Preface: phys. stat. sol. (b) 244/3
Authors: Wojciechowski Krzysztof W. , Alderson Andrew , Alderson Kim L. , Maruszewski Bogdan , Scarpa Fabrizio 
Published: February 2007

This is the 2nd special issue of physica status solidi (b) dedicated to materials exhibiting negative Poisson's ratio (auxetic) or other unusual or counter‐intuitive physical behaviour. This issue contains selected papers from the 2nd Workshop on Auxetics and Related Systems held at Będlewo near Poznań, Poland, on 19–23 August 2005 (http://www.ifmpan.poznan.pl/zp10/auxet2/main.html). With around 40 participants at the workshop from across the world, the workshop proved to be a successful follow‐up to the 1st workshop held the previous year.

The selected papers fall into one (or more) of the following broad categories: ‘Mechanisms and bounds on auxetic behaviour’; ‘Optimisation and design of auxetic composites’; ‘Processing of auxetic materials’; and ‘Other unusual property materials’.

In advancing our understanding of mechanisms for auxetic behaviour a common approach is to establish a geometrical framework and explore how this might deform to give rise to the negative Poisson's ratio effect. The paper by Grima et al. on “Auxetic behaviour from rotating semi‐rigid units” employs molecular mechanics and analytical modelling methodologies to explore the role of a framework of deformable rotating squares in producing auxetic behaviour. It is demonstrated how this model is applicable to interesting materials such as zeolites with analogous structural features at the molecular length scale. Kimizuka et al. report in their paper “Atomic characterisation of structural and elastic properties of auxetic crystalline SiO2” on the use of first‐principles calculations to predict the elastic constants for α‐quartz and α‐cristobalite. The role of deformation mechanisms of the 3D framework of connected SiO4 tetrahedra is considered and the enhancement of the auxetic effect under ‘negative pressure’ is explored. In the paper “Elastic properties of two‐dimensional soft polydisperse trimers at zero temperature” Narojczyk and Wojciechowski describe computer simulations of a molecular auxetic model of cyclic trimers. They show that the Poisson's ratio grows with increasing size polydispersity of the particles. The system remains, however, auxetic for a broad range of interaction potentials and polydispersities what may allow one to manufacture real auxetics built of trimers. Monte Carlo simulations of periodic and aperiodic solids comprising assemblies of 2D hard body systems are reported by Tretiakov and Wojciechowski in their paper “Poisson's ratio of simple planar ‘isotopic’ solids in two dimensions”. It is shown how the Poisson's ratio increases with decreasing density, and that auxetic behaviour is achieved near close packing by increasing the number of hard discs in the ‘cyclic multimer’ molecules. The possibility of producing highly interwoven regular structures from filamentous objects is considered in a theoretical treatment by Pikhitsa (“Architecture of cylinders with implications for materials with negative Poisson's ratio”). It is implied that random wool‐like filament‐based auxetic materials may be possible, including auxetic nanowire or carbon nanotube ‘wool’.

In two papers by Paszkiewicz and Wolski (“Anisotropic properties of mechanical characteristics and auxeticity of cubic crystalline media” and “Young's and shear moduli and Poisson's ratio for elastic media of high and middle symmetry”) expressions relating the inverse moduli and the Poisson's ratio to the components of the compliance tensor for crystals across a range of symmetry levels are considered. The expressions enable the regions for auxetic behaviour to be established in terms of compliance coefficient maps, and enable the isotropic and anisotropic components of the mechanical properties to be delineated. Xinchun and Lakes use an integral method and Rayleigh quotient to demonstrate in their paper “Stability of elastic material with negative stiffness” how the negative range of Poisson's ratio (ν) for a cylinder of isotropic material can be extended to –∞ < ν < –1. Classical elasticity theory provides for a range of –1 < ν < +0.5 and so this is a remarkable proposition and is achieved by considering the material to possess negative stiffness under partial constraint with an appropriate combination of shear and bulk moduli values.

Auxetic composites are attracting attention for their potential in the development of improved advanced composite systems having enhanced physical properties (such as impact resistance) for lower weight. Harkati et al. consider the effect of fibre type and orientation within composite laminates in their paper on “Modelling the influence of the orientation and fibre reinforcement on the negative Poisson's ratio in composite laminates”. It is shown how the negative through‐thickness Poisson's ratio can be tailored by the choice of fibre reinforcement material (carbon or Kevlar) and laminae stacking sequence. The intriguing potential to develop composite systems having positive Poisson's ratio behaviour in pure axial loading but negative Poisson's ratio behaviour in pure bending, and vice versa, is considered in the paper “On simultaneous positive and negative Poisson's ratio laminates” by Lim. A theoretical 3‐ply laminate is considered to demonstrate analytically the appropriate design of a composite having the proposed loading mode‐dependent sign of Poisson's ratio. In the paper “Exploration of high and negative Poisson's ratio elastomer‐matrix laminates” by Peel, the use of elastomer matrix material having stiffness of the order of 105 times lower than the reinforcing graphite fibre is considered in the development of composites having very large positive or negative in‐plane Poisson's ratios. Both balanced and unbalanced symmetric laminates are investigated and the merits of enhanced shear deformation under axial loading for the unbalanced system are considered in respect of damping applications.

