a fabric will do. Every deformation it produces is checked segment by segment for a thread that has changed length, which is the whole discipline of the model.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

A trellis sheared 30°. The net at an angle, with every thread segment exactly the length it started at. The extension along the diagonal is the bias stretch, and it is a change of shape rather than a change of length.

The bias is a mechanism

Cloth cut at forty-five degrees stretches by a third and springs back, while the threads in it stretch by nothing at all. Almost every explanation given for this is wrong, and the right one is not about elasticity.

mechanics · Bias Wrinkles 127 mm apart. A 300 mm width of a 120 g/m² cloth whose bending length is 20 mm, held under 5 newtons per metre across it and compressed. It cannot carry the compression in the plane, so it leaves the plane, at a wavelength the bending rigidity and the tension settle between them: 127 mm, which is 2.4 wrinkles across the width. The amplitude is drawn and is not computed — this arithmetic sets the spacing and says nothing about the depth.

A cloth cannot carry a push

The net model that runs this site's mechanics has no bending stiffness at all, so it buckles under any compression whatever, into wrinkles of any wavelength whatever. What picks the wavelength is the competition the net leaves out — and the answer is a quarter power, which is why a wrinkle is so hard to change.

mechanics · Buckling What a coating does to the rest of the site. Seven quantities this site computes for uncoated fabric, with what each becomes once a film bonds the crossings: the shear a cloth will take — changed in kind; tear strength — changed in kind; the loss from a hole — reversed; wicking — halved; air permeability — reversed; the sett's effect on strength — unchanged in sign; areal weight — added to. Two of the seven reverse outright. The table is a collection rather than a computation, and each row points at the essay whose result it qualifies.

Coated is a state

Every mechanism on this site assumes threads that can move relative to one another — the bias is a mechanism because the crossings rotate, a tear runs because threads gather, a cloth takes a hole without minding because the neighbours pick the load up. A film bonds the crossings. Two of those results reverse outright, the rest change in kind, and no number on this site has ever said which state it belongs to.

finishing · Coating The shear a dome demands, against how far round it the cloth reaches. A flat sheet of inextensible threads takes a double curvature only by shearing, and the shear it needs depends on how far round the dome it has to reach rather than on how big the dome is — a knee, a shoulder and a beach ball demand exactly the same at the same fraction of their own radius. The horizontal line is the locking angle for a sheeting, where the threads are touching side by side and the mechanism has nowhere left to go. Reaching one radius round takes the cloth to 85% of that, and reaching 1.2 radii passes it. What the plot cannot show is the frictional part: a shear well inside the locking angle is still a shear at crossings friction is holding, so a knee that is domed a thousand times keeps a little of each one.

A knee is a dome imposed a thousand times

A flat sheet of inextensible threads takes a double curvature only by shearing, and how much shear it needs depends on how far round the dome it has to reach — not on how big the dome is. So a knee and a beach ball demand the same, and a trouser knee covered to its own equator is at 85 per cent of the angle at which the threads touch side by side.

applied · Damage

Named alongside it

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

BiasDrapeInextensibleShearAreal weightBaggingBending lengthBucklingCantileverCoatingDartDouble curvature

All concepts