Fabrication methods for auxetic foams

Auxetic materials have a negative Poisson's ratio, that is, they expand laterally when stretched longitudinally. Negative Poisson's 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 Poisson's 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. This revised version was published online in November 2006 with corrections to the Cover Date.     

Stiffness and energy dissipation in polyurethane auxetic foams

Auxetic open cell polyurethane (PU) foams have been manufactured and mechanically characterised under cyclic tensile loading. The classical manufacturing process for auxetic PU foams involves multiaxial compression of the conventional parent foam, and heating of the compressed specimens above the T_m of the foam polymer. Eighty cylindrical specimens were fabricated using manufacturing routes modified from those in the open literature, with different temperatures (135 °C, 150 °C), compression ratios and different cooling methods (water or room temperature exposure). Compressive tensile cyclic loading has been applied to measure tangent modulus, Poisson’s ratios and energy dissipated per unit volume. The results are used to obtain relations between manufacturing parameters, mechanical and hysteresis properties of the foams. Compression, both radial and axial, was found to be the most significant manufacturing parameter for the auxetic foams in this work.     

Physical and thermal effects on the shape memory behaviour of auxetic open cell foams

This study examines the processing envelope related to auxetic open cell foams and their shape memory properties, with the analysis of four different phases of multi-component foams (conventional, 1st auxetic, returned and 2nd auxetic). The analysis of the shape memory and its correlation with negative Poisson’s ratio behaviour are a novelty in the field of auxetic materials. This study describes the differences between the multi-component foams used as precursors for each phase, exploring their mechanical and thermal characteristics at each stage of the conversion. The results show the important differences related to the mechanical behaviour of the foams, due essentially to the axial compression adopted during the manufacturing process.     

Kinematical studies on rotation-based semi-auxetics

Auxetic materials are those which exhibit negative Poisson’s ratio, i.e. these solids expand transversely when stretched longitudinally. In recent years the concept of semi-auxetics has been examined for cellular solids based on combination of re-entrant and hexagonal microstructures. In this paper we identify a type of rotating unit that gives positive Poisson’s ratio so that a study can be made on rotating sub-structures that exhibit both positive and negative Poisson’s ratio characteristics. A second type of rotating geometry, whose Poisson’s ratio shifts from negative to positive as stretching increases, has also been identified. Based on kinematical studies we explore the relationship between the on-axis Poisson’s ratios in terms of novel lattice geometry and the magnitude of deformation.     

Equivalent mechanical properties of auxetic lattices from discrete homogenization

Auxetic materials having a network like structure are analyzed in terms of their deformation mechanisms and equivalent homogenized mechanical properties thanks to the discrete asymptotic homogenization method. This systematic and predictive methodology is exemplified for five different 2D periodical lattices: the re-entrant hexagonal, hexachiral, cross chiral, rafters and the re-entrant square. The equivalent moduli and Poisson’s ratio are expressed in closed form versus the microbeam geometrical parameters and rigidities. As a novel result, the predicted homogenized properties depend on the slenderness of the beam, hence providing more accurate results in comparison to the literature. The studied lattices allow to explore the two main mechanisms responsible for negative Poisson’s ratio, the re-entrant and the rolling-up mechanism. Non-standard overall behaviors, such as traction-shear coupling occurring for the cross chiral lattice, are evidenced. Negative values of the Poisson’s ratio are obtained in a certain range of the configuration parameter of each lattice. Comparisons of the obtained homogenized moduli with finite element simulations show a very good accuracy of the predicted effective mechanical behavior.     

