Poisson's Ratio Behavior Research Articles

Crash performance of cellular foams with reduced relative density part 2: rib deletion

The finite element method has been used to investigate the crashworthiness of regular conventional and re-entrant cellular foams in pristine and defect forms. Defects were introduced by randomly deleting vertical ribs (cell walls), diagonal ribs and vertical-plus-diagonal ribs from the honeycomb models, which with suitable boundary conditions approximated to three-dimensional foams. Generally, the calculations show that deleting ribs leads to a reduction in magnitude of the Young's moduli and Poisson's ratios, although there are some notable exceptions. In particular, the Young's modulus and Poisson's ratio along the x-axis (perpendicular to the vertical ribs) actually increase in magnitude slightly when vertical ribs are deleted. In the case of the re-entrant honeycomb, a transition from auxetic (negative Poisson's ratio) to non-auxetic (positive Poisson's ratio) behaviour occurs at a critical threshold for diagonal rib deletion. For the conventional honeycomb, the Poisson's ratio for loading in the y-direction remains approximately constant when diagonal ribs are deleted.

Smart shape memory alloy chiral honeycomb

An auxetic (or negative Poisson's ratio) material expands in all directions when pulled in only one, behaving in an opposite way compared with “classical” materials. A structure not super-imposable with its mirror image is defined as chiral. A chiral structural honeycomb (noncentresymmetric) features auxeticity, i.e., a negative Poisson's ratio behaviour in the plane. Although chirality is common in nature and organic chemistry, it is an unusual characteristic in structural materials and components. We have manufactured truss assemblies based on cells of chiral honeycomb topology using shape memory alloy (SMA) ribbons as core material. The main objective of this work is to obtain a new functional structure combining the chiral honeycomb topology and shape memory alloys as a new concept of smart cellular solid. The chiral SMA honeycomb can be used in new types of deployable antenna reflectors, allowing the compression of the structure in a small volume of space for subsequent deployment. The new honeycomb concept could also be used in packaging applications to store strain energy during an impact loading and as a core for a sandwich structure for damping or for crashworthiness.

Atomistic characterization of structural and elastic properties of auxetic crystalline SiO2

AbstractThe structural and elastic changes with volume expansion in α ‐quartz and α ‐cristobalite, the typical polymorphs of silicon dioxide (SiO2), have been studied through first‐principles calculations using the projector‐augmented‐wave (PAW) method, with particular emphasis on their negative Poisson's ratio behavior under negative pressure. The dominant mechanism of expansion is the increase of the Si–O–Si angles within their crystalline structures, whereas the SiO4 tetrahedron undergoes only a slight distortion. We provide theoretical ab initio results for a complete set of independent elastic constants of quartz and cristobalite with volume expansion. The present simulations confirm that the negative Poisson's ratio behavior is enhanced in the expansive phases of both polymorphs under negative pressures, with retaining strong elastic anisotropy. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Preface: phys. stat. sol. (b) 244/3

The 21st Winterschool on Electronic Properties of Novel Materials (IWEPNM 2007) took place from 10 March to 17 March 2007. It continued the tradition of winterschools of this type in Kirchberg/Tirol in its well-known atmosphere of collegiality and emphasis on scientific exchange between young and experienced scientists. The sessions at the IWEPNM 2007 focused on quantum information, carbon nanostructure synthesis, purification and separation, the characterization and properties of carbon nanostructures, fullerenes, endohedrals, and fullerides, excitons in carbon nanotubes, the chemical treatment of carbon nanotubes, nanotube filling and double-walled nanotubes, graphite and graphene, non-carbonaceous nanostructures, electron and heat transport in carbon nanostructures, composites with carbon nanotubes, and on theory and applications of these materials. This proceedings volume is divided into according sections. The program of the Winterschool was composed of invited oral presentations, poster presentations and mini-workshops. The oral presentations were scheduled in morning and evening sessions, the mini-workshops took place during the afternoons, and the posters were presented and discussed in two late-evening sessions. In 2007 the Winterschool celebrated an anniversary: It had been of taking place for the 20th time at the Hotel Sonnenalp, a hotel ideally suited for the close interactions of international participants from many countries. We are grateful to the manager of Hotel Sonnenalp, Frau Edith Mayer, and her staff for the local arrangements as well as for her patience with many special requests during the meeting. We owe special thanks to the hotel staff for their careful organization of the celebration. The event benefited substantially from support of the Universitat Wien and the Verein zur Forderung der Winterschulen in Kirchberg, as well as from numerous industrial sponsors. We greatly appreciate their financial contribution without which the meeting would have hardly become possible. Finally, special acknowledgments go to all contributors of the IWEPNM 2007 and to the authors of this volume, the proceedings of the Winterschool. Viera Skakalova was instrumental in compiling and editing the proceedings. In the name of all participants who have enjoyed the Winterschools since 1985 we express special thanks to Hans Kuzmany for his outstanding engagement in organizing the IWEP for so many years. His experience and advice will be needed for future Winterschools. The next Winterschool in this series will take place from 1 March to 8 March 2008, again in Kirchberg/Tirol, and will be organized by Christian Thomsen from Berlin. Wien, Darmstadt, Stuttgart, Berlin, 2007

