I was thinking about generating shapes via laser-cut geometry, and it occurred to me that laser-cut fabric can inexpensively form netting with quite flexible 3-D geometry, which can be applied to a variety of important applications.
I just watched the presentations of “Beyond Developable” from SIGGRAPH 2016 and “Rapid Deployment of Curved Surfaces via Programmable Auxetics” from SIGGRAPH 2018, collectively by Mina Konaković-Luković, Julian Panetta, Keenan Crane, Mark Pauly, Sofien Bouaziz, Bailin Deng, and Daniel Piker. (I think this is mostly Mark Pauly’s group at EPFL LGG.)
In the 2016 paper, they cut relatively rigid sheets of material into an auxetic triangular metamaterial pattern which can linearly stretch by up to a factor of 2, but more or less uniformly — that is, if a region of it is stretched by a factor of 1.3 along the x-axis, it’s also stretched by about 1.3 along the y-axis, along the x = y line, along the x = -y line, and so on. The stretch can vary from one region of the material to another, but only gradually. These work out to mean that it expands conformally, which turns out to mean that it can be relatively easily hand-bent into computer-designed shapes or adapt to the form of the wearer’s body.
In the 2018 paper, they extend this work in a couple of ways: cutting some of the material “pre-expanded”, distorting the triangular mesh to vary the properties of the metamaterial, and sometimes replacing the cut sheet of material with a bunch of solid triangles linked together, with the sizes varied to limit the expansion. Then they force it to expand in different ways: by inflating it with a polyethylene bag or a balloon or by allowing it to hang freely from a frame.
Although I haven’t tried, converting fabric to netting by laser cutting should be straightforward: you just cut some holes in it. This is probably better to do with acrylic†, cotton, or silk fabric than nylon or polyester, although Engadget says it is also used with nylon and polyester. Cotton cut this way without further treatment will probably fray, but the other materials might form melted edges that impede fraying.
If you draw a Voronoi diagram of the hole centers, each vertex of the Voronoi diagram is in the middle of a piece of cloth which is connected along lines to adjacent vertices; these adjacent vertices are connected by cloth “bridges” under the Voronoi lines. If we expand the holes without allowing them to cross these lines, the bridges become thinner, but the overall surface retains the same Gaussian curvature as the original cloth, which had better be zero if we are going to be doing this on a garden-variety laser cutter.
If we want to allow a region of the netting to develop positive Gaussian curvature, the simplest thing we can do is to make the Voronoi lines of that region follow the bias rather than the threads of the fabric, assuming it’s a woven or nonwoven fabric. (Actually, even simpler is to use a knit fabric, which is stretchy enough to curve any which way, but that gives up precisely the control I’m exploring here.)
However, we can do better than that. By making the fabric bridges squiggle, we can make them longer — potentially by orders of magnitude, serpentining almost arbitrarily far across the space from one node to another, filling in most the neighboring holes with their squiggling. The inside radii of these squiggles need to be large enough to prevent stress risers, also known as “rips”, from starting; in some cases this will require discarding a teardrop shape from the inside of the curve, but in other cases the outside radius of a neighboring squiggle can fill the space, thus maximizing the use of cloth.
In this way, it should be possible to expand a 100-mm square of fabric (or even less) into a 1-m square (or more) of netting which assumes some complicated three-dimensional shape when fully inflated — either a fully determined form, if the graph of net nodes consists entirely of triangles (Bucky Fuller’s “omnitriangulated”), or a more flexible form if some or all of the holes in the net have other shapes. By applying the process to heavy, strong fabrics such as twill, denim, seatbelt webbing, canvas, or burlap, it should be possible to quickly manufacture fairly complex, strong three-dimensional forms.
In some cases, particularly without omnitriangulation, squiggling is not necessary, because the nodes can be mapped into the plane of the original fabric in such a way as to put network-nearby nodes far apart. Consider, for example, a series of concentric rings of cloth linked together by quarter-turn spirals: if hung from the center of the cloth, the spirals untwist and become lines along a cone from its vertex, while the rings run around the cone. Some teardrops will still be needed at junctions to prevent stress risers.
Uniform amounts of squiggling over an area will not produce positive curvature when fully extended, but zero Gaussian curvature; in that case, a local reduction in squiggling will produce a region of negative Gaussian curvature, as demonstrated in the 2018 paper mentioned above.
† “Acrylic” fiber is polyacrylonitrile, which is not the same chemical as the poly(methyl methacrylate) “acrylic glass” (Lucite, Plexiglas, or Perspex) which is so popular as a laser-cutting medium. So it might not be as safe or convenient.
