WO1999025530A1

WO1999025530A1 - Scale-up of negative poisson's ratio foams

Info

Publication number: WO1999025530A1
Application number: PCT/US1998/024485
Authority: WO
Inventors: Roderic S. Lakes; Marco A. Loureiro
Original assignee: Wisconsin Alumni Research Foundation
Priority date: 1997-11-19
Filing date: 1998-11-16
Publication date: 1999-05-27
Also published as: AU1461799A

Abstract

Pieces of foam having a negative Poisson's ratio and volumes on the order of thousands of cubic centimeters may be prepared by assembling a mold (10) having wall members (12, 14, 16, 18 and 20) about a piece of foam, e.g. standard open-cell polyurethane foam, in such a manner that the foam is compressed in all three dimensions. While it is compressed, the foam is heated to a plastic or semi-plastic state and then cooled, thereby causing the foam cells to assume re-entrant configurations.

Description

Scale-Up of Negative Poisson's Ratio Foams Inventors: Roderic Lakes, Marco A. Loureiro

Cross-Reference to Related Applications

This application claims priority under 35 USC § 119(e) to U.S. Provisional Patent Application 60/065,487 filed November 19, 1997, the entirety of which is incorporated by reference herein.

Field of the Invention

This disclosure concerns an invention relating generally to negative Poisson's ratio foams, and more specifically to a method of producing such foams in sizes useful for commercial applications.

Background of the Invention

In the 17th century, the French scientist S.D. Poisson observed that a body subjected to axial tensile force not only elongates longitudinally, but also contracts laterally. Similarly, compressive forces cause longitudinal contraction and lateral expansion of the material. Poisson's ratio, symbolized by v, is defined as the negative lateral strain of a body divided by its longitudinal strain. Poisson's ratio is dimensionless, and for most solids its value is positive and ranges between 0.25 and 0.33. For most solid foam materials (e.g. , polyurethane foams), Poisson's ratio is about 0.3. However, rubbery materials can have values close to 0.5. Cork, in contrast, is a cellular solid with a Poisson's ratio close to zero.

U.S. Patent No. 4,668,557 to Lakes (an inventor named above), issued May 26, 1987, describes negative Poisson's ratio foams having "re-entrant" cell structures, i.e. , wherein the ribs/walls of the foam cells are buckled inwardly. Longitudinal elongation of these foams results in lateral expansion; conversely, longitudinal compression results in lateral contraction. A re-entrant foam can be produced by inserting a foam specimen into a cavity of smaller size, consequently causing a triaxial compression of the specimen. The foam is heated within the cavity and then cooled to room temperature to result in the re-entrant cell structure. The difference between the conventional and re-entrant cell structures is illustrated in FIGS. 1 and 2, wherein FIG. 2 illustrates an idealized re-entrant cell obtained after heating the idealized conventional cell of FIG. 1 while it is in compression.

Non-affine (locally inhomogeneous) unfolding of the re-entrant structure is the causal mechanism responsible for the negative Poisson's ratio in these materials. Following the work of Lakes, other negative Poisson's ratio materials were identified, including certain microcellular foams, hierarchical laminates, chiral lattices, α-cristobalite, and closed cell polymer foams. The Poisson's ratios for the foams identified over the last decade can be as low as -0.7 for re-entrant polymer foams, and -0.8 for reentrant metal foams.

The development of these foams was viewed with significant interest since their unique properties appeared to make them ideal for use in a variety of applications, such as for fasteners, cushioning/shock absorbing materials, sound dampening materials, filters, sponges, etc. Unfortunately, exploitation of the foams met with a substantial practical hurdle: it was not known how to produce foam samples having sizes suitable for use in most commercial applications. For example, 2.2 cm x 2.2 cm x 8.5 cm (approximately 40 cc) foam specimens were readily prepared by the process of the Lakes patent, but the same process could not be successfully extended to significantly larger specimens. Initially, it was found to be surprisingly difficult to manually compress the samples to the necessary extent that they could be inserted within appropriate molds. The foam samples would often experience tearing, particularly at their edges, which rendered them unsuitable for use. Further, it was found that as the compressed foam samples grew larger, the foams resulting after heating had more irregular properties, with the Poisson's ratio varying widely within their volumes (often into the positive range).

Because larger samples of negative Poisson's ratio foams would have many valuable uses if they could be produced, significant effort has been expended in "scaling up" the processes of the Lakes patent to larger foam specimens. However, to the best of the inventors' knowledge, all prior efforts to extend the Lakes process to larger foam samples have met with failure. Therefore, there existed a need for methods of scaling up the Lakes processes to make larger pieces of negative Poisson's ratio foam.