Mass transport properties of auxetic (negative Poisson's ratio) foams

AbstractAn auxetic foam structure is described which has the property of widening when stretched (negative Poisson's ratio behaviour), in contrast to the situation with most materials which narrow when stretched. The fabrication of this material involves a combination of heat and compressive treatments of a conventional commercial air‐filtration foam. The resulting microstructure is examined by scanning electron microscopy (SEM). The pertinent mechanical properties are described in terms of the changes in specimen dimensions and associated strains. From these quantities, Poisson's ratios are determined for the large strain regime involved. The property of being able to open pores by stretching the material is a useful feature in various types of filtration application. In particular, where the long‐term efficiency of the process is hindered by ingress of particles into the system which block the active pore structure, the marriage of permeability and mechanical deformation via a negative Poisson's ratio offers an alternative to other methods of clearance. This notion is illustrated by the use of some very simple tests in which the foam is challenged by glass beads of uniform diameter. Simple air pressure‐drop tests are also performed on auxetic and conventional foams to demonstrate that the change in permeability due to mechanical deformation enables a means of varying the pressure‐drop acting across an auxetic foam to a far greater degree than is possible for the conventional foams. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Strain rate dependence of stiffness and Poisson's ratio of auxetic open cell PU foams

AbstractThe paper describes the manufacturing and tensile testing of auxetic (negative Poisson's ratio) thermoplastic polyurethane and polyester urethane foams, under quasi‐static and constant strain rate loading. The foams are produced from conventional flexible polyurethane basis following a manufacturing route developed in previous works. The Poisson's ratio behaviour over compressive strain has been analyzed using an Image Data processing technique based on Edge Detection from digital images recorded using camcorders and high speed cameras. The measurements indicate that higher strain rate loading implies stiffening effects on the stress–strain curves, and significant increase of the magnitudes of the Poisson's ratios with increasing compressive strains. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theoretical approach to Poisson ratio behavior during structural changes in metallic glasses

Recently, various studies dealing with the relationship between the elastic constants and various of the macroscopic properties of metallic glasses have been published. Particularly, the correlations between Poisson's ratio of the glass and both the super cooled liquid viscosity behavior and the brittle-ductile transition have aroused much interest. We use a model developed by Knuyt et al. (1990 and 1991) based on a Gaussian distribution for the nearest-neighbor distance in an ideal unicomponent metallic glass in order to describe qualitatively the dependence of Poisson ratio on changes of the atomic structure. The results are used to explain the experimental results obtained in structural relaxation and hydrostatic pressure tests of metallic glasses.

Evaluation of Mechanical Properties and Negative Poisson's Ratio Behavior in Crystalline SiO2 Materials: An Atomistic Approach

The structural changes with volume expansion in low-temperature (a) phases of quartz and cristobalite, the typical polymorphs of silicon dioxide (SiO2), have been studied through first-principles calculations using the projector-augmented-wave (PAW) method, with particular emphasis on their negative Poisson's ratio behavior. The dominant mechanism of expansion is the increase of the Si-O-Si angles within their crystalline structures, whereas the SiO4 tetrahedron undergoes only a slight distortion. We provide theoretical ab initio results for a complete set of independent elastic constants of quartz and cristobalite with volume expansion. For comparison, the adiabatic elastic constants of both polymorphs are evaluated at finite temperatures, using the molecular-dynamics simulations with a nonempirical pairwise potential. Our calculated elastic properties are found to be in good agreement with the experimental data.

