Auxetic Response Research Articles

Finite Element Analysis of the Ballistic Impact on Auxetic Sandwich Composite Human Body Armor.

In this study, the ballistic impact behavior of auxetic sandwich composite human body armor was analyzed using finite element analysis. The auxetic core of the armor was composed of discrete re-entrant unit cells. The sandwich armor structure consisted of a front panel of aluminum alloy (Al 7075-T6), UHMWPE (sandwich core), and a back facet of silicon carbide (SiC) bonded together with epoxy resin. Numerical simulations were run on Explicit Dynamics/Autodyne 3-D code. Various projectile velocities with the same boundary conditions were used to predict the auxetic armor response. These results were compared with those of conventional monolithic body armor. The results showed improved indentation resistance with the auxetic armor. Deformation in auxetic armor was observed greater for each of the cases when compared to the monolithic armor, due to higher energy absorption. The elastic energy dissipation results in the lower indentation in an auxetic armor. The armor can be used safely up to 400 m/s; being used at higher velocities significantly reduced the threat level. Conversely, the conventional monolithic modal does not allow the projectile to pass through at a velocity below 300 m/s; however, the back face becomes severely damaged at 200 m/s. At a velocity of 400 m/s, the front facet of auxetic armor was destroyed; however, the back facet was completely safe, while the monolithic panel did not withstand this velocity and was completely damaged. The results are encouraging in terms of resistance offered by the newly adopted auxetic armor compared to conventional monolithic armor.

3D Printing Auxetic Architectures for Hypertrophic Scar Therapy

AbstractFitting the human body for different purposes such as flexible electronics and functional garments can be a challenging task. Pressure garments are used to treat hypertrophic scars (HSs)pr. However, they have often failed to provide consistent pressure during joint movement. To increase the therapy efficacy, the application is proposed of 3D printed thermoplastic polyurethane (TPU) with an auxetic architecture insert for pressure therapy. Auxetic material can undergo an out‐of‐plane bending into a synclastic curvature, which can easily accommodate the contours of the human body. In this study, the synclastic effect of the auxetic structure under out‐of‐plane bending is illustrated through finite element analysis (FEA) first. Next, the formability, structural deformation, and auxetic response of re‐entrant (RE) and double‐arrowhead (DAH) auxetic structures when loading by a spherical surface in out‐of‐plane direction are unprecedentedly evaluated experimentally and numerically. It can be observed the internal angle of auxetic structure plays an important role regarding shape formability. Nevertheless, the result of wear trial reveals this design facilitates a stable level of pressure during the body motion which promotes the recovery of HS. It is believed the characterized result of auxetic architectures not only contribute to HS therapy, but also any type of biomedical devices.

Flexible planar metamaterials with tunable Poisson’s ratios

This research reports on the design, fabrication, and multiscale mechanical characterization of flexible, planar mechanical metamaterials with tailorable mechanical properties. The tunable mechanical behavior of the structures is realized through the introduction of orthogonal perforations with different geometric features. Various configurations of the perforations lead to a wide range of Poisson’s ratios (from −0.8 to 0.4), load-bearing properties, and energy absorption capacities. The correlations between the configuration of the perforations and the auxetic response of the structures are highlighted through computational and experimental characterizations performed at multiple length scales. It is demonstrated that the local in-plane rotation of the solid ligaments in a uniaxially loaded structure is the primary factor that contributes to its strain-dependent auxetic behavior at macroscopic scales. Confinement of these local rotations is then used as a practical strategy to activate a self-strengthening mechanism in the auxetic structures. It is further shown that the fabrication of planar flexible structures with controllable Poisson’s ratios is feasible through spatial adjustment of perforations in the structure. Finally, discussions are provided regarding the practical applications of these structures for a new generation of highly energy-absorbing protective equipment.