Summary of the Invention The invention, which is defined by the claims set out at the end of this disclosure, is directed to methods for producing pieces of negative Poisson's ratio foam which are significantly larger than those that were previously made, and which are also larger than what was previously believed to be possible to produce. In preferred embodiments of these methods, foam having a negative Poisson's ratio is produced by placing the foam within a mold, compressing the foam by moving the interior walls of the mold inwardly, heating the foam under compression until it is in a softened state wherein re-entrant foam cells form, and then cooling the foam under compression so that the cells set in their re-entrant configuration. By using a mold wherein opposing interior mold walls are movable with respect to each other, the mold can effectively be expanded to accommodate large pieces of foam and can then be collapsed upon (or assembled around) the foam to compress it. Preferably, the foam is triaxially compressed by moving the interior mold walls inwardly in each of its three orthogonal dimensions. This is beneficially done by subjecting the foam to a substantially equal percentage of compression in all dimensions, i.e. , by applying the same percentage of reduction to each of the length, width, and height dimensions. It is recommended that prior to compressing the foam, lubricant should be applied between the foam and the mold walls. The invention can produce foam pieces having substantially uniform negative

Poisson's ratios throughout their volumes, and having sizes up to thousands of cubic centimeters in volume, several orders of magnitude greater than foams produced by the prior Lakes method and similar methods. The collapsible mold allows triaxial compression to be uniformly applied throughout the entire volume of large foam pieces (i.e.. compression is uniform along each dimension of the foam), particularly where the aforementioned lubrication is used. This has been found to result in Poisson's ratios which are both negative and substantially uniform throughout the foam piece, characteristics that were lacking when the prior Lakes and other methods were extended to larger foam pieces. The ability to attain these characteristics in larger pieces of foam by use of the inventive method is somewhat surprising since the uniform application of triaxial compression was never found to greatly assist in the production of negative Poisson's ratio foams in the prior studies, wherein small foam pieces were compressed by stuffing them into smaller cavities. Since the prior methods failed when extended to larger foam pieces, it seemed that the prior cavity- stuffing methods and their results were simply confined to small foam pieces, and could not be extended on a more macroscopic scale to foam pieces sized for commercial applications. Further, since uniform compression was not necessary for success with small foam pieces, there was no expectation that this would be required for larger pieces.

As will be described in greater detail below, the methods of the present invention have been found capable of generating pieces of negative Poisson's ratio foam of sufficient size that they can be used as seat cushions or the like. Sample cushions having (unstressed) dimensions of 10 cm x 26 cm x 53 cm have been prepared, and it is expected that the methods described herein could be used to make even larger specimens if desired.

Further advantages, features, and objects of the invention will be apparent from the following detailed description of the invention in conjunction with the associated drawings.

Brief Description of the Drawings FIG. 1 is a perspective view of an idealized conventional (positive Poisson's ratio) tetrakaidecahedron foam cell. FIG. 2 is a perspective view of an idealized re-entrant (negative Poisson's ratio) tetrakaidecahedron foam cell.

FIG. 3 is a perspective view of an exemplary mold suitable for use in the present invention. FIG. 4 shows Poisson's ratio vs. axial compressive strain for conventional foam.

FIG. 5 shows Poisson's ratio vs. axial compressive strain for conventional foam after 20 minutes of processing towards a re-entrant state, for several values of permanent volumetric compression. FIG. 6 shows Poisson's ratio vs. axial compressive strain for conventional foam after 40 minutes of processing towards a re-entrant state, for several values of permanent volumetric compression.

FIG. 7 shows Poisson's ratio vs. axial compressive strain for conventional foam after 60 minutes of processing towards a re-entrant state, for several values of permanent volumetric compression.

FIG. 8 shows compressive stress-strain curves for conventional and re-entrant foams.