Modelling of the mechanical and mass transport properties of auxetic molecular sieves: an idealised inorganic (zeolitic) host–guest system

Force field based simulations have been employed to model the structure, and mechanical and mass transport properties of the all-silica zeolite MFI (ZSM5—Si96O192). Undeformed and deformed MFI subject to uniaxial loading in each of the three principal directions were investigated. The mechanical properties are predicted to include negative on-axis Poisson's ratios (auxetic behaviour) in the x 1–x 3 plane of the undeformed structure, and are strain-dependent. Transformation from positive-to-negative Poisson's ratio behaviour, and vice versa, is predicted for most on-axis Poisson's ratios at critical loading strains. Simulations of the simultaneous sorption of neopentane and benzene guest molecules onto the undeformed host MFI framework indicate a low neopentane-to-benzene loading ratio, consistent with experimental observation. The sorption of these two molecular species onto deformed MFI is Poisson's ratio- and strain-dependent. Uniaxial tensile loading along a direction containing a negative on-axis Poisson's ratio leads to an increase in the loading of the larger neopentane molecules with respect to benzene, strongly correlated with the increase in volume associated with auxetic behaviour.

Modelling of the mechanical and mass transport properties of auxetic molecular sieves: an idealised organic (polymeric honeycomb) host–guest system

Force field-based simulations have been employed to model the mechanical properties of a range of undeformed molecular polymeric honeycombs having conventional and re-entrant hexagon pores. The conventional and re-entrant hexagon honeycombs are predicted to display positive and negative in-plane Poisson's ratios, respectively, confirming previous simulations. The structure, and mechanical and mass transport properties of a layered re-entrant honeycomb ((2,8)-reflexyne) were studied in detail for a uniaxial load applied along the x 2 direction. The mechanical properties are predicted to be stress- (strain-) dependent and the trends can be interpreted using analytical expressions from honeycomb theory. Transformation from negative to positive Poisson's ratio behaviour is predicted at an applied stress of σ2 = 2 GPa. Simulations of the loading of C60 and C70 guest molecules into the deformed layered (2,8)-reflexyne host framework demonstrate the potential for tunable size selectivity within the host framework. The entrapment and release of guest molecules is attributed to changes in the size and shape of the pores in this host–guest system.

Evaluation of hexagonal chiral structure for morphing airfoil concept

In this paper a concept of hexagonal chiral honeycomb is proposed as a truss-like internal structure for adaptive wing box configurations. In contrast with classical centresym-metric cellular structures like rectangular or hexagonal grids, the proposed honeycomb did not present inversion symmetry, and featured an in-plane negative Poisson's ratio behaviour. The cellular structure considered exhibited this Poisson's ratio behaviour under a large range of strain. A set of numerical (finite element, FE) simulations have been carried out in order to correct the initial theoretical predictions to take into account axial, shear and elastic deformations of all elements composing the unit cell when subjected to uniaxial loading. The homogenized linear elastic mechanical properties were then introduced in an FE wing box model of a racecar wing coupled to a panel code to simulate unidirectional static fluid—structure coupling between the wing box and the flow surrounding the airfoil. The cellular solid proposed as the internal layout of the wing box allowed conforming deformations with the external flow, giving a variation of the camber line and trailing edge displacement, and acting as an aileron

Preface: phys. stat. sol. (b) 242/3

AbstractThis special issue of physica status solidi (b) is dedicated to papers presented, or in a few cases additional to, the Workshop on Auxetics and Related Systems held during 27–30 June 2004 at Będlewo near Poznań, Poland. There were around 40 participants at the workshop from Poland, the United Kingdom, Japan, USA, Belarus, China, Denmark, Germany, Greece, Italy, Malta, Russia, Slovakia and Ukraine. More details on the workshop can be found at http://www.ifmpan.poznan.pl/zp10/auxet/main.html.Auxetic materials exhibit negative Poisson's ratio behaviour. In other words, they expand (contract) transversely when stretched (compressed) lengthwise. They are, thus, examples of one class of 'negative' materials which are currently attracting significant interest. Other negative materials include those having negative stiffness, negative thermal expansion, negative refractive index, negative permittivity and negative permeability. Naturally‐occurring auxetic materials are known and continue to be discovered. However, it was the production of the first synthetic auxetic material (polyurethane foam) by Lakes, closely followed by the discovery of auxetic behaviour in a preconditioned commercially‐available expanded form of polytetrafluoroethylene by Evans, both in the late 1980s, which provided the impetus for the current research into auxetic materials. The range and diversity of attendees at the workshop in Poland reflects the extent to which the field has subsequently developed.Auxetics are of interest both intellectually and also from the point of view of potential applications. From the fundamental perspective, research activities concentrate on structure–property relationships through consideration of materials and mechanisms leading to auxetic behaviour from the nanoscale to the macroscale. The effect of a negative value of Poisson's ratio on the enhancement of related properties is also of keen interest. A combination of theoretical and experimental approaches is being pursued in this respect. In terms of applications‐based research for auxetics, the emphasis is on processing and fabrication of an increased range of auxetic materials, and characterisation of their mechanical and other physical properties (e.g. vibroacoustic damping properties). The papers presented here cover auxetic metals, ceramics, polymers, composites, foams and honeycombs in a variety of forms (e.g. bulk, fibre and thin film).Auxetics represent only one of many materials currently being developed as a result of counterintuitive properties. Papers presented here and also at the workshop include those relating to liquids at negative pressure, nanocrystalline magnets, negative thermal expansion polymer thin films, fractal structures containing negative stiffness components, and nanomechanical properties of metals. It is clear that there are considerable challenges and potential benefits to be gained from the development of multifunctional materials having one or more of the novel properties relating to the materials presented here (and elsewhere). The workshop was successful in achieving the aim of gathering scientists from a range of disciplines from across the world to exchange information relating to materials with unusual mechanical properties in order to provide greater insight into such materials and also to define future research perspectives and priorities. The collection of papers in this special issue captures the current state‐of‐the‐art in this area and provides clear indicators for future developments.We would like to gratefully acknowledge the support by the sponsors of the workshop (Centre of Excellence MMMFE, European Union 6th Framework Programme; Institute of Molecular Physics, Polish Academy of Sciences; State Committee for Scientific Research; UK EPSRC Auxetic Materials Network (AuxetNet)), the Scientific Committee, the Local Organising Committee, and the participants of the workshop.

