Making negative Poisson's ratio foam

Original Reference: Roderic Lakes, "Foam structures with a negative Poisson's ratio", Science 235:1038-1040 (1987) 27 Feb.

If you are interested in making this foam for educational, scientific, or curiosity purposes, go ahead and enjoy. If you are interested in making it for commercial purposes, please contact the Wisconsin Alumni Research Foundation (WARF) .

Remark on polymer foams. (Metal foams are discussed below.) Each kind of polymer foam has its own softening point and transition temperature. These instructions are for polyester and polyether polyurethane foams. For other foams the transition temperature is to be found empirically. Scott Industrial Foam with 10 to 20 pores per inch works best; it is a reticulated open cell foam used for air filters. Scott foam with smaller pores also works well. Open-cell polymeric packing foams can be used; they may be more sensitive to processing temperature and humidity. Initial foam density should be low. Foam of 0.043 g/cm³ [2.7 lb/ft³] is suitable. If the initial solid volume fraction is too high, there may be insufficient space in the structure to achieve the required permanent compression. Closed-cell foam can be processed but the procedure is more difficult.

The mold : We have used aluminum square tube, 1" (25 mm) square, for a mold. If too large a mold is used, heat transfer will be poor, and only the outer portion of the foam will be transformed.

1. Preheat furnace to about 160-170 deg C.

2. Either measure or mark foam for later determination of strains. Mark foam in all 3 orthogonal directions, i.e., two adjacent corners and down one side.

3. [optional: this is not necessary if sufficient care is taken in removing wrinkles] Lubricate sides of square aluminum tube with vegetable oil. Spray cooking oil (PAM) can also be used, but does not seem to work better. DO NOT use a petroleum distillate base lubricant; it will smell terrible when heated.

4. Stuff the foam in the tube. It works well to start the foam slightly by hand and then work it up gently with a tongue depressor to remove wrinkles.

5. Pull the foam a little on both ends to get rid of creases created by stuffing the material. This procedure will result in a pre stretched sample in the tube. The actual original length of the sample must be used when determining the amount of pre compression to apply.

6. Place the compression device and end plates on the stuffed tube.

7. If the desired specimen length is less than the square tube size, select the correct length of cut tubing [pipe] within the mold to compress the foam longitudinally by the same amount as transversely. Alternatively, cut the foam proportionally longer than the square tube length and do not use pipe.

8. Push the pipe down on the loose end plate such that the foam is compressed evenly at the end. Try not to push too fast, this may contribute to the uneven distribution of compression along the length of the specimen.

9. Gently tighten down the side screws to hold the cut pipe in place.

10. Place assembly in center of furnace or oven. A kitchen oven is sufficient.

11. Leave the foam in the oven for a predetermined amount of time. The gray polyester foams transform better at a slightly lower temperature for a longer amount of time, about 20 minutes maximum. The white/cream colored polyether foam seems to be more sensitive with respect to melting together; 17-18 min. is appropriate.

12. Remove and cool the specimen completely. Taking the specimen out of the mold before complete cooling may result in premature release of the pre compression. It may be helpful to release foam ribs which have stuck together: stretch the specimen gently in each of three directions. Congratulations! You have made negative Poisson's ratio foam (also called anti-rubber, dilational material, or auxetic material).

13. Measure the amount of permanent compression retained by the specimen by either measuring the new distance between the marks or by measuring the size of the transformed sample.

14. Other kinds of molds are possible and have been used successfully by others.

If a definitive pedigree is required, order the foam from a supplier, otherwise use packing foam. For Scott Industrial Foam, consider Reilly Foam Corporation, Main Office, 1101 Hector Street, Conshohocken, PA. 19428, (610) 834-1900, Fax: (610) 834-0769.
New England Sales Office & Plant, 16 Britton Drive, Bloomfield, CT. 06002, (860) 243-8200, Fax: (860) 242-6199,

The volumetric compression V_i/V_f should be from a factor two to a factor of five. A factor three volumetric compression corresponds to a factor 1.44 linear compression. Actual compression may be less than predicted, due to recovery.

§4. Procedures for coring circular cross section foam samples

1. Brass tubes are available at a hardware store. They are typically available in one foot lengths.

2. The smaller tubes can be put directly into the chuck of the drill just like a regular drill bit. The larger tubes (more than 3/8") need to be attached to a smaller piece of material that will fit into the chuck. Pot the tubes around a cut end of a bolt (1/4-3/8") with cast plastic. This works well, but it is very important to get the tube potted exactly concentric with the cut bolt. Otherwise, nonconcentric rotation results and the core drill will produce an uneven specimen.

3. It is necessary to use a rather short (less than 2" sticking out of the chuck) piece of tubing in either the small or large core drills. If the tubing is any longer, any slightly nonuniformity in placement or tubing will be maximized on by the rotational inertial effect and will cause nonconcentric rotation along the core drill.

§4.2 Drilling the cores

1. Use both a hard plate and a soft cushion under the specimen when drilling. The hard plate protects the lab surface and the soft cushion keeps the core drill from being dulled or bent on the hard surface. It works well to tape sand paper to the hard plate to help keep the soft cushion from rotating.

2. It works best to press down hard on the sample and drill very fast when coring both the reentrant foam and the regular foam.
Remark on metal foams
Ductile metal foams, such as those based on aluminum or copper, can be converted into negative Poisson's ratio foams as follows.
The resulting properties are given in the manuscripts referred to in the main Poisson page. Use a vise or other compression device to plastically deform the metal foam in one direction by about 5% or less. Repeat in another direction at right angles to the first direction. Repeat in a third direction at right angles to the prior directions. Repeat the entire process until the volume of the foam is reduced by a factor between two and four. The optimum value depends on the initial density of the foam. These foams are considerably stiffer than the above polymer foams. Consequently deformation associated with Poisson's ratio is too small to be observed with the unaided eye. Poisson's ratio may nevertheless be measured using optical methods.
If the initial foam is slightly anisotropic it can be made isotropic by compressing it a bit more in the direction of greatest initial stiffness.

Other materials
Other negative Poisson's ratio materials including honeycombs, lattices with repeating structure and materials near phase transformations are possible. For instructions on making them, see the main negative Poisson's ratio page. Lattices, for example, can be made by 3D printing (additive manufacturing). Lattices have a regular repeating structure in contrast to foams.

If you have made these foams, you deserve a brass badger. This brass badger served on the battleship USS Wisconsin; it is now in the State Capitol in Madison. The nose of the badger is shiny because people like to squeeze it.