Detailed Description of Preferred Embodiments of the Invention

FIG. 3 illustrates an exemplary mold 10 used in the methods of the present invention. The mold 10 includes five wall members 12, 14, 16, 18, and 20, wherein each wall member provides a single internal mold wall except for wall component 20, which provides two mold walls 22 and 24. The mold 10 is adapted to accommodate a conventional piece of foam between its wall members, which may then be assembled about the foam piece to compress it along its different axes in sequence. As an example, one might initially place the foam piece on wall 22 of wall component 20, and then push wall component 18 towards wall 24 of wall component 20 until they leave just so much space therebetween that wall members 14 and 16 may be inserted. Wall members 14 and 16 may then be pushed inwardly, and finally wall component 12 may be moved inwardly towards wall 22 of wall component 20. In this fashion, the internal dimensions of the mold 10 are adjustable in three dimensions so as to allow expansion of the mold's interior to accommodate a large piece of foam, and the mold may then be assembled around or collapsed upon the foam piece to provide triaxial compression of the entirety of the foam piece resting therein. Other types of molds may also be used to provide triaxial compression while at the same time allowing foam pieces to be easily inserted and removed; for example, wall component 20 could be affixed to wall component 14 so that the interior of the mold 10 would be defined by four wall components 12, 16,

18, and 20, or similarly the wall component 20 could be severed between mold walls 22 and 24 so that six separate wall components are provided.

Prior to insertion of foam within the mold 10, it is preferable to first lubricate its wall members 12, 14, 16, 18, and 20 so as to prevent the foam inserted therein from sticking to the wall members. If localized sticking (or sticking along an entire face of the foam piece) occurs, this could give rise to nonuniform compression of the foam, and thus nonuniform generation of re-entrant cell structure and nonuniform Poisson's ratio. In contrast, if friction is minimized between the wall members and the foam, compression should be relatively uniform along all axes. After the mold 10 is used to place the foam sample into triaxial compression, the mold 10 can be heated for appropriate times at appropriate temperatures to process the conventional foam into a re-entrant form. During heating, it must be recalled that foams tend to be thermal insulators, and thus molds having the shape shown in FIG. 3 (wherein one dimension is relatively small with respect to the others) might allow lesser processing times since heat will transfer to the center of the foam relatively rapidly along the short dimension. However, where dimensions of the foam grow larger and/or substantially even in all dimensions — i.e. as they become more bulky and cube-like — it may be necessary to use longer heating times, perhaps coupled with (1) lower temperatures to avoid thermal degradation of the foam, and/or (2) a slowly ramped-up temperature so that the temperature of the entire foam piece is substantially uniform throughout, thereby avoiding varying degrees of plasticity in different parts of the heated foam and enhancing the possibility that re-entrant cell structures are formed to an equal degree throughout the entire piece. Thus far, only conductive heating has been tried with the inventive method. Since conductive heating is relatively slow, it may be desirable to use convective heating (e.g. , immersion of the foam into hot air or oil) or radiant heating (e.g. , via microwaves), either alone or in conjunction with each other or with conductive heating, if more rapid heating (and lower processing time) is desired. As noted above, the methods of the prior U.S. Patent 4,668,557 to Lakes were found to work well with small foam pieces, but could not be successfully scaled up to larger foam pieces insofar as the larger foam samples had highly irregular Poisson's ratios. In contrast, the method of the present invention was found to work very well in providing large foam pieces with relatively uniform negative Poisson's ratios. This is believed to occur largely because the compression provided along each axis of the foam is substantially uniform along that axis' length, with (at least in foams having idealized cells) all foam cells along each axis each being subject to compression into a re-entrant form. The benefits of exerting substantially uniform compression along each of the axes of the foam were somewhat surprising in that this was not previously regarded as being very significant; after all, the small-scale samples of the Lakes patent and other prior experiments simply stuffed the foam into small spaces without fully eliminating localized non-uniform compression. However, these small-scale samples still exhibited a significantly uniform negative Poisson's ratio. In light of these experiments, it appears that the concern of substantially equal compression becomes more significant on a macroscopic level.

It is also hypothesized that more uniform properties may be obtained when the mold exerts substantially the same percentage of compression in each dimension

(i.e. , the same percentage of dimensional reduction). The desirability of substantially identical percentage compression in each dimension is best visualized with reference to FIGS. 1 and 2. If the conventional cell of FIG. 1 is not compressed equally in its three dimensions, the re-entrant structure may develop unequally within certain dimensions/planes, or may not develop at all in certain dimensions/planes. If a foam piece is to be subjected to a substantially equal percentage of compression along each dimension, the mold must be designed with attention to its dimensions in both the "expanded" and "collapsed" states so that the same size ratios between its length, width, and height dimensions occur in both the enlarged state wherein the conventional foam sample is accommodated, and in the collapsed state wherein the mold has fully compressed the foam sample. As an example, where an expanded mold has a height/length ratio of 1 and a width/length ratio of 0.5, it should preferably also have the same ratios when it is collapsed, even though all of the length, width, and height dimensions have changed.