A generalised three-dimensional tethered-nodule model for auxetic materials

Models for the nano/micro-structural deformation and mechanical properties of auxetic materials (i.e. materials with a negative Poisson’s ratio) have been previously developed. However, most of these models have been two-dimensional, were usually designed specifically to describe some particular class of auxetic materials, and generally only described the behaviour of one particular plane whilst completely ignoring the out-of-plane behaviour of the material. A three-dimensional model has been developed which can be applied to several classes of auxetic materials, including microporous expanded polymers such as e-PTFE, e-UHMWPE and e-PA, body-centered cubic metals and foams. It is generalised that its underlying structure is not specific to a lengthscale or material as the previous list shows. The new model offers a better insight into the underlying principles behind the observed auxetic behaviour and offers a significant improvement in the agreement of the models with existing experimental data. It is shown that there are geometric limitations to the number of planes that can simultanesously display auxetic behaviour. This has ramifications on the design of ordered auxetic materials.     

The effect of processing parameters on the mechanical properties of auxetic polymeric fibers

Auxetic polymeric fibers have been produced using a melt-spinning technique. The effect of the processing parameters on the fibers has been examined. It was found that the auxetic effect occurs over a very tight temperature window with screw speed, take-off speed and die geometry affecting homogeneity and auxeticity. This is an important finding as it provides a method of producing more homogeneous auxetic fibers with tailored values of Poisson’s ratio.     

Three-Point Bending Behavior of Foam-Filled Conventional and Auxetic 3D-Printed Honeycombs

Cellular hexagonal (conventional) and re-entrant (auxetic) honeycombs are applicable in automotive, construction, and protective engineering. Auxetic structures own excellent energy absorption and flexural behavior due to their special deformation under loading. This work explores the performance of additively manufactured polylactic acid (PLA)- and thermoplastic polyurethane (TPU)-based hexagonal and re-entrant honeycombs under flexural loading via experimental three-point bending (TPB) tests and finite-element analysis (FEA). 3D-printed conventional and auxetic cellular structures are filled with polyurethane (PU) foam and their energy absorption capacity and flexural modulus are compared with hollow structures. The results reveal that TPU-based structures’ energy absorption capacity and flexural modulus improve significantly, whereas the PLA-based structures’ performance deteriorates when filled with PU foam. Moreover, re-entrant honeycombs are better reinforced with foam in comparison to the hexagonal honeycombs, as the re-entrant's unit cell is more spacious than the hexagonal unit cell. Finally, parametric studies are performed via FEA to investigate the influence of geometric parameters of structures and flexural loading setup on the performance of the honeycombs, showing that structures with thicker struts and higher cell angle can act stiffer under TPB. The outcomes of this research indicate the promising performance of foam-filled TPU-based auxetic structures.     

An Auxetic structure configured as oesophageal stent with potential to be used for palliative treatment of oesophageal cancer; development and in vitro mechanical analysis

Oesophageal cancer is the ninth leading cause of malignant cancer death and its prognosis remains poor. Dysphagia which is an inability to swallow is a presenting symptom of oesophageal cancer and is indicative of incurability. The goal of this study was to design and manufacture an Auxetic structure film and to configure this film as an Auxetic stent for the palliative treatment of oesophageal cancer, and for the prevention of dysphagia. Polypropylene was used as a material for its flexibility and non-toxicity. The Auxetic (rotating-square geometry) structure was made by laser cutting the polypropylene film. This flat structure was welded together to form a tubular form (stent), by an adjustable temperature control soldering iron station: following this, an annealing process was also carried out to ease any material stresses. Poisson’s ratio was estimated and elastic and plastic deformation of the Auxetic structure was evaluated. The elastic and plastic deformation behaviours of the Auxetic polypropylene film were evaluated by applying repetitive uniaxial tensile loads. Observation of the structure showed that it was initially elastically deformed, thereafter plastic deformation occurred. This research discusses a novel way of fabricating an Auxetic structure (rotating-squares connected together through hinges) on Polypropylene films, by estimating the Poisson’s ratio and evaluating the plastic deformation relevant to the expansion behaviour of an Auxetic stent within the oesophageal lumen.     