Auxetic compliant flexible PU foams: static and dynamic properties

AbstractThe paper describes the manufacturing and tensile testing of auxetic (negative Poisson's ratio) thermoplastic polyurethane foams, both under constant strain rate and sinusoidal excitation. The foams are produced from conventional flexible polyurethane basis following a manufacturing route developed in previous works. The Poisson's ratio behaviour over tensile strain has been analyzed using an Image Data processing technique based on Edge Detection from digital images recorded during quasi‐static tensile test. The samples have been subjected to tensile and compressive tests at quasi‐static and constant strain‐rate values (up to 12 s–1). Analogous tests have been performed over iso‐volumetric foams samples, i.e., foams subjected to the same volumetric compression of the auxetic ones, exhibiting a near zero Poisson's ratio behaviour. The auxetic and non‐auxetic foams have been also tested under sinusoidal cycling load up to 10 Hz, with maximum pre‐strain applied of 12%. The hysteresis of the cycling loading curve has been measured to determine the damping hysteretic loss factor for the various foams. The measurements indicate that auxetic foams have increased damping loss factor of 20% compared to the conventional foams. The energy dissipation is particularly relevant in the tensile segment of the curve, with effects given by the pre‐strain level imposed on the samples. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Morphology and Deformation Behaviour of a Liquid Crystalline Polymer Containing Laterally Attached Pentaphenyl Rods

AbstractSummary: The morphology and deformation behaviour of a liquid crystalline polymer consisting of both laterally attached transverse rods and terminally attached rods were studied. A plaque specimen of the polymer was prepared using the melt‐compression method, which exhibited highly anisotropic Poisson's ratio behaviour. In its through‐thickness direction, its Poisson's ratio was approximately 0.54, and in the in‐plane it was approximately 0.43. This anisotropic behaviour is explained by the anisotropic morphology of the polymer plaque resulting from its compression preparation. The high Poisson's ratio in the through‐thickness direction is due to the unusual chain structure of the polymer. A simple analytical model is presented to describe the non‐linear strain dependent Poisson's ratio behaviour of the material.Representation of the arrangement of the main chain and transverse rod molecules, prior to, during, and at complete extension.magnified imageRepresentation of the arrangement of the main chain and transverse rod molecules, prior to, during, and at complete extension.

Auxetic polypropylene films

Auxetic materials are those exhibiting negative Poisson's ratio (ν) behavior. Polymeric auxetic extruded products in the form of cylinders and fibers have previously been reported. This article reports the successful production of auxetic polypropylene films (∼0.15-mm thick) using a melt extrusion process. Video extensometry and tensile testing techniques have been used to measure the in-plane Poisson's ratios and Young's moduli of the auxetic film, both on an Instron tensile testing machine and a Deben microtensile testing machine. The film is elastically anisotropic with the Poisson's ratio and Young's modulus along the extrusion (x) direction being νxy = −1.12 ± 0.06 and Ex = 0.34 ± 0.01GPa, respectively, while the Poisson's ratio and Young's modulus in the transverse (y) direction to the extrusion direction are νyx = −0.77 ± 0.01 and Ey = 0.20 ± 0.01GPa, respectively. POLYM. ENG. SCI., 45:517–528, 2005. © 2005 Society of Plastics Engineers

Elastic model of an entangled network of interconnected fibres accounting for negative Poisson ratio behaviour and random triangulation