The shapes you can make from the fully extended omnitriangulated nets will necessarily be pretty convex; they can’t have “pockets” in them, in the machining sense of a cavity eaten out of a surface, rather than the sartorial sense. Moreover, the net geometry, even if omnitriangulated, only controls the local curvature of the surface, not its global curvature. Once an omnitriangulated surface curves around to form a closed surface, the global curvature becomes fully determined, but until then it is potentially kind of floppy. For clothing this is usually considered advantageous, but not for some other possible applications.
Long protrusions are possible, but limited — they necessarily imply cloth density limited to their circumference-to-length ratio. That is, if they are twenty times longer than their circumference, they cannot have more than 5% cloth coverage.
Although ordinary textiles are probably the best material to use for this for many purposes, other possibilities exist. Nonwoven polyester (polar-fleece and friselina) can be dramatically cheaper and may be more computationally predictable, though not as strong or as stiff. Paper or Tyvek are cheaper still, and probably faster to cut. EVA foam (“foam rubber”) is laser-cuttable and is widely used for shoes.
I haven’t personally seen gel-spun UHMWPE fabric yet, whether woven or knit, but if you can get it woven, it might offer better strength and enormously better dimensional control than the other fabrics mentioned above. I’ve seen advertisements for pantyhose and bras (Katherine Homuth’s SheerlyGenius, now Sheertex) and backpacks (Loctote) made from gel-spun UHMWPE fabric, knit in both cases.
Other sheet-cutting processes, such as high-powered laser cutting, waterjet cutting, and CNC torch cutting, could be used to cut sheet metal into similar netting-like structures, though its behavior under strain would be different; if you do manage to stretch it into shape, it will probably work-harden in the process, especially if you’re using annealed copper or aluminum. Your dimensional precision is going to be shit.
Cloth made from carbon fiber, glass fiber, or basalt fiber would also provide higher strength and better dimensional control than more common fibers, but they might not be cuttable with a low-power laser.
Woven aluminum or steel window-screen material is another candidate for a higher-strength, higher-dimensional-precision material (though perhaps inferior to UHMWPE), and it could be cut very rapidly, possibly in several layers at a time, with plasma torches or high-powered lasers.
The amount of fabric in an area has an upper bound determined by the degree of expansion that area experiences when going from the original flat fabric to the fully extended net, and a lower bound determined by the required strength of the netting. However, these will commonly be quite wide limits. This means that you can vary the net coverage in an area to moderate its color. In particular, white netting over a black background should be able to produce significant changes in luminance, though the maximum contrast will be limited as described.
Moreover, by using three or four layers of netting nested inside one another — red, green, blue, and possibly white — full-color images should be feasible, as long as moiré patterns and coregistration can be kept under adequate control.
Clothing and hammocks are the most immediately obvious uses. A laser-cut woven or nonwoven netting layer can provide shape, while a fine knit layer underneath can prevent the netting from being uncomfortable or transparent when those are not desired. Netting shirts are already popular for hot days and for dance clubs.
Aeron-style chairs typically use knit netting for the seats and backs, providing much better ventilation than more traditional styles of chairs; laser-cut netting should be a reasonable alternative. Director’s chairs and foldable camping chairs traditionally have canvas seats, but breathable fine netting would be an improvement.
Some other household items can be feasibly made in this way. My shoes hang in the closet in a cloth organizer that I think could be made from netting. A collapsible bucket for carrying water can consist of a hoop, some a plastic-bag liner, and netting to support the bag. Stuffed animals can be made of netting to give shape to fine knit cloth containing the stuffing. Houseplants can be potted in netting pockets suspended from railings. Backpacks, curtains, and clothes hampers can be made from netting.
Breathable shoe uppers can be made from EVA-foam “netting”, and other uses might include objects like toolboxes that would benefit from being flexible and lightweight but cannot afford cloth netting’s tendency to snag on anything sharp.
Inflatable sculptures, like those made by Ophélie Dorgans, can be easily inflated to multi-meter size, but historically it has been somewhat difficult to control their shape; most bouncy castles and advertising balloon critters are, geometrically speaking, kind of shitty. This approach offers an alternative: inflate a big shapeless plastic bag inside a shaping net. (This is demonstrated in the 2018 paper mentioned above.) As explained above, the shaping net can also provide color.
