Auxetic Foams Research Articles

Room-Temperature, Near-Instantaneous Fabrication of Auxetic Materials with Constant Poisson's Ratio over Large Deformation.

A novel compressed carbon dioxide assisted fabrication method is demonstrated to produce auxetic PU foam. Auxetic PU foams can be fabricated at room temperature (25°C) in several seconds with compressed CO2. This technology overcomes some key challenging issues in the large-scale production of auxetic PU foams.

On the successful fabrication of auxetic polyurethane foams: Materials requirement, processing strategy and conversion mechanism

This study aims to provide fundamental understandings in several issues critical to the fabrication of auxetic polyurethane (PU) foams by thermal compression process: conversion and auxetic structure fixation mechanisms, materials characteristics essential for the successful auxetic conversion, and optimal conditions for auxetic conversion. Three flexible PU foams with similar morphology were selected for the study. First the commonalities as well as the differences between these foams in terms of their chemical composition, microstructure and thermomechanical properties were thoroughly analyzed. This is followed by the auxetic convertibility study of these three foams. Mechanisms for fixing the structure were elucidated and the windows for processing were interpreted in the context of polymer relaxation. Guided by these understandings, a series of auxetic foams were manufactured at a wide range of conditions. The processing conditions agreed very well with those suggested from the mechanistic investigation, validating the proposed auxetic conversion and structure fixation mechanisms. The mechanism was further confirmed by direct observation of the morphology of the fabricated auxetic foams.

A Comparison of Novel and Conventional Fabrication Methods for Auxetic Foams for Sports Safety Applications

This study compares fabrication methods for auxetic foam intended for use in sports safety equipment. Thermo-mechanical conversion methods were applied using: i) cubic moulds (150x150x150mm), ii) cuboidal moulds (150x150x30mm) & iii) cuboidal moulds (150x150x30mm) with through-thickness pins. The cuboidal moulds having one reduced dimension relative to the cubic moulds enable faster heat transfer and more consistent through-thickness compression to the foam during conversion. The through-thickness pins allow greater control of in-plane compression throughout the bulk of the converted foam. Samples were compared using: i) density measurements and measurements of total surface folding (length multiplied by depth), ii) quasi-static compressive load/unload tests to obtain specific strain energy, stress/strain relationship and Poisson's ratio, iii) impact testing on a bespoke drop rig based on a standard for cricket pads (BS 6183-3: 2000, EN 2001) at 5, 10 and 15J & iv) microscopic images of dissected samples to confirm their auxetic (re-entrant) structure. Samples fabricated in cuboidal moulds show less variation in final density, axial compressive stiffness and specific strain energy between samples than those cut from monoliths fabricated in cubic moulds. Samples created with through-thickness pins exhibited reduced surface folding. Greater control over final properties paves the way for further work designing auxetic foams for sport safety equipment.

Crashworthiness assessment of auxetic foam-filled tube under quasi-static axial loading

This present study investigates experimentally and numerically the crush response and energy absorption performances of auxetic foam-filled square tubes under quasi-static axial loading. Three different structures: empty, conventional and auxetic foam-filled square tubes have been compared and examined with respect to the deformation modes and load–displacement curves. Standard compression tests were conducted on the tubes to evaluate the influence of auxetic foam in the energy absorption of empty tubes. Moreover, results from computer simulation have also been supplemented to further examine the abovementioned effect. It is discovered that the auxetic foam-filled square tube is superior to empty and conventional foam-filled square tubes in terms of all studied crashworthiness indicators.

How does negative Poisson’s ratio of foam filler affect crashworthiness?

Abstract As an effective candidate for enhancing energy absorption, a range of foam materials have gained considerable popularity, in which the density, Young’s modulus and plasticity of foam materials are considered critical to crashworthiness. Relatively speaking, less attention has been paid to the roles played by the Poisson’s ratio of foam or cellular materials. More importantly, the interaction between different Poisson’s ratios and thin-walled structures has been a critical yet under-studied issue. This paper aims to explore the effects of negative, zero and positive Poisson’s ratio of auxetic foams, ranging from −1 to 0.5, on structural crashworthiness and seek optimal design for different foam-filled square, circular and conic tubes. In this study the specific energy absorption (SEA) and mean crushing force (MCF) are taken as the objective functions by using mathematical regression analysis. The sequential quadratic programming (SQP) and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are employed for single and multiobjective design of foam-filled tubes with different Poisson’s ratios, respectively. The optimal Poisson’s ratio is obtained for these three different types of foam-filled tubes. By comparison we found that the crashworthiness of foam filled conic tube is the best, followed by circular and then squared tubes. The study provides new insights into material selection and design with a more favorable Poisson’s ratio for crashworthiness.