A model is designed for predicting the elastic constants of a random planar network of interconnected fibres while accounting for two features of such networks: negative Poisson ratio behaviour and random triangulation. The model is based on a periodic network involving both plates and fibres segments, with possibility of reentrant cell shapes. The plates are intended to represent the effect of triangulation. Bounds for the elastic constants are obtained by calculating volume weighted averages of the elastic properties for periodic networks characterised by a uniform distribution of in-plane fibre orientations. Predictions are derived for the dependence of the in-plane Young’s modulus, out-of-plane Young’s modulus, and in-plane shear modulus on out-of-plane fibre orientation for a fibre volume fraction of 0.20. These predictions are assessed by reference to experimental results for transversely isotropic networks, with very low average out-of-plane fibre orientation, made by sintering compressed mats of stainless steel fibres. A comparison is also made with the predictions of a model for truss lattice core, which is liable to represent the case of a fully triangulated network.

Technique development and measurement of Poisson's ratio, lateral creep behavior, and thermal and hygroscopic expansion of individual layers in magnetic tapes

AbstractAn experimental technique was developed to measure the Poisson's ratio (lateral contraction over longitudinal elongation), lateral creep, and both thermal and hygroscopic expansion of thin polymeric films. A so‐called profile‐matching method was developed to measure the lateral and longitudinal deformation with the help of a laser scan micrometer. A thermomechanical analyzer was used to measure the coefficient of thermal expansion (CTE). The laser scan technique was also used to measure the coefficient of hygroscopic expansion (CHE). The measurements were performed on magnetic tapes, substrates, and tapes with front coat or back coat, or with both coats stripped. A model based on the rule of mixtures was developed to determine the Poisson's ratio, lateral and longitudinal deformation behavior, and thermal expansion of the front coat and back coat. To investigate the mechanical degradation of the substrates during tape manufacturing, the data for substrate with the front and back coats removed from the tape, were compared with the data for the never‐coated virgin film. The relationship between the molecular structure and the degradation mechanism of the substrates is discussed. The magnetic tapes used in this research include two metal particle (MP) tapes and two metal evaporated (ME) tapes that use polyethylene terephthalate (PET) and polyethylene naphthalate (PEN) substrates. Longitudinal and lateral deformation tests were performed at 25 ± 0.5°C and 50 ± 2%RH, and thermal expansion was measured from 15 to 70°C. The CHE was measured at 25 ± 0.5°C and 15–80%RH. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2082–2096, 2003

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Developing a New Processing Route to Manufacture Honeycomb Ceramics with Negative Poisson's Ratio

Materials with negative Poisson's ratios (auxetic materials) have several advantages compared to conventional materials, including increased plane strain fracture resistance and increased shear modulus. A method for the manufacture of honeycomb ceramics with a structure, which yields negative Poisson's ratio is described. Ceramics with cellular or honeycomb structures have applications as substrates in catalytic converters for the emissions from internal combustion engines. In such devices due to the extreme temperature variations, the structure has to provide high thermal shock resistance. It is possible to increase the thermal shock resistance by incorporating specific web geometries. Such structures can absorb or compensate for compressive and tensile stresses generated in the body during thermal expansion and contraction. It is shown that such structures can be produced by the extrusion of ceramic pastes through polymer dies produced by rapid prototyping (selective laser sintering), CAD technology was used to design the die. A ceramic paste based on a zirconia powder was used to make the cellular extruded tube. The negative Poisson's ratio behaviour was confirmed by employing a simple test. (orig.)

Influence of Cell Size on Re-Entrant Transformation of Negative Poisson's Ratio Reticulated Polyurethane Foams

Several foams of different cell-size, including Scott Industrial polyurethane foam with large cells (20 pores per inch, ppi, or 1.2 mm per pore, black), medium cells (65 ppi, or 0.4 mm per pore, green), and near-microcellular (100 ppi, 0.25 mm per pore, white), were processed over various time and temperature regimes to ascertain the role of cell size in transformation to negative Poisson's ratio materials. These foams were transformed successfully, and exhibited negative Poisson's ratio behavior. Poisson's ratio was measured using a new laser based setup. For all as-received (unprocessed) foams with different cell sizes, Poisson's ratio decreased with compressive axial strain and increased with tensile strain up to a maximum. The maximum Poisson's ratio in tension decreased as cell size increases. The strain at which maximum Poisson's ratio occurs, increased with cell size. In negative Poisson's ratio foams, minimum Poisson's ratios of −0.8, −0.5, and −0.4 for 20 ppi, 65 ppi, and 100 ppi foams, respectively were observed. Furthermore, the cell size effects on transformation parameters were also found.