The GAM (General Auxetic Metamaterial): A Tuneable Internal Structural Configuration to Change the Auxetic Response with the Same Unit Cell Boundary Geometry

The GAM (General Auxetic Metamaterial): A Tuneable Internal Structural Configuration to Change the Auxetic Response with the Same Unit Cell Boundary Geometry

Influence of Liquid Crystallinity and Mechanical Deformation on the Molecular Relaxations of an Auxetic Liquid Crystal Elastomer.

Liquid Crystal Elastomers (LCEs) combine the anisotropic ordering of liquid crystals with the elastic properties of elastomers, providing unique physical properties, such as stimuli responsiveness and a recently discovered molecular auxetic response. Here, we determine how the molecular relaxation dynamics in an acrylate LCE are affected by its phase using broadband dielectric relaxation spectroscopy, calorimetry and rheology. Our LCE is an excellent model system since it exhibits a molecular auxetic response in its nematic state, and chemically identical nematic or isotropic samples can be prepared by cross-linking. We find that the glass transition temperatures () and dynamic fragilities are similar in both phases, and the -dependence of the relaxation shows a crossover at the same for both phases. However, for , the behavior becomes Arrhenius for the nematic LCE, but only more Arrhenius-like for the isotropic sample. We provide evidence that the latter behavior is related to the existence of pre-transitional nematic fluctuations in the isotropic LCE, which are locked in by polymerization. The role of applied strain on the relaxation dynamics and mechanical response of the LCE is investigated; this is particularly important since the molecular auxetic response is linked to a mechanical Fréedericksz transition that is not fully understood. We demonstrate that the complex Young’s modulus and the relaxation time remain relatively unchanged for small deformations, whereas for strains for which the auxetic response is achieved, significant increases are observed. We suggest that the observed molecular auxetic response is coupled to the strain-induced out-of-plane rotation of the mesogen units, in turn driven by the increasing constraints on polymer configurations, as reflected in increasing elastic moduli and relaxation times; this is consistent with our recent results showing that the auxetic response coincides with the emergence of biaxial order.

Auxetic structures from 3D printed hybrid textiles

Auxetic structures have been produced using 3D printing and knitted textile materials. A review of other auxetic textiles is presented along with the new materials. A range of configurations were developed, prototyped, and tested to demonstrate significant auxetic response, including Poisson’s ratio up to negative one. The concept of 4D textiles was employed to create environmentally responsive hinges in some structures, allowing the material to change shape in response to thermal stimulus.

Understanding the physics of the auxetic response in a liquid crystal elastomer

This article explains the auxetic behavior of a liquid crystalline elastomer, which occurs at a molecular level, by deducing the strain-induced changes in order parameters and interpreting them as out-of-plane rotations of the molecules.

Wool nonwovens as candidates for commodity auxetic materials

Advances in the field of auxetics have realized fabricated auxetic materials such as foams, fabrics, and fibers as well as a better theoretical understanding of the auxetic response. Because of their unique properties and applications, commodity auxetic materials are particularly desirable. Needle-punched nonwovens, several kinds of paper, and many knitted and woven fabrics have the potential to be auxetic, either as-produced or through a processing or design solution. In this study, we examine the out-of-plane Poisson’s ratio of as-produced and heat-compressed wool nonwovens. The wool nonwovens were found to be out-of-plane auxetic as-produced, and their auxetic character became more pronounced at higher treatment temperatures. Their behavior could be similar to that of paper, where straightening of a bent fiber was responsible for thickness increase. The prescribed processing conditions to enhance auxeticity could potentially be incorporated in their existing production, providing a pathway to generating commodity auxetics.

Low velocity impact response of 3D printed structures formed by cellular metamaterials and stiffening plates: PLA vs. PETg

This work studies the low-velocity impact response of 3D-printed layered structures made of thermoplastic materials (PLA and PETg), which form sacrificial claddings for impact protection. The analyzed structures are composed of crushable cellular cores placed in between terminal stiffening plates. The cores tessellate either honeycomb hexagonal unit cells, or hexagonal cells with re-entrant corners, with the latter exhibiting auxetic response. The given results highlight that the examined PETg protectors exhibit higher energy dissipation ratios and lower restitution coefficients, as compared to PLA structures that have the same geometry. It is concluded that PETg qualifies as an useful material for the fabrication of effective impact protection gear through ordinary, low-cost 3D printers.