Nonlinear elasticity of auxetic open cell foams modeled as continuum solids

Structure evolution during deformation of isotropic auxetic foams is investigated by simple compression experiments. It is shown that the main feature observed in the experimental data can be accurately described by an isotropic hyperelastic model with an Ogden-type strain energy function. The model can be easily implemented in a finite element code and, hence, can be used to simulate foams undergoing complex structural deformations.

Low‐kinetic energy impact response of auxetic and conventional open‐cell polyurethane foams

This paper reports quasi‐static and low‐kinetic energy impact testing of auxetic and conventional open‐cell polyurethane foams. The auxetic foams were fabricated using the established thermo‐mechanical process originally developed by Lakes. Converted foams were subject to compression along each dimension to 85% and 70% of the unconverted dimension during the conversion process, corresponding to linear compression ratios of 0.85 and 0.7, respectively. The 0.7 linear compression ratio foams were confirmed to have a re‐entrant foam cell structure and to be auxetic. Impact tests were performed for kinetic energies up to 4 J using an instrumented drop rig and high speed video. A flat dropper was employed on isolated foams, and a hemispherical‐shaped dropper on foams covered with a rigid polypropylene outer shell layer. The flat dropper tests provide data on the rate dependency of the Poisson's ratio in these foam test specimens. The foam Poisson's ratios were found to be unaffected by the strain rate for the impact energies considered here. Acceleration‐time data are reported along with deformation images from the video footage. The auxetic samples displayed a six times reduction in peak acceleration, showing potential in impact protector devices such as shin or thigh protectors in sports equipment applications.

Auxetic epoxy foams produced by solid state foaming

Auxetic epoxy resin foams were produced by solid-state foaming thanks to the use of properly shaped precursors. In fact, a re-entrant hexagonal shape of the precursors is preserved during foaming and results in a foam with a complex structure: a thin macro-structure with the re-entrant geometry filled with foam. The auxetic behavior was observed by using tensile tests at different temperatures (room temperature, 80℃, and 100℃). Indentation tests were also carried out to evaluate the gradient properties across the lines of the thin re-entrant macro-structure. In order to show that the auxetic behavior depended on the internal macro-structure, tests were also performed on foam panels obtained by cylindrical tablets and, therefore, with a standard-hexagonal macro-structure. In conclusion, the auxetic behavior was observed only for the foam panels with re-entrant hexagonal structure at 80℃. In this case, a negative Poisson’s ratio is immediately achieved at small strains and tends to a zero plateau value for longitudinal strains up to 1%.

Auxetic Foams for Sport Safety Applications

Auxetic materials offer potential to be applied to sports safety equipment. This work reports quasi-static and impact testing of auxetic open-cell polyurethane foam - fabricated with a compression and heat treatment process - in comparison to its conventional counterpart. The foam was compressed to 70% of its original dimension along each dimension during the conversion process. Quasi-static compression testing confirmed the converted foam to be auxetic, with a Poisson's ratio of -0.08. Impact testing was performed for energies up to 5.6J with an instrumented drop rig and high-speed video. Peak accelerations were ∼3 times lower for the auxetic foams, because they prevented bottoming. This work has shown further potential for auxetic foam to be applied to sports safety devices. Future work should look to optimise foam selection and the conversion process, while comparing auxetic foam with existing materials and products.

Experimental Investigation on Energy Absorption of Auxetic Foam-filled Thin-walled Square Tubes under Quasi-static Loading

Auxetic materials are modern class of materials that have recently been gaining popularity within the research community due to their enhanced mechanical properties. Unlike conventional materials, they exhibit a negative Poisson's ratio when subjected to a uniaxial loading. This present research experimentally investigates the crush response and energy absorption performances of auxetic foam-filled square tubes under axial loading. For comparison, the crush response and energy absorption of empty and conventional foam-filled squares tubes have also been examined with respect to deformation modes and force displacement curve. Standard compression tests were conducted on a series number of thin-walled tube samples. An additional compression test on conventional and auxetic foam has also been conducted to observe the behavior of foam itself. It is evident that the auxetic foam-filled square tubes are superior to empty and conventional foam-filled square tubes in terms of energy absorption capacity. It shows that such tube is preferable as an impact energy absorber due to their ability to withstand axial loads effectively. Furthermore, it is found that the load capacity increases as the crush length increases. The primary outcome of this study is design information for the use of auxetic foam-filled square tubes as energy absorbers where impact loading is expected particularly in crashworthiness applications.

