9.1.1 Weave geometry

The definition of the geometry of the textile can be explained looking at the right side of the figure:
\includegraphics[]{./Images/TextileLamina.png}

The subscripts f,w mean fill and warp, respectively. When the fabric is woven on a loom, the tows that run along the length of the roll of fabric are called warp (or weft in England) because the go up and down sinusoidally to accommodate the fill tows that go across, effectively filling the space between the wefts. Arbitrarily, we picked the fill as the x-direction for the analysis.

CADEC models a representative unit cell (RUC), as shown in the figure. The RUC is the smallest (repetitive) cell that has all the features required to fully describe the textile. A plain weave has a 2X2 RUC.

So, with reference to the figure, we have:

a is the fill/warp width of 1/2 the pitch minus the gap g of the fabric in the fill/warp direction. The pitch is the period 2a+2g of the sinusoidal shape.

h is the thickness of the fill/warp tow.

$h_ m$ is the thickness of pure unreinforced matrix at the cusp of the fill/warp tows. This resin-rich thickness is usually distributed 50/50 on top/bottom of the lamina, as shown in the figure.

$n_ g$ is the harness, which is the minimum number of tows required to get a repetitive pattern on the fabric. It is called harness because that is the mane of the mechanism that the loom uses to lift the weft tows to create the required pattern. The cheapest loom has harness of 2, and that gives you the ability to weave only plain weave fabrics. More harness requires a more expensive loom. CADEC can model any harness (at no additional cost :S). However note that CADEC can do only square fabrics; that is, the harness must be the same in weft and fill directions. Also, CADEC can do only 2D (not 3D), biaxial (not triaxial) fabrics. The harness is 5 in the figure.

$n_ i$ is the interlacing, which is the number of warps that the fill goes over/under starting at x=y=0. The interlacing is 2 in the figure. Next, a weaver would just say twill, or satin, and the description would be done, but for computer programming we need one additional parameter.

$n_ s$ is the skip. You can see in the figure that the RUC is made of $n_ g\times n_ g$ sub-cells (5 X 5 in this example). If we move the pattern one sub-cell up and one left, we get the same pattern, right? You may have to draw it to convince yourself. Well, whatever it has to be moved, it is called skip. In this way CADEC can do twill and satin, in addition to plain weave of course.