Experimental Testing

Conventional (Unprocessed) Foam Used In the Experiments The foam specimens used in the following experiments consisted of low-density open-cell polyurethane foam of the polyether type, commercially known as ultra-max foams, high comfort foams, or HR foams. This material is commonly used in furniture, bedding and for packaging. The cell sizes in the foam vary widely, unlike the industrial foam described in the Lakes patent and the polyurethane foams described in prior studies. TABLE 1 lists the foam's physical properties and the dimensions of the test specimens.

TABLE 1. Conventional foam physical properties and specimen dimensions.

Density: 29.6 kg/m³ (1.85 pcf) (0.03 g/cm³) Appearance: White cream colored

Poisson's ratio (prior to processing): = 0.30

Specimens Initial Dimensions (cm) Volume (in cm³)

Type 1 8.9 x 22.9 x 48.3 9,844

Type 2 10.2x25.4x50.8 13,161 Type 3 10.8 x 27.3 x 55.9 16,482 Poisson's ratio for the conventional foam is plotted in FIG. 4 as a function of the compressive longitudinal strain. At small strain, Poisson's ratio has a value near 0.3 , and it approaches zero as more compression is applied. A stress/strain plot for the conventional foam (as received) is also illustrated in FIG. 8, where it can be seen that Young's modulus E (the ratio of tension stress along an object's axis to the resulting strain along the same axis in the linear stress/strain region) was 9.3 kPa. Above the linear region, a "plateau" region of reduced slope was observed. Young's modulus is of interest because the lateral strain in a body subjected to longitudinal loading is equal to the negative product of Poisson's ratio and the longitudinal stress, divided by Young's modulus. Hence, Poisson's ratio and Young's modulus together define the interrelationship of stress and strain along a body's various axes.

The Mold

The mold used in the experiments has the same approximate configuration as the mold of FIG. 3, and was made of aluminum for good heat transfer. The major surfaces of the wall members 10/20, 14/16, and 18 respectively measured 43.2 x 21 centimeters, 43.2 x 8.3 centimeters, and 21 x 8.3 centimeters. The mold walls were 1.3 millimeters thick, which is stiff enough to resist bending or bulging when the aforementioned ultra-max foam specimens are compressed. Ordinary vegetable oil was used as a mold lubricant, and was found to help eliminate wrinkles that otherwise occurred when compressing the foam. Since wrinkles spaced along a length of the foam indicate nonuniform compression along that axis, their elimination during compression was evidence that substantially uniform compression was being obtained.

Processing

Three different sizes of foam blocks were processed by use of the inventive method, and since the mold's dimensions were the same for each size, three different permanent volumetric compression ratios were obtained for each set of processing conditions. This allows the negative Poisson's ratio effect for a sample to be observed in terms of its volumetric compression ratio.

In all tests, the furnace was first preheated to a desired temperature. The mold was placed in the furnace for the noted times, and was then removed and allowed to cool at room temperature.

Initial dimensions, volumetric compression ratios, processing temperatures, and heating times for the test samples are set out in the following TABLES 2-4, as well as the measured Poisson's ratios and other factors to be discussed below.

Testing Procedures

Recovery following processing was done by measuring the block dimensions after removal from the mold and cooling, and again after several days to obtain the final dimensions after recovery. Volumetric recovery was calculated and is presented in TABLES 2-4 as a percent difference. Evaluation of Poisson's ratio was done as follows. Fiduciary marks were made on the foam specimen. One side of the specimen was placed against a flat vertical surface while the opposite side was uniformly compressed with the aid of a steel plate. Deformation was measured with a calibrated scale, which provided sufficient resolution (0.8mm) in view of the large size of the specimens. Poisson's ratios were measured based on compression in the longest direction of each specimen and transverse deformation in the second longest direction. In the tables, the given Poisson's ratio value is expressed as a maximum magnitude for the specific compressive longitudinal strain.

Stress-strain behavior was evaluated using a Tinius Olsen Universal Testing Machine with a load cell of capacity 5,000 lbs. The low load scale (up to 250 lbs) was used. Specimen dimensions were 10.2 cm x 10.2 cm x 7.6 cm. Block-like specimens rather than columnar specimens were used since columns of compliant foam tend to buckle sideways under compression. Both sides of the compression cell were lubricated in an attempt to avoid undue restraint on the Poisson effect. Experimental Results

FIGS. 3-8 graphically illustrate the results of TABLES 2, 3 and 4 below, and show the variation of Poisson's ratio as a function of strain for foam specimens processed under different conditions. Curves are fitted via cubic polynomials. The results for each of the processing conditions will now be individually discussed.

