Auxetic materials negative Poissons ratio

Although the possibility of materials with a negative Poisson s ratio had been recognised theoretically, it is only comparatively recently, since the mid-1980s, that examples of such materials have become available. These materials expand laterally when stretched and contract laterally when compressed, and are called auxetic from the classical Greek word auxetos meaning increase. 

The subject of geometrical structures and models in relation to auxetic polymers has been reviewed by Liu and Hu [110], 

The work on auxetic polymers arising from microporous structure has continued. Aider-son et al. [120], in an attempt to produce auxetic material in a more easily usable form, have used melt-spinning to produce auxetic polypropylene fibres. This work was developed further, by way of a study of the processing parameters for melt-spinning of auxetic polypropylene, polyester and nylon fibres [121]. Ravirala et al. [122] have produced auxetic polypropylene film using melt extrusion. Less conventionally, Alderson et al. [123] have produced auxetic polyethylene by a combination of powder compaction and sintering, without an extrusion step. 

As a practical means of creating material with negative Poisson s ratio, it has been proposed to use auxetic networks of polymer fibres within a conventional matrix to produce composites that are themselves auxetic. Here the individual fibres are not in general auxetic. 

(1955) International Union of Theoretical and Applied Mechanics Colloquium (Madrid), Springer-Verlag, Berlin, p. 251. 

Note that this equation differs from the classical aggregate model equation in two respects  

The denominator of the second term as the left-hand side is 2G, and not G. 

The definition of sin 6 differs from that for sin O in that the average is carried out in the plane of the chains and is not a three-dimensional average R 9o) refers to the initial chain distribution and R (0) the final distribution under stress. 

Initially, there is expansion in both the axial and lateral directions as the fibrils 

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Fig. A6. A model of an auxetic material, i material with negative Poisson ratio...

In this section, three illustrative examples of the impact of scale on mechanical properties are outlined. First, solid lubricants are discussed, underlining the connection between crystal structure and the observed mechanical properties. Second, auxetic materials, in which crystal structure and microsttuc-ture combine to produce materials with negative values of Poisson s ratio, are discussed. Last, thin films, in which mechanical properties are measured by methods similar to that used in the bulk, are considered. 

In the families of cordierite, yS-eucryptite, /3-cordierite and NZP, a mechanism similar to that giving rise to auxetic (negative Poisson s ratio) materials seems to occur (Section 10.3.2). The stmcture is built from inflexible layers, similar to those found in clay minerals (see Sub-section... 

The negative sign is to ensure that the numerical value of Poisson s ratio is positive for a normal material that becomes thinner as it is stressed. Auxetic materials have a negative value of is, and become fatter when stressed. 

Most materials have o between 0.0 and 0.5. Cork is close to 0.0, polysilicon is around 0.22, single crystal silicon is around 0.28, most steels are around 0.3, and rubber is almost 0.5. A perfectly incompressible material deformed elastically at small strains would have a Poisson s ratio of exactly 0.5. Some materials, mostly polymer foams, have a negative Poisson s ratio if these auxetic materials are stretched in one direction, they become thicker in perpendicular directions. 

Table 15.1 shows the Poisson s ratios of some materials. An incompressible material that does not change volmne when elongates would have a Poisson s ratio of exactly 0.5. For example, rabber has a Poisson s ratio of nearly 0.5. Cork s Poisson ratio is close to 0, indicating very little transverse contract when stretched. Auxetic materials, such as polymer foams, have negative Poisson s ratios, and they become thicker in perpendicular directions when stretched. Most other materials, including metals, ceramics, and polymers, have Poisson s ratios ranging from 0 to 5. 

Materials Exhibiting Negative Poisson s Ratios (Auxetic).136... 

Wojciechowski, K. W. and Brartka, A. C. Auxetics — Materials and models with negative Poisson s ratios. Mol. Phys. Rep. 6, 1994, 71-85. 

Some materials (e.g., specially prepared polymer foams) when pulled in tension actually expand in the transverse direction. In these materials, both e, and of Equation 6.8 are positive, and thus Poisson s ratio is negative. Materials that exhibit this effect are termed auxetics. 

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