Overall constitutive properties of stratified lattices with alternating chirality.

The present research focuses on a continuum description of stratified metamaterials achieved through the superposition of layers with alternating chirality. Each layer is constructed as a periodic assembly of centre-symmetric periodic cells, formed by a recurring arrangement of rigid circular discs connected by elastic ligaments. The layers are interconnected through elastic pins passing through the centres of aligned discs, allowing for either restrained or free relative rotation. A micropolar continuum model is used to describe each individual layer. The overall response of the metamaterials to in-plane forces is derived using a multi-field non-local model, expressed in terms of the average and difference of displacement and rotational fields. The overall micropolar and standard (Cauchy) constitutive tensors have been determined in closed form. The validity of the equivalent generalized micropolar model has been confirmed through comparison with discrete Lagrangian solutions of representative examples. In addition, a detailed analysis of a pseudo-indentation test has been carried out. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Structure-Property Relationships in Auxetic Liquid Crystal Elastomers-The Effect of Spacer Length.

Auxetics are materials displaying a negative Poisson's ratio, i.e., getting thicker in one or both transverse axes when subject to strain. In 2018, liquid crystal elastomers (LCEs) displaying auxetic behaviour, achieved via a biaxial reorientation, were first reported. Studies have since focused on determining the physics underpinning the auxetic response, with investigations into structure-property relationships within these systems so far overlooked. Herein, we report the first structure-property relationships in auxetic LCEs, examining the effect of changes to the length of the spacer chain. We demonstrate that for LCEs with between six and four carbons in the spacer, an auxetic response is observed, with the threshold strain required to achieve this response varying from 56% (six carbon spacers) to 81% (four carbon spacers). We also demonstrate that Poisson's ratios as low as -1.3 can be achieved. Further, we report that the LCEs display smectic phases with spacers of seven or more carbons; the resulting internal constraints cause low strains at failure, preventing an auxetic response. We also investigate the dependence of the auxetic threshold on the dynamics of the samples, finding that when accounting for the glass transition temperature of the LCEs, the auxetic thresholds converge around 56%, regardless of spacer length.

Experimental Study of Auxetic Structures Made of Re-Entrant ("Bow-Tie") Cells.

This article presents a study of metamaterial structures that exhibit auxetic properties. This unusual phenomenon of simultaneous orthogonal expansion of the metamaterial in tension, and vice versa in compression, with vertical and horizontal contraction, is explored for structures made of re-entrant unit cells. The geometry of such structures is analysed in detail, and the relationships are determined by the value of the Poisson's ratio. It is shown that the Poisson's ratio depends not only on the geometry of the unit cell but also on the degree of strain. Depending on the dimensions of the structure's horizontal and inclined struts, the limit values are determined for the angle between them. By creating physical structures made of re-entrant cells, it is demonstrated that the mechanism of change in the structure's dimensions is not due to the hinging but to the bending of the struts. The experimental section contains the results of compression tests of a symmetrical structure and tensile tests of a flat mesh structure. In the case of the mesh structure, a modification of the re-entrant cells was used to create arched strut joints. This modification makes it possible to obtain greater elongation of the mesh structure and larger NPR values.

A Split-Plot Experimentation Strategy for Making Causal Inferences in Advanced Materials: Auxetic Polyurethane Foam Manufacturing and Processing Analysis.

Development of advanced materials is often time consuming and expensive because of the large number of variables involved and experiments needed. An effective experimentation strategy would accelerate development by reducing the required amount of experiments without sacrificing the obtainable information. In this paper, the development of auxetic polyurethane (PU) foams was discussed as a case study. Auxetic materials are materials with a negative Poisson's ratio and have potential in many structural and functional applications. Auxetic PU foams are the most studied auxetic materials, and their manufacturing and properties are affected by many processing and environmental factors. This paper introduces a sophisticated design of experimental methodology to help reduce the experimental effort while effectively screening these factors. This methodology is then applied in an experiment to illustrate its utility and distinct advantages that greatly facilitate material development.

Auxetic Biomedical Metamaterials for Orthopedic Surgery Applications: A Comprehensive Review.

Poisson's ratio in auxetic materials shifts from typically positive to negative, causing lateral expansion during axial tension. This scale-independent characteristic, originating from tailored architectures, exhibits specific physical properties, including energy adsorption, shear resistance, and fracture resistance. These metamaterials demonstrate exotic mechanical properties with potential applications in several engineering fields, but biomedical applications seem to be one of the most relevant, with an increasing number of articles published in recent years, which present opportunities ranging from cellular repair to organ reconstruction with outstanding mechanical performance, mechanical conduction, and biological activity compared with traditional biomedical metamaterials. Therefore, focusing on understanding the potential of these structures and promoting theoretical and experimental investigations into the benefits of their unique mechanical properties is necessary for achieving high-performance biomedical applications. Considering the demand for advanced biomaterial implants in surgical technology and the profound advancement of additive manufacturing technology that are particularly relevant to fabricating complex and customizable auxetic mechanical metamaterials, this review focuses on the fundamental geometric configuration and unique physical properties of negative Poisson's ratio materials, then categorizes and summarizes auxetic material applications across some surgical departments, revealing efficacy in joint surgery, spinal surgery, trauma surgery, and sports medicine contexts. Additionally, it emphasizes the substantial potential of auxetic materials as innovative biomedical solutions in orthopedics and demonstrates the significant potential for comprehensive surgical application in the future.