Implications for Auxetic Response in Liquid Crystalline Polymers: X‐Ray Scattering and Space‐Filling Molecular Modeling

Five transverse rod (TR)‐containing main‐chain liquid crystalline polymers (LCPs) are examined in both the powder and fiber forms by wide angle X‐ray diffraction. Data from the diffraction experiments are consistent with the site‐connectivity‐driven TR‐reorientation mechanism for intrinsic auxetic character in these macromolecules. Shifts in peak maxima, intensity distributions in the interchain interaction region, and calculated volume increase accompanying fiber formation are all in line with expectations from considerations of this mechanism. The narrow window for experimental conditions necessary for fiber preparation and subsequent X‐ray observation of this phenomenon is detailed. A close examination of space‐filling Corey–Pauling–Koltun (CPK) molecular models reveals the details of local packing of rods and connected polymer chains in the quiescent nematic polymer melt prior to fiber drawing. It is found that two rod‐reorientation possibilities exist each of which leads to increased interchain separation as required for auxetic response. Suggestions for future experiments and materials design for new LCPs are described.

Osmo-inelastic response of the intervertebral disc annulus fibrosus tissue.

The aim of this article is to provide some insights on the osmo-inelastic response under stretching of annulus fibrosus of the intervertebral disc. Circumferentially oriented specimens of square cross section, extracted from different regions of bovine cervical discs (ventral-lateral and dorsal-lateral), are tested under different strain-rates and saline concentrations within normal range of strains. An accurate optical strain measuring technique, based upon digital image correlation, is used in order to determine the full-field displacements in the lamellae and fibers planes of the layered soft tissue. Annulus stress-stretch relationships are measured along with full-field transversal strains in the two planes. The mechanical response is found hysteretic, rate-dependent and osmolarity-dependent with a Poisson's ratio higher than 0.5 in the fibers plane and negative (auxeticity) in the lamellae plane. While the stiffness presents a regional-dependency due to variations in collagen fibers content/orientation, the strain-rate sensitivity of the response is found independent on the region. A significant osmotic effect is found on both the auxetic response in the lamellae plane and the stiffness rate-sensitivity. These local experimental observations will result in more accurate chemo-mechanical modeling of the disc annulus and a clearer multi-scale understanding of the disc intervertebral function.

Some unexpected predictions from strongly anisotropic hyperelastic constitutive models of soft tissue

It is shown that a widely used class of constitutive models for the mechanical response of elastic arteries, which includes the so-called HGO model, responds as if it were inextensible in simple tension in the zero limit of a non-dimensional ratio of material parameters. A significant auxetic response is predicted for an incompressible hyperelastic elastic sheet reinforced with inextensible cords. Thus, a significant lateral deformation of arterial specimens modelled by this class of materials should be observed in simple tension for small values of the non-dimensional parameter. However, such a response has not been observed experimentally. The analysis therefore suggests that predictions for this class of strongly anisotropic constitutive models for arteries should be treated with caution.

Mechanical properties of 3D auxetic closed-cell cellular structures

A novel 3D closed-cell cellular structure with different negative Poisson's ratio under tension and compression was presented. The 3D closed-cell cellular structure was generated by assembling the plane repeat units and sinusoidal wavy sheets units into the frame seamlessly. Four kinds of cellular structures with different responses under tension and compression are introduced. The mechanical properties of the proposed models were investigated. By choosing different repeated units, either positive or negative Poisson's ratio in three orthogonal directions can be achieved. Experiments and numerical simulations results show that the 3D closed-cell cellular structures have different responses under tension and compression loads. Considering material nonlinearities, the numerical results are analyzed using the instantaneous Poisson's ratio. The instantaneous Poisson's ratio can transit from negative to positive as the loads increase in 4 models. The results show that we can predict the auxetic response in a specific direction based on the repeated units that assembled into the frame. This designed structure provides an effective way to achieve a combination of negative, positive or zero Poisson's ratio.