New Approach for Fabrication of Auxetic Foam and Determination of Poisson's Ratio

Conventional foam could be converted to auxetic foam under auxeticity process. A new and simple technique to fabricate auxetic foam and to further determine its Poisson’s ratio is described in this paper. It is evident that the present modified technique in fabricating auxetic foam could be adopted to produce desirable auxeticity characteristics. Moreover, the approach used for determination of Poisson’s ratio has considerably merit with great cost effectiveness. This method is, however, specific to auxetic foam sample under compression loading.

Characterization of auxetic polyurethanes foam for biomedical implants

AbstractAging, accidents and diseases are the leading causes of disability in today’s world. Therefore, implants and prostheses for hard and soft tissues are becoming increasingly common to restore daily activity and improve the quality of life of patients. Although implants have been extensively developed and are in the clinical use, deformation mechanism, inflexibility and mismatch of the elastic and mechanical behavior of the implants with native tissues are challenges for tissue engineering. The objective of this study was to characterize auxetic polyurethane foam as an auxetic soft tissue implant based on mathematical modeling using a nonlinear elasticity theory. The compressibility effects on auxetic soft tissue implants due to equibiaxial loading were studied. Numerical results were computed using experimentally obtained data and compared with the non-auxetic behavior of a soft tissue.

Fatigue Properties of Polyurethane Foams, with Special Emphasis on Auxetic Foams, Used for Helicopter Pilot Seat Cushion Inserts

Abstract Seat cushion inserts in military helicopters crew seats, as suggested by the helicopters manufacturers, are made of traditional polyurethane foams. Elastic polyurethane auxetic foams are materials that exhibit different utility properties compared to traditionally used polyurethane foams, such as polyether or polystyrene foams. All the differences result from the primary physical property of elastic polyurethane auxetic foams which is a negative Poisson’s ratio. Auxetic materials are characterized by better utility properties than conventional foam materials – they can potentially increase safety in the event of a crash and offer higher comfort during regular use. Application of auxetic materials as seat cushion inserts would also decrease harmful health effects of vibrations. This paper presents the results of the fatigue tests carried out on different foam samples by pressing an indenter into the foams' surface that was much larger than the indenter’s surface. A maximum value of the load used during the test was within a defined range in every fatigue cycle. In order to test 150×150×50 mm foam samples a special indenter was designed and manufactured according to the PN-EN ISO 3385 and PN-EN ISO 2439 standards. The indenter’s dimensions were consistent with the standards in relation to the tested foams' size. The fatigue tests of both conventional and auxetic foams were carried out according to the above given standards by applying 80,000 load cycles at 70 cycle/min frequency. Tests of viscoelastic foam and multilayer foam specimens, for which the upper layer was made of viscoelastic foam, were carried out according to the ASTM D 3574 standard applying 12,000 load cycles at 10 cycle/min frequency. All the tests were carried out using the MTS 370.10 strength testing machine. Changes in thickness and density were determined throughout the tests. Moreover, the influence of the volumetric compression ratio on the fatigue properties of auxetic foam samples and the dependence of foam deflection on the number of cycles were examined. Finally, the test results obtained for conventional and auxetic foams were compared and discussed.

The effect of irregularity, residual convex units and stresses on the effective mechanical properties of 2D auxetic cellular structure

The purpose of the present study is to investigate the influences of changes in the microstructure of the re-entrant auxetic foam during the conversion-based fabrication on its elastic and plastic behaviors. The 2D re-entrant honeycomb is used for the finite element (FE) study. The FE method is firstly validated with theoretical calculations. Then, for the first time, the irregularity of the re-entrant honeycomb is considered in the study of irregularity–mechanical relationship. Compared to the regular re-entrant honeycomb, the irregular structures tend to have lower magnitudes of the effective elastic modulus, yield strength and Poisson׳s ratio. It is also highlighted that the irregularity has indirect effects on the effective mechanical properties of the re-entrant honeycomb by changing its relative density. Moreover, the residual convex units (the uncompressed convex corners of the conventional foams during the conversion-based fabrication) make the Poisson׳s ratio of the re-entrant honeycomb less negative. Therefore, the superior abilities brought by the negative Poisson׳s ratio such as the shear modulus and indentation hardness can be impaired by the residual convex units. Besides, the role of the residual stress is also explored with FE methods. The present study is helpful to the understanding of the structure–mechanical relationship in the auxetic foams.