Torsion of semi-auxetic rods

A method for quantifying the overall Poisson’s ratio of a rod undergoing torsional loading is proposed and applied for a concentrically compound rod with inner core and outer shell of similar shape but opposite Poisson’s ratio signs. Results show that a concentric compound rod with auxetic core exhibit same effective Poisson’s ratio signs but with greater magnitude under torsional loading than under axial loading. However, a concentric compound rod with auxetic shell exhibits a range of volume fraction whereby the overall auxeticity of the rod is loading mode dependent, i.e., it behaves as a conventional rod under axial loading but as an auxetic rod under torsional loading. Hence a compound rod with conventional core and auxetic shell can be used as a smart structure that gives different response depending on the type of loading imposed on it.     

Interlocking hexagons model for auxetic behaviour

A 2D ‘Rough Particle’ model consisting of interlocking hexagons is reported. Analytical expressions for the in-plane Poisson’s ratios and Young’s moduli due to particle translation along the geometrically matched male and female interlocks are derived for the model. The dependency of the mechanical properties on each of the model (geometrical and stiffness) parameters is provided, and it is shown that the assembly of interlocking hexagons deforming by particle translation along the interlocks displays auxetic (negative Poisson’s ratio) behaviour. The model predictions are compared with experimental mechanical properties for auxetic polypropylene (PP) films and fibres. The model predicts the experimental Poisson’s ratio values very well (model: ν_xy = −1.30, ν_yx = −0.77; experiment (PP films): ν_|| = −1.12, ). The model generally overestimates the Young’s moduli of the films, but is in reasonable agreement with the axial Young’s modulus of the fibres.     

Modelling concurrent deformation mechanisms in auxetic microporous polymers

A 2D model for the deformation of auxetic microporous polymers (those with a negative Poisson’s ratio) has been previously developed, consisting of a network of rigid rectangular nodules interconnected by fibrils. This model has now been extended to describe the deformation of the network via concurrent fibril hinging and stretching mechanisms. Expressions for the strain-dependent Poisson’s ratios and Young’s moduli are derived and fully investigated with respect to their dependence on the model parameters. These expressions are compared with the experimental strain-dependent data for auxetic microporous polytetrafluoroethylene (PTFE) and ultra-high molecular weight polyethylene (UHMWPE). The use of concurrent deformation mechanisms makes a very significant improvement in the agreement of theory with experiment for both cases. Slight discrepancies are discussed in terms of the use of the assumptions of a 2D network of regular, rectangular nodules and a constant force coefficient ratio governing the two deformation mechanisms. This revised version was published online in November 2006 with corrections to the Cover Date.     

Holographic study of conventional and negative Poisson's ratio metallic foams: elasticity,yield and micro-deformation

An experimental study by holographic interferometry is reported of the following material properties of conventional and negative Poisson's ratio copper foams: Young's moduli, Poisson's ratios, yield strengths and characteristic lengths associated with inhomogeneous deformation. The Young's modulus and yield strength of the conventional copper foam were comparable to those predicted by microstructural modelling on the basis of cellular rib bending. The re-entrant copper foam exhibited a negative Poisson's ratio, as indicated by the elliptical contour fringes on the specimen surface in the bending tests. Inhomogeneous, non-affine deformation was observed holographically in both foam materials.     

Composites with auxetic inclusions showing both an auxetic behavior and enhancement of their mechanical properties

Composite materials made of auxetic inclusions and giving rise overall to negative Poisson’s ratio are considered, adopting a two-steps micromechanical approach for the calculation of their effective mechanical properties. The inclusions consist of periodic beam lattices, whose equivalent mechanical properties are calculated by a discrete homogenization scheme in a first step. The hexachiral and hexagonal reentrant lattices are considered as representative of the two main deformation mechanisms responsible for auxeticity. In a second step, the equivalent properties of the composite are calculated from numerical homogenization using the finite element method. It is shown that both an auxetic behavior and enhanced moduli can be obtained for not too slender micro-beams.     

Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading

Finite element models are developed for the in-plane linear elastic constants of a family of honeycombs comprising arrays of cylinders connected by ligaments. Honeycombs having cylinders with 3, 4 and 6 ligaments attached to them are considered, with two possible configurations explored for each of the 3- (trichiral and anti-trichiral) and 4- (tetrachiral and anti-tetrachiral) connected systems. Honeycombs for each configuration have been manufactured using rapid prototyping and subsequently characterised for mechanical properties through in-plane uniaxial loading to verify the models. An interesting consequence of the family of ‘chiral’ honeycombs presented here is the ability to produce negative Poisson’s ratio (auxetic) response. The deformation mechanisms responsible for auxetic functionality in such honeycombs are discussed.     

Comparison of the Mechanical Behaviour of Standard and Auxetic Foams by X‐ray Computed Tomography and Digital Volume Correlation

The tensile behaviour of standard and auxetic polyurethane foams are contrasted by digital volume correlation of 3D images collected by in situ X‐ray computed tomography (CT). It was found that subset sizes of 32 and 64 voxels for the auxetic and standard foams were optimal for strain resolutions in the order of 0.1%. For the standard foam, good uniformity of strain was observed at low strains giving a tangent Poisson's ratio of 0.5. Some heterogeneity of strain was observed at higher strains, which may be related to the fixtures. The behaviour of the auxetic foam was totally different, with strain being spatially heterogeneous with transverse strains both positive and negative but giving a negative Poisson's ratio on average. This suggests that the unfolding tendency of some groups of cells was higher than others because of the complex frozen starting microstructure. Further different methods of deriving Poisson's ratio gave different results. Besides revealing interesting microstuctural mechanisms of transverse straining, the study also shows digital volume correlation of tomography sequences to be the perfect tool to study complex mechanical behaviour of cellular materials.     

3D Fabrics with Negative Poisson’s Ratio: A Review

Applied Composite Materials - Three-dimensional (3D) fabrics with negative Poisson’s ratio (NPR) are known as 3D auxetic fabrics. They expand (or contract) in the direction perpendicular to...     

Development,characterization and analysis of auxetic structures from braided composites and study the influence of material and structural parameters

Auxetic materials are gaining special interest in technical sectors due to their attractive mechanical behaviour. This paper reports a systematic investigation on missing rib design based auxetic structures produced from braided composites for civil engineering applications. The influence of various structural and material parameters on auxetic and mechanical properties was thoroughly investigated. The basic structures were also modified with straight longitudinal rods to enhance their strengthening potential in structural elements. Additionally, a new analytical model was proposed to predict Poisson’s ratio through a semi empirical approach. Auxetic and tensile behaviours were also predicted using finite element analysis. The auxetic and tensile behaviours were observed to be more strongly dependent on their structural parameters than the material parameters. The developed analytical models could well predict the auxetic behaviour of these structures except at very low or high strains. Good agreement was also observed between the experimental results and numerical analysis.     

Development of novel auxetic structures based on braided composites

Auxetic materials are a class of materials that expand transversely when stretched longitudinally. Recently, auxetic materials are gaining special interest in the technical sectors mainly due to their attractive mechanical behavior. This paper reports, for the first time, the development of auxetic structures from composite materials and the characterization of their auxetic as well as mechanical properties. Five different auxetic structures were developed varying their structural angle using core reinforced braided composite rods, containing glass fibers for axial reinforcement, polyester filaments for braided structure and epoxy resin as the matrix. Auxetic behavior of these structures was studied in a tensile testing machine using an image-based tracking method. Additionally, an analytical model was used to calculate Poisson’s ratio of these structures. According to experimental and analytical results, auxetic behavior and tensile characteristics of these structures were strongly dependant on their initial geometric configuration (i.e. structural angle). These novel auxetic structures exhibited Poisson’s ratio in the range of −0.30 to −5.20.