Efficacy of auxetic lattice structured shoe sole in advancing footwear comfort-From the perspective of plantar pressure and contact area.

Introduction: Designing footwear for comfort is vital for preventing foot injuries and promoting foot health. This study explores the impact of auxetic structured shoe soles on plantar biomechanics and comfort, motivated by the integration of 3D printing in footwear production and the superior mechanical properties of auxetic designs. The shoe sole designs proposed in this study are based on a three-dimensional re-entrant auxetic lattice structure, orthogonally composed of re-entrant hexagonal honeycombs with internal angles less than 90 degrees. Materials fabricated using this lattice structure exhibit the characteristic of a negative Poisson's ratio, displaying lateral expansion under tension and densification under compression. Methods: The study conducted a comparative experiment among three different lattice structured (auxetic 60°, auxetic 75° and non-auxetic 90°) thermoplastic polyurethane (TPU) shoe soles and conventional polyurethane (PU) shoe sole through pedobarographic measurements and comfort rating under walking and running conditions. The study obtained peak plantar pressures (PPPs) and contact area across seven plantar regions of each shoe sole and analyzed the correlation between these biomechanical parameters and subjective comfort. Results: Compared to non-auxetic shoe soles, auxetic structured shoe soles reduced PPPs across various foot regions and increased contact area. The Auxetic 60°, which had the highest comfort ratings, significantly lowered peak pressures and increased contact area compared to PU shoe sole. Correlation analysis showed that peak pressures in specific foot regions (hallux, second metatarsal head, and hindfoot when walking; second metatarsal head, third to fifth metatarsal head, midfoot, and hindfoot when running) were related to comfort. Furthermore, the contact area in all foot regions was significantly associated with comfort, regardless of the motion states. Conclusion: The pressure-relief performance and conformability of the auxetic lattice structure in the shoe sole contribute to enhancing footwear comfort. The insights provided guide designers in developing footwear focused on foot health and comfort using auxetic structures.

The anisotropic and region-dependent mechanical response of wrap-around tendons under tensile, compressive and combined multiaxial loads.

The present work reports on the multiaxial region and orientation-dependent mechanical properties of two porcine wrap-around tendons under tensile, compressive and combined loads based on an extensive study with n=175 samples. The results provide a detailed dataset of the anisotropic tensile and compressive longitudinal properties and document a pronounced tension-compression asymmetry. Motivated by the physiological loading conditions of these tendons, which include transversal compression at bony abutments in addition to longitudinal tension, we systematically investigated the change in axial tension when the tendon is compressed transversally along one or both perpendicular directions. The results reveal that the transversal compression can increase axial tension (proximal-distal direction) in both cases to orders of 30%, yet by a larger amount in the first case (transversal compression in anterior-posterior direction), which seems to be more relevant for wrap-around tendons in-vivo. These quantitative measurements are in line with earlier findings on auxetic properties of tendon tissue, but show for the first time the influence of this property on the stress response of the tendon, and may thus reveal an important functional principle within these essential elements of force transmission in the body. STATEMENT OF SIGNIFICANCE: The work reports for the first time on multiaxial region and orientation-dependent mechanical properties of wrap-around tendons under various loads. The results indicate that differences in the mechanical properties exist between zones that are predominantly in a uniaxial tensile state and those that experience complex load states. The observed counterintuitive increase of the axial tension upon lateral compression points at auxetic properties of the tendon tissue which may be pivotal for the function of the tendon as an element of the musculoskeletal system. It suggests that the tendon's performance in transmitting forces is not diminished but enhanced when the action line is deflected by a bony pulley around which the tendon wraps, representing an important functional principle of tendon tissue.

Composite patch with negative Poisson's ratio mimicking cardiac mechanical properties: Design, experiment and simulation.

Developing patches that effectively merge intrinsic deformation characteristics of cardiac with superior tunable mechanical properties remains a crucial biomedical pursuit. Currently used traditional block-shaped or mesh patches, typically incorporating a positive Poisson's ratio, often fall short of matching the deformation characteristics of cardiac tissue satisfactorily, thus often diminishing their repairing capability. By introducing auxeticity into the cardiac patches, this study is trying to present a beneficial approach to address these shortcomings of the traditional patches. The patches, featuring the auxetic effect, offer unparalleled conformity to the cardiac complex mechanical challenges. Initially, scaffolds demonstrating the auxetic effect were designed by merging chiral rotation and concave angle units, followed by integrating scaffolds with a composite hydrogel through thermally triggering, ensuring excellent biocompatibility closely mirroring heart tissue. Tensile tests revealed that auxetic patches possessed superior elasticity and strain capacity exceeding cardiac tissue's physiological activity. Notably, Model III showed an equivalent modulus ratio and Poisson's ratio closely toward cardiac tissue, underscoring its outstanding mechanical potential as cardiac patches. Cyclic tensile loading tests demonstrated that Model III withstood continuous heartbeats, showcasing outstanding cyclic loading and recovery capabilities. Numerical simulations further elucidated the deformation and failure mechanisms of these patches, leading to an exploration of influence on mechanical properties with alternative design parameters, which enabled the customization of mechanical strength and Poisson's ratio. Therefore, this research presents substantial potential for designing cardiac auxetic patches that can emulate the deformation properties of cardiac tissue and possess adjustable mechanical parameters.