Series 1: Foam Processed for 20 Minutes

TABLE 2 illustrates the results for conventional foam processed for 20 minutes — a processing condition referred to as Series 1 — and FIG. 5 illustrates Poisson's ratio as a function of compressive longitudinal strain for these samples.

As illustrated in FIG. 5, the type 2 (Vi/Vf = 1.10) and type 3 (Vi/Vf = 1.20) specimens have an irregular dependence of Poisson's ratio on strain, while the type 1 specimen (Vi/Vf = 1.01) retained a more regular dependence resembling that of the conventional (unprocessed) foam. The analysis also considered the recovery aspect of the foam blocks after transformation. The Series 1 specimens recovered, on an average, 16.5 % of their initial volume, which suggests a high recovery when compared to the 2.7 % recovery observed for specimens of Series 2 (discussed below). Young's modulus was 6.2 kPa for the foam with the greatest volumetric compression in this series. In these results the specimens did not achieve re-entrant characteristics, a fact which suggests that the heating time was insufficient. These partially transformed specimens exhibited irregular behavior of Poisson's ratio versus compressive longitudinal strain.

Series 2: Foam Processed for 40 Minutes

As illustrated by TABLE 3 and FIG. 6, all the transformed specimens in Series 2 (40 minutes processing time) exhibited a negative Poisson's ratio effect (FIG. 6), much less recovery, and better resilience than specimens in Series 1. Comparing the results with those for Series 1 , a heating time of 40 minutes seems more appropriate for blocks of having the stated dimensions. Young's modulus was 7.8 kPa for the foam with the greatest volumetric compression in this series.

Series 3: Foam Processed for 60 Minutes

As shown in TABLE 4, the Series 3 foam blocks were processed under the same previously adopted transformation temperature, but with an extended heating period of 60 minutes. The results, plotted in FIG. 7, show smoother curves than those for Series 2. Poisson's ratio became more negative as the permanent volumetric compression ratio was increased. Young's modulus was 5.6 kPa for the foam with the greatest volumetric compression in Series 3.

Series 3 foams exhibited resilient behavior in which a linear relationship of stress and strain up to more than 40% strain was disclosed. FIG. 8 compares the resilience of the transformed blocks to that of the conventional foam which, in common with other polymer foams, shows a change in slope near 5 % strain.

Comparisons

Comparing the average recovery, specimens that originated from Series 3 (60 minutes processing) yielded slightly better results (2.3 % recovery) compared with Series 2 (40 minutes processing, 2.7% recovery). This indicates that Series 3 specimens were better transformed and more capable of retaining their final cellular configuration. Moreover, it appears that 60 minutes is a more appropriate processing time for the large block specimens, presumably owing to the greater time needed for heat transfer through the larger volume.

The dependence of Poisson's ratio and Young's modulus on permanent volumetric compression ratio for the ultra-max foam may be compared with prior results for re-entrant foam having uniform cell size. Lakes and his colleagues previously discovered, in Scott Industrial foam having uniform cell size, that the largest magnitude of negative Poisson's ratio (-0.7) at small strain is produced with a volumetric compression ratio of 3.7. The negative Poisson's ratio effect at such densities is best seen in tension, since the magnitude of the effect decreases sharply with compressive strain. The present test results for compression show the most negative Poisson's ratio to occur with a smaller volumetric compression ratio of 1.95; no higher ratios were examined. This is consistent with the prior results insofar as these showed a volumetric compression ratio of 2.0 to be successful in generating a good negative Poisson's ratio effect over a range of strain in compression.

The present ultra-max foam exhibited an increase in Young's modulus with processing, in contrast with prior results for Scott Industrial foam having relatively uniform cell size, in which Young's modulus decreased with processing. The difference is believed to arise from the more irregular cell sizes and structures in the ultra-max foams as compared to the Scott Industrial foams of the prior experiments.

It is noted that a more negative (and more uniform) Poisson's ratio might be expected to occur when processing foams wherein the cell sizes are more substantially uniform, rather than widely varied. Where cell sizes widely vary, the differently-sized cells will presumably have different susceptibilities toward assuming a re-entrant structure when subjected to heat and/or compression. Further, the degree of compression on a cell and heat transferred to the cell will be dependent on the properties of its surrounding cells. The net effect is thus expected to be less negativity of the Poisson's ratio in ultra-max foams and other foams with irregular cell sizes. Of course, this could in some instances be beneficial depending on the foam properties one is trying to obtain.