In order to realise the potential of auxetics and related materials it is important to be able to process them into useable forms. With this in mind, a number of papers have been selected dealing with improving the understanding of the effects of processing on the properties of materials. In their paper on “Mass transport properties of auxetic (negative Poisson's ratio) foams”, A. Alderson et al. describe the adaptation of the existing combined heat treatment and compression route for the conversion of conventional thermoplastic foam into auxetic foam to give rise to auxetic and non‐auxetic foams having similar topology and density. The foams are then used to demonstrate the potential of auxetic porous materials in filtration and other mass transport applications. K. Alderson et al. investigate the effects of processing on the formation of the nodule‐fibril microstructure required for auxetic behaviour in microporous polymer cylinders in their paper “Microstructural evolution in the processing of auxetic microporous polymers”. Ultra High Molecular Weight Polyethylene is studied in detail and microscopy characterisation is employed to develop the processing–structure relationships, particularly relating to the sintering and extrusion stages of the fabrication process, which will lead to improved and new auxetic polymers produced by this route. Real materials are often characterised by a degree of disorder and inhomogeneity. This aspect is considered in the paper “Influence of disorder (atomic polydispersity) on the Poisson's ratio” by Narojczyk and Wojciechowski who consider the simulation of 2D soft trimer molecular assemblies. A combined multiscale method encompassing a tight‐binding scheme with the molecular dynamics approach is reported in “Combining tight‐binding and molecular dynamics methods to model the behaviour of metals in the plastic regime” by Bobrowski et al. This method has been developed to understand the effects of ultra‐precision machining of metals, the effects of stress on the breaking of nanowires and fracture of nanoscale materials, for example.

The remainder of the papers are selected based on the potential importance of other materials displaying unusual behaviour. In some cases the materials are at a more advanced stage of development and fundamental understanding than auxetic materials. A number of the papers have very clear synergy with some of the preceding papers on auxetics, ably demonstrating the need to consider a wider range of materials, phenomena and functionality as we drive to improved advanced materials developments. For example, as already noted above, the extension by Xinchun and Lakes of the range of negative Poisson's ratio values for isotropic materials requires the material to possess the related novel property of a negative stiffness. Such a material can be stable under partial constraint without the need for a positive definite strain energy. Imre considers the presence of metastable negative pressure states in the paper “On the existence of negative pressure states”. The limiting negative pressure is considered for both liquids and solids and leads to interesting possibilities relating to the work of Kimizuka et al. above, and others published elsewhere, on the relationship between negative pressure and the auxetic effect. The ‘transport’ theme discussed already in the paper on auxetic foam filters by A. Alderson et al. is developed in other areas in papers by Mukherjee and Singh (“Novel structure and swelling dynamics of nanocomposite ultrathin films”) and Strek and Jopek (“Computer simulation of heat transfer through ferrofluid”). In the former paper the structure and swelling dynamics of ultrathin films of CdS–polyacrylamide nanocomposite ultrathin films were investigated when exposed to H2O vapour. The structure and swelling dynamics are interpreted in terms of the polymer–particle interactions. Strek and Jopek use computational fluid dynamics, modified to account for the magnetic term, to investigate the magneto‐thermo‐mechanical problem of heat flow through a ferromagnetic fluid in the channel between two parallel flat plates under a magnetic field.

Thermoviscoelastic behaviour of the vortex field describing the magnetic flux penetration of a type‐II superconductor is considered by Maruszewski in the paper “On a classical thermoviscomechanical stress in the vortex field in the type‐II superconductor”. The importance of the geometry of the relevant structure upon which phenomena are based is once again demonstrated by the arrangement of vortices of supercurrent in a flux‐line lattice array. Through consideration of soft vortices, a thermoviscoelastic stress–strain constitutive law is developed demonstrating an anomalous thermomechanical property of the vortex field. Continuing along the theme of magnetic functionality, Guskos et al. investigate the potential of incorporating magnetic nanoparticles within a nonmagnetic matrix in their paper on “Magnetic nanoparticles in a nonmagnetic matrix”. Finally, the paper “Non‐finite‐difference algorithm for integrating Newton's motion equations” by Brzostowski et al. describes a numerical algorithm for use in molecular dynamics simulations. It is important, particularly for modelling materials with unusual properties, to maximise the accuracy of the numerical algorithms to ensure the predicted properties are based on the science of the system being studied and are not artefacts of the algorithm being employed in the simulation. The method is applied to the forced linear and nonlinear oscillator and the 2D Lennard–Jones potential.

We would like to gratefully acknowledge the support by the sponsors of the workshop (Academic Computer Centre in Gdansk; UK EPSRC Auxetic Materials Network (AuxetNet); Nonlinear Dynamics and Computer Simulations Laboratory (IFM PAN); Poznan Supercomputing and Networking Centre (Poland); Poznan University of Technology (Poland); University of Bristol (UK)). We also are indebted to the Scientific Committee, the Local Organising Committee, and the participants of the workshop.