Thermal, Microstructural, and Mechanical Analysis of Complex Lattice Structures Produced by Direct Energy Deposition.

Lattice structures have gained attention in engineering due to their lightweight properties. However, the complex geometry of lattice structures and the high melting temperature of metals present significant manufacturing challenges for the large-scale fabrication of these structures. Direct Energy Deposition (DED) methods, such as the Wire Arc Additive Manufacturing (WAAM) technique, appear to be an interesting solution for overcoming these limitations. This study provides a detailed analysis of the manufacturing process of carbon steel lattice structures with auxetic geometry. The study includes thermal analysis using infrared thermography, microstructural characterization through metallography, and mechanical evaluation via hardness and mechanical testing. The findings reveal the significant impact of heat input, thermal cycles, and deposition sequence on the morphology and mechanical properties of the lattice structures. Fast thermal cycles are related to areas with higher hardness values, smaller strut diameters, and porous formations, which shows that controlling heat input and heat dissipation is crucial for optimizing the properties of lattice structures produced using WAAM.

In-Plane Compressive Responses of Non-Homogenous Re-Entrant Honeycombs Fabricated by Fused Deposition Modelling.

Auxetic structures, with re-entrant (inverted hexagonal or bow tie) unit cells, have received considerable interest due to their negative Poisson's ratio property that results in superior mechanical properties. This study proposes a simple method to create non-homogeneous re-entrant honeycombs by modifying the size of chevron crosslinks. The various structural designs were conceived by changing the geometrical dimensions of the crosslinks, namely the length (lcl) and the thickness (tcl), while maintaining the parameters of the re-entrant cell walls. The influence of the design parameters of chevron crosslinks on the mechanical behaviour of additively manufactured re-entrant honeycombs was investigated experimentally and numerically. The structures were fabricated using the Fused Deposition Modelling (FDM) technique from polylactic acid (PLA) plastic. In-plane quasi-static compression tests were conducted to extract the elastic, plastic, and densification properties of the structures. Furthermore, a Finite Element (FE) model was developed via LS-DYNA R11.0 software, validated experimentally, and was then used to obtain a deeper insight into the deformation behaviour and auxetic performance of various designs. The obtained results revealed that the mechanical performance of re-entrant honeycombs can only be tuned by controlling the geometrical configuration of chevron crosslinks.

Reduced stress propagation leads to increased mechanical failure resistance in auxetic materials.

Materials with a negative Poisson ratio have the counterintuitive property of expanding laterally when they are stretched longitudinally. They are accordingly termed auxetic, from the Greek auxesis meaning to increase. Experimental studies have demonstrated auxetic materials to have superior material properties, compared with conventional ones. These include synclastic curvature, increased acoustic absorption, increased resilience to material fatigue, and increased resistance to mechanical failure. Until now, the latter observations have remained poorly understood theoretically. With this motivation, the contributions of this work are twofold. First, we elucidate analytically the way in which stress propagates spatially across a material following a localized plastic failure event, finding a significantly reduced stress propagation in auxetic materials compared with conventional ones. In this way, a plastic failure event occurring in one part of a material has a reduced tendency to trigger knock-on plastic events in neighboring regions. Second, via the numerical simulation of a lattice elastoplastic model, we demonstrate a key consequence of this reduced stress propagation to be an increased resistance to mechanical failure. This is seen not only via an increase in the externally measured yield strain, but also via a decreased tendency for plastic damage to percolate internally across a sample in catastrophic system-spanning clusters.

Evaluation of the parallel coupling constitutive model for biomaterials using a fully coupled network-matrix model.

In this article we discuss the effective properties of composites containing a crosslinked athermal fiber network embedded in a continuum elastic matrix, which are representative for a broad range of biological materials. The goal is to evaluate the accuracy of the widely used biomechanics parallel coupling model in which the tissue response is defined as the additive superposition of the network and matrix contributions, and the interaction of the two components is neglected. To this end, explicit, fully coupled models are used to evaluate the linear and non-linear response of the composite. It is observed that in the small strain, linear regime the parallel model leads to errors when the ratio of the individual stiffnesses of the two components is in the range 0.1-10, and the error increases as the matrix approaches the incompressible limit. The data presented can be used to correct the parallel model to improve the accuracy of the overall stiffness prediction. In the non-linear large deformation regime linear superposition does not apply. The data shows that the matrix reduces the stiffening rate of the network, and the response is softer than that predicted by the parallel model. The correction proposed for the linear regime mitigates to a large extent the error in the non-linear regime as well, provided the matrix Poisson ratio is not close to 0.5