Comparing quantum, molecular and continuum models for graphene at large deformations

In this paper, the validity and accuracy of three interatomic potentials and the continuum shell model of Ghaffari and Sauer [1] are investigated. The mechanical behavior of single-layered graphene sheets (SLGSs) under uniaxial stretching, biaxial stretching and pure bending is studied for this comparison. The validity of the molecular and continuum models is assessed by direct comparison with density functional theory (DFT) data available in the literature. The molecular simulations are carried out employing the MM3, Tersoff and REBO + LJ potentials. The continuum formulation uses an anisotropic hyperelastic material model in the framework of the geometrically exact Kirchhoff-Love shell theory and isogeometric finite elements. Results from the continuum model are in good agreement with those from DFT. The results from the MM3 potential agree well up to the point of material instability, whereas those from the REBO + LJ and Tersoff potentials agree only for small deformations. Only the Tersoff potential is found to yield auxetic response in SLGSs under uniaxial stretch. Additionally, the transverse vibration frequencies of a pre-stretched graphene sheet and a carbon nanocone are obtained using the continuum model and molecular simulations with the MM3 potential. The variations of the frequencies from these approaches agree within an error of ≈5%.

Auxetic deformation of the weft-knitted Miura-ori fold

Negative Poisson’s ratio (NPR) material with unique geometry is rare in nature and has an auxetic response under strain in a specific direction. With this unique property, this type of material is significantly promising in many specific application fields. The curling structure commonly exists in knitted products due to the unbalanced force inside a knit loop. Thus, knitted fabric is an ideal candidate to mimic natural NPR materials, since it possesses such an inherent curly configuration and the flexibility to design and process. In this work, a weft-knitted Miura-ori fold (WMF) fabric was produced that creates a self-folding three-dimensional structure with NPR performance. Also, a finite element analysis model was developed to simulate the structural auxetic response to understand the deformation mechanism of hierarchical thread-based auxetic fabrics. The simulated strain–force curves of four WMF fabrics quantitatively agree with our experimental results. The auxetic morphologies, Poisson’s ratio and damping capacity were discussed, revealing the deformation mechanism of the WMF fabrics. This study thus provides a fundamental framework for mechanical-stimulating textiles. The developed NPR knitted fabrics have a high potential to be employed in areas of tissue engineering, such as artificial blood vessels and artificial folding mucosa.

In-Plane Behavior of Auxetic Non-Woven Fabric Based on Rotating Square Unit Geometry under Tensile Load.

This paper reports the auxetic behavior of modified conventional non-woven fabric. The auxetic behavior of fabric was achieved by forming rotating square unit geometry with a highly ordered pattern of slits by laser cutting. Two commercial needle-punched non-woven fabric used as lining and the reinforcement fabric for the footwear industry were investigated. The influence of two rotating square unit sizes was analyzed for each fabric. The original and modified fabric samples were subjected to quasi-static tensile load by using the Tinius Olsen testing machine to observe the in-plane mechanical properties and deformation behavior of tested samples. The tests were recorded with a full high-definition (HD) digital camera and the video recognition technique was applied to determine the Poisson’s ratio evolution during testing. The results show that the modified samples exhibit a much lower breaking force due to induced slits, which in turn limits the application of such modified fabric to low tensile loads. The samples with smaller rotating cell sizes exhibit the highest negative Poisson’s ratio during tensile loading through the entire longitudinal strain range until rupture. Non-woven fabric with equal distribution and orientation of fibers in both directions offer better auxetic response with a smaller out-of-plane rotation of rotating unit cells. The out-of-plane rotation of unit cells in non-homogenous samples is higher in machine direction.