Conclusions

The test results illustrate that production of foam pieces having substantially uniform negative Poisson's ratios and volumes on the order of at least 9,000 cc is now feasible. This is a significant advance over the processes of the Lakes patent, which were only capable of producing foam pieces with substantially uniform negative Poisson's ratios having a volume of approximately 40 cc, which is too small for most commercial applications. On the other hand, foams having volumes in the thousands of cubic centimeters may be used in a wide variety of applications, seat cushions being an example. While the invention has been illustrated and described in detail in the foregoing description, the same is to be considered as illustrative and not restrictive in character, it being understood that only the preferred embodiments have been shown and described, and that all changes and modifications that come within the spirit of the invention are desired to be protected.

Claims

ClaimsWhat is claimed is:

1. A method of producing a foam piece having a negative Poisson's ratio comprising: a. compressing a foam piece between a first pair of opposing walls in a first direction, at least one of the opposing walls of the first pair being movable with respect to the other one of the opposing walls of the first pair; b. compressing the foam piece between a second pair of opposing walls in a second direction; c. compressing the foam piece between a third pair of opposing walls in a third direction; d. heating the foam piece while it is compressed in the first, second, and third directions; e. cooling the foam piece while it is compressed in the first, second, and third directions; and f. releasing the foam piece from the first, second, and third pairs of walls.

2. The method of claim 1 wherein at least one of the opposing walls of the second pair is movable with respect to the other one of the opposing walls of the second pair.

3. The method of claim 2 wherein at least one of the opposing walls of the third pair is movable with respect to the other one of the opposing walls of the third pair.

4. The method of claim 1 wherein the steps of compressing the foam piece between the first, second, and third pairs of opposing walls are done sequentially.

5. The method of claim 1 wherein the foam piece is subjected to a substantially equal percentage of compression in each of the first, second, and third directions.

6. The method of claim 1 wherein the first, second, and third directions are at least substantially orthogonal.

7. The method of claim 1 further comprising the step of applying lubrication between the foam piece and the first pair of opposing walls prior to compressing the foam piece between the first pair of opposing walls.

8. The method of claim 1 wherein the foam piece is heated in such a manner that at least substantially uniform temperature is attained throughout the foam piece while such temperature rises.

9. The method of claim 1 wherein the foam piece is compressed in the first, second, and third directions to a volume no less than 100 cc.

10. A foam piece produced by the method of claim 1 having a negative Poisson's ratio and a volume greater than 100 cc.

11. A method of producing a foam piece having a negative Poisson's ratio comprising: a. placing the foam piece within the interior walls of a mold; b. compressing the foam piece by moving the interior walls of the mold inwardly; c. heating the foam piece while it is compressed; d. cooling the foam piece while it is compressed; and e. moving the interior walls of the mold outwardly, thereby releasing the foam piece from the mold.

12. The method of claim 11 wherein the foam piece has an original length, original width, and original height when placed within the interior walls of the mold, and wherein the step of compressing the foam piece includes subjecting it to a substantially equal percentage of reduction in its original length, original width, and original height.

13. The method of claim 11 further comprising the step of applying lubrication between the foam piece and the interior walls of the mold prior to compressing the foam piece.

14. The method of claim 11 wherein the foam piece is heated in such a manner that at least substantially uniform temperature is attained throughout the foam piece while such temperature rises.

15. The method of claim 11 wherein the step of compressing the foam piece includes moving the interior walls of the mold inwardly in each of three orthogonal directions.

16. The method of claim 15 wherein the interior walls of the mold are moved inwardly in the three orthogonal directions in sequence.

17. The method of claim 15 wherein the foam piece is subjected to a substantially equal percentage of compression in each of the three orthogonal directions.

18. The method of claim 15 wherein the step of heating the foam piece includes placing the entirety of the mold within a heated space.

19. The method of claim 11 wherein the foam piece is compressed to a volume no less than 100 cc.

20. A method of producing a foam piece having a negative Poisson's ratio comprising: a. providing a mold having pairs of opposing walls oriented along each of three orthogonal dimensions, wherein at least one wall within each of the pairs is movable towards its opposing wall; b. inserting the foam piece within the mold; c. moving at least one wall within each of the pairs towards its respective opposing wall, thereby compressing the foam piece; d. heating the foam piece while it is compressed; e. cooling the foam piece while it is compressed; and f. releasing the foam piece from the mold.