Negative Poisson’s ratio behavior of idealized elastomeric auxetic cellular structures for various carbon black nanoparticles loadings

Auxetic materials exhibit a negative Poisson’s ratio behavior that makes them useful for a variety of structural applications by virtue of their ability to counterintuitively deform due to a reentrant cellular structure. This property allows the cellular material to expand laterally when pulled in the longitudinal direction or, conversely, contract laterally when compressed, with the manner of deformation of the internal structure depending upon the configuration of the cellular structure. The purpose of this research was to develop carbon black nanoparticle-reinforced natural rubber vulcanizates and to investigate the effects of carbon black reinforcement on the mechanical behavior of an idealized auxetic foam structure using modeling and numerical simulation techniques. This has been achieved by mechanically characterizing vulcanized natural rubber of various nanoparticle loadings and then using the test data to perform finite element (FE) simulations on the foam models. Material models have been developed in the FE simulation software ANSYS by curve fitting experimental data (hyperelastic) to theoretical material models. Large deformation analysis of this foam structure has been carried out to determine structural reorganizations and negative Poisson’s ratio effect in the foam structure.

A continuum hyperelastic model for auxetic materials

We propose a simple mathematical model to describe isotropic auxetic materials in the framework of the classical theory of nonlinear elasticity. The model is derived from the Blatz–Ko constitutive equation for compressible foams and makes use of a non-monotonic Poisson function. An application to the modelling of auxetic foams is considered and it is shown that the material behaviour is adequately described with only three constitutive parameters.

Auxetic Materials and Related Systems

to mechanical metamaterials and related systems with particular emphasis on auxetic systems. Such materials show counter-intuitive, negative behaviours. For example, auxetic materials exhibit negative Poisson’s ratios which mean that these systems get fatter rather than thinner when stretched. Due to the superior properties exhibited by these systems, their study and characterisation has experienced a signifi cant increase, particularly in the last decade, something which may be perceived from the always increasing number of publications and patents in these areas. In fact, this issue is the seventh in a series of special issues published in physica status solidi (b) dedicated to auxetic materials and related systems (see [1–6]).

Modeling auxetic foams through semi-rigid rotating triangles

Auxetic foams have been widely studied in view of their superior properties and many useful applications and various models have been developed to help explain the auxetic behavior in such foams. One such model involves the description of auxetic foams in terms of rotating units (e.g. the joints where different cell walls meet), a mechanism, which has also been observed experimentally. In the models, the rotating units are taken, to a first approximation, to be representable through rotating rigid triangles, which correspond to the 2D projection of these rotating units and although this model has been improved significantly since it was first proposed, current models still do not fully capture all the deformations that may occur in real foams. In this work, we propose an extended model which not only allows for relative rotation of the units (joints), represented by non-equilateral triangular units, but also for differing amount of material at the joints as well as deformation of the joints themselves, a scenario that is more representative of real auxetic foams. This model shows that, by permitting deformation mechanisms other than rotation of the triangles, the predicted extent of auxeticity decreases when compared to the equivalent idealized rotating rigid triangles model, thus resulting in more plausible predictions of the Poisson's ratios. Furthermore, it is shown that in the manufacturing process, a minimum compression factor, which is dependent on the amount of materials at the joints, is required to obtain an auxetic foam from a conventional foam, as one normally observed in experimental work on foams.

Auxetic Materials for Sports Applications

In this paper, the auxetic effect is introduced, the range of auxetic materials is briefly reviewed, and research demonstrating benefits having potential in sports applications is highlighted. These include the use of auxetic materials in impact protector devices (pads, gloves, helmets and mats) exploiting better conformability for comfort and support, and enhanced energy absorption for lighter and/or thinner components. FE simulations are reported for a new type of auxetic honeycomb having potential in helmet applications, along with indentation testing of auxetic and non-auxetic foams for assessment in protective pads and running shoes applications, for example.

Experimental studies on the impact properties of auxetic materials

This paper reports an experimental investigation on the effect of auxeticity towards impact loads. Both conventional and auxetic polyurethane (PU) foams were subjected to impact drop tests, and the damaged surfaces were visually inspected. Although it is known that auxetic materials resist indentation due to densification along the load line, experimental impact tests on conventional and auxetic PU foams reveal that auxetic foams are not necessarily advantageous over conventional ones for very high impact. This paper proposes a geometrical model that resembles the microstructure of auxetic foams, as well as elucidates both the auxetic behavior and the limiting strength at high impact.