An experimental and numerical study on the transverse deformations in tensile test of tendons

The transverse deformations of tendons assessed in tensile tests seems to constitute a controversial issue in literature. On the one hand, large positive variations of the Poisson’s ratio have been reported, indicating volume reduction under tensile states. On the other hand, negative values were also observed, pointing out an auxetic material response. Based on these experimental observations, the following question is raised: Are these large and discrepant transverse deformations intrinsically related to the constitutive response of tendons or they result from artifacts of the mechanical test setup? In order to provide further insights to this question, an experimental and numerical study on the transverse kinematics of tendons was carried out. Tensile experiments were performed in branches of deep digital flexor tendons of domestic porcine, where the transverse displacements were measured by two high-speed, high-accuracy optical digital micrometers placed transversely to one another. Aiming at a better understanding of the effects of the mechanical test setup in the transverse measurements, a three-dimensional finite element model is proposed to resemble the tensile experiment. The main achieved results strongly support the following hypotheses regarding tensile tests of tendons: the clamping region considerably affects the kinematics of the specimen even at a large distance from the clamps; the transverse deformations are mainly ruled by stiff fibers embedded in a soft matrix; the generalization of the Poisson’s ratio to draw conclusions about changes in volume of tendons may lead to misinterpretations.

Incremental auxetic response of composite lattices under isotropic prestress

This work studies the constitutive response of two- and three-dimensional lattice materials subject to isotropic prestress, with a focus on the elastic stiffness moduli that can be directly measured through experimental tests. The elementary unit cell of the examined lattices is formed by an arbitrary number of junctions attached to a junction. Analytic formulae for the elastic stiffness coefficients of stretching-dominated lattices are provided. In addition, numerical results for the incremental elastic moduli of composite lattices equipped with hard and soft rods are presented. The given results highlight that isotropically pre-tensioned lattices may exhibit marked variations of the elastic stiffness moduli in the prestressed state, over the values competing to the stress-free configuration. This study also discloses that prestressed lattices may feature incremental auxetic response, when composite architectures suitably combining hard and soft materials are employed for their fabrication.

Analytic analysis of auxetic metamaterials through analogy with rigid link systems.

In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value. This paper develops a novel methodology in the analysis of auxetic metamaterials which exhibit elastic instability through analogy with rigid link lattice systems. The results of our analytic approach are confirmed by finite-element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson's ratio. The method gives insight into the relationships between mechanisms within lattices and their mechanical behaviour; as such, it has the potential to allow existing knowledge of rigid link lattices with auxetic paths to be used in the design of future buckling-induced auxetic metamaterials.

Computation of the homogenized nonlinear elastic response of 2D and 3D auxetic structures based on micropolar continuum models

We develop mechanical and numerical homogenization models for the large strains response of auxetic structures in order to derive their effective elastic response accounting for large changes of the geometry. We construct a strain driven nonlinear scheme for the computation of the stress-strain relation of these repetitive networks over a reference representative unit cell (abbreviated as RUC). Homogenization schemes are developed to evaluate the effective nonlinear mechanical response of periodic networks prone to an auxetic behavior, in both planar and 3D configurations, which are substituted by an effective micropolar continuum at the intermediate mesoscopic level. The couple stress part of the homogenized constitutive law takes into account the impact of the local rotations at the mesoscopic level and allows computing the bending response. This methodology is applied to four planar auxetic periodic lattices (the re-entrant hexagonal honeycomb and alternative honeycomb topologies, including the arrowhead, Milton and hexachiral structures), and to the 3D re-entrant and pyramid-shaped lattices. We have considering successively the in-plane and out-of-plane responses of these structures. The transition to an auxetic behavior is shown to be triggered by the imposed strain over the unit cell boundary. The computed evolutions of Poisson’s ratio versus the imposed stretch traduce an enhanced auxetic response as the stretch is increased. A satisfactory agreement is obtained between the homogenized stress-strain responses and the responses computed numerically by finite element simulations performed over a repeating unit cell.