Such an inflatable sculpture could be inflated with methane, hydrogen, or helium and unleashed over a city, as with the 1970s UFO art prank Theo Jansen participated in and the earlier Los Angeles Meteor prank. (I can’t remember if that last one is still anonymous or not.)
Blow molding of plastic bottles and vacuum molding of sheets of PET and other thermoplastics should be feasible using netting forms made in these ways, particularly if the fabric is cotton or nylon. As with clothing, a layer of fine knit fabric between the net and the hot plastic may be a useful mechanism for reducing netting marks on the surface.
With a reasonably flexible and gritproof liner — again, perhaps fine knit cotton — these netting forms could be suspended from frames and used as molds for poured-in plaster, concrete (which additionally demands alkali resistance, which cellulose and polyester have), lime cement, fluidized greensand, waterglass-bonded sand, or perhaps even slip (barbotina) for slipcasting.
Many of the above-mentioned castable materials are most interesting as refractory mold materials for metal casting, but of course in metal casting usually you want pocketing, which is, as I said above, impossible — assuming that the molding materials are on the convex side of the netting. An alternative might be to inflate the netting with a plastic bag, then pour plaster (or cement or whatever) around it to make the mold.
By painting, epoxy-impregnating, airplane-doping, sizing, stuccoing, spraycreting, or applying barbotina to an inflated net, perhaps with knit-fabric layers on one side or the other, you should be able to make a thin composite material, reinforced by the fabric layer or layers to reduce its brittleness. Depending on the composition, this composite may be adequately sturdy even for some metal-casting processes.
In some cases, just filling the netting with sand may be sufficient; I suspect this may be one of the lowest-cost ways to get acoustic panels.
The only laser-cutting machine I’ve used can cut 6-mm MDF at about 24 mm/s, but can cut thinner materials faster. Many interesting laser-cuttable fabrics are in the neighborhood of 200 μm thick, suggesting that the laser could cut them at a speed on the order of 1 m/s. However, particularly cutting complex shapes, the machine is mechanically capable only of a dramatically lower speed than that.
As I understand it, typical mass textile fabrication is done by cutting a thick stack of fabric to the pieces of the pattern with a bandsaw knife before sending the pieces out to be pieced together. Hundreds or thousands of layers of cloth are cut at once. (Mistakes here are ruinously expensive, ruining thousands of meters of cloth with a single bad cut.)
Typically the laser-cutting shop is not willing to cut multiple sheets of material at once, perhaps because they blow apart under the air blast, ruining the laser focus. But perhaps we could laminate several layers of cloth together with an adhesive to form a board similar to MDF, cut them, and later remove the adhesive.
One promising adhesive for this purpose is food starch: it is a polysaccharide like cellulose, so it doesn’t stink when it burns, and it is commonly used for stiffening common fabrics, even polyester, which is a material notoriously resistant to being stuck to. As “wheat paste”, it is also commonly used as an adhesive in bookbinding and papier-mâché. In fabrics that can withstand boiling — basically anything but polyester — removing it is also easy.
Papier-mâché practice demonstrates a risk of the cloth-board approach: drying time is necessary between layers in order to avoid trapping excessive moisture within the material. A warm air blast should be able to speed up this process.
This approach should make it possible to cut dozens of layers of cloth at once at MDF-like speeds, thus greatly reducing the cost of complex shapes, if you wanted more than one of them, anyway.
Other candidate dissolvable adhesives for this purpose include sugar, PMMA, polystyrene, carrageenan, gelatin (or hide glue), calcium stearate, albumin, urea, and pectin. All of these could also be used as sizing to paint inflated netting to solidify it, as described earlier.
Salt is probably bad because it would produce HCl, chlorine, and sodium gases; waterglass is probably bad because it wouldn’t cut with a low-power laser, and might swell up and block the cut instead; baking soda might work but might produce NaOH when cutting; nitrates are probably bad because they might offgas nitric acid and nitrate the cellulose when fiercely heated; sulfates probably wouldn’t cut (and might offgas acid sulfur oxides and produce toxic sodium sulfide); and soluble phosphates might have similar problems. (Ammonium phosphates in particular decompose to ammonia and molten anhydrous phosphoric acid upon fierce heating.) Some of these, especially waterglass and in-situ-formed phosphates of calcium or copper, might be suitable for painting onto an already-cut inflated netting form.
In other contexts, the possibility of selectively and precisely forming such gases on a surface or within a material with a laser-cutting machine might be very useful. Ben Krasnow on his Applied Science YouTube channel has reviewed a tactile-printing paper whose surface swells up when locally heated, for example.