K. E. Evans

Models for the elastic deformation of honeycombs

A theoretical model has been developed for predicting the elastic constants of honeycombs based on the deformation of the honeycomb cells by hexme, stretching and hinging. This is an extension of earlier work based on flexure alone. The model has been used to derive expressions for the tensile moduli, shear moduli and Poisson’s ratios. Examples are given of structures with a negative Poisson’s ratio. It is shown how the properties can be tailored by varying the relative magnitudes of the force constants for the different deformation mechanisms. Off-axis elastic constants are also calculated and it is shown how the moduli and Poisson’s ratios vary with applied loading direction. Depending on the geometry of the honeycomb the properties may be isotropic (for regular hexagons) or extremely anisotropic. Again, the degree of anisotropy is also affected by the relative magnitude of the force constants for the three deformation mechanisms. 0 1997 Elsevier Science Ltd. All rights reserved.

Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties

A microporous, anisotropic form of expanded polytetrafluoroethylene has been found to have a large negative major Poissons ratio. The value of Poissons ratio varies with tensile strain and can attain values as large as -12. The microporous structure of the material is described and the mechanisms that lead to this large negative Poissons ratio are identified. Micro-rotational degrees of freedom are observed, suggesting that a micropolar elasticity theory may be required to describe the mechanical properties.

Auxetic behavior from rotating squares

Auxetic materials exhibit the very unusual properties of becoming wider when stretched and narrower when squashed [1], that is they have negative Poisson’s ratios. Apart from the pure scientific interest of having materials showing such an unconventional property, a negative Poisson’s ratio gives a material several other beneficial effects such as an increased shear stiffness, an increased plane strain fracture toughness and an increased indentation resistance. These properties make auxetics superior to conventional materials for many practical applications [1, 2]. In recent years several auxetics have been fabricated by modifying the microstructure of existing materials, including foams [2] and microporous polymers [3]. A number of molecular auxetics have also been proposed [4–9] one example being α-cristobalite [7]. The auxetic behavior in these materials can be explained in terms of their geometry and deformation mechanism. Thus, the hunt for new auxetic materials is frequently approached through searching for geometric features which may give such behavior [9, 10]. In this letter we present a new mechanism to achieve a negative Poisson’s ratio. This is based on an arrangement involving rigid squares connected together at their vertices by hinges as illustrated in Fig. 1. This may be viewed as a two dimensional arrangement of squares or as a projection of a particular plane of a three dimensional structure. This latter type of geometry is commonly found in inorganic crystalline materials [8, 9, 11]. Referring to Fig. 1, for squares of side length “l” at an angle θ to each other, the dimensions of the unit cell in the Oxi directions are given by:

A novel mechanism for generating auxetic behaviour in reticulated foams: missing rib foam model

Abstract Foams have previously been fabricated with a negative Poissons ratio (termed auxetic foams). A novel model is proposed to explain this and to describe the strain-dependent Poissons function behaviour of honeycomb and foam materials. The model is two-dimensional and is based upon the observation of broken cell ribs in foams processed via the compression and heating technique usually employed to convert conventional foams to auxetic behaviour. The model has two forms: the “intact” form is a network of ribs with biaxial symmetry, and the “auxetic” form is a similar network but with a proportion of cell ribs removed. The model output is compared with that of an existing two-dimensional model and experimental data, and is found to be superior in predicting the Poissons function and marginally better at predicting the stress–strain behaviour of the experimental data than the existing model, using realistic values for geometric parameters.

Auxetic polymers: a new range of materials

Abstract Materials with a negative Poissons ratio (auxetic materials) have the fascinating property of becoming fatter when stretched. This article describes some of the consequences of this phenomenon and some of the routes for making polymers with this property. Potential applications for these materials are reviewed.

Do Zeolites Have Negative Poisson's Ratios?

Consequently, the size of the resulting nanoparticles matches the dimension of the nanometer-sized cavities inside these swollen domains. The possibility of controlling the growth of the metal nanoclusters by changing the morphological features of the support represents a unique feature of resin supports, in which the metal nanoparticles are generated inside the swollen polymer network and not simply at its surface. It can be inferred that functional resins characterized by a narrower distribution of nanoporous domains will make it possible to control even more precisely the size and size distribution of the metal nanoclusters generated inside them, a task that we are going to turn to in the near future.

Microporous materials with negative Poisson's ratios. II. Mechanisms and interpretation

For pt.I see ibid., vol.22, p.1877-82 (1989). In a previous paper the morphology of a microporous material made from expanded poly(tetrafluoroethylene) was described and results presented for its mechanical behaviour. The material was shown to be highly anisotropic and exhibited a large negative Poissons ratio. In this paper a simple model for the microstructure is described to account for this effect. The model is based on an interconnected array of anisotropic particles that deforms so as to produce a large transverse displacement under longitudinal tensile loading. Very good agreement is found between the model and experimental results, providing an explanation for the variation of Poissons ratio with tensile strain, in terms of changes in material morphology.

The fabrication of microporous polyethylene having a negative Poisson's ratio

Abstract A novel thermoforming processing route has been developed that produces a microporous form of ultra high molecular weight polyethylene that demonstrates large negative Poissons ratios. The microstructure consists of nodules interconnected by fibrils. Poissons ratios as low as −1.2 have been obtained, depending on the degree of anisotropy in the material.

Fabrication methods for auxetic foams

Auxetic materials have a negative Poissons ratio, that is, they expand laterally when stretched longitudinally. Negative Poissons ratio is an unusual property that affects many of the mechanical properties of the material, such as indentation resistance, compression, shear stiffness, and certain aspects of the dynamic performance. The unusual mechanical properties of auxetic foams are attributed to the deformation characteristics of re-entrant microstructures. One way of obtaining negative Poissons ratio is by using a re-entrant cell structure. Auxetic foam was fabricated from a conventional polymeric foam. The fabrication method for making both small and large auxetic foam specimens is described.

The design of doubly curved sandwich panels with honeycomb cores

Abstract Conventional sandwich panels that are made from a thick, two-dimensional honeycomb core with laminated outer skins are normally only fabricated as flat panels. Attempts to produce doubly curved panels lead to failure of the core by local buckling of the honeycomb cell walls. It is shown that, by modifying the honeycomb geometry, a range of doubly curved panel cores can be formed that can be either synclastic or anticlastic. Varying the cell geometry produces different combinations of curvature, honeycomb density and mechanical properties. The inter-relationship between these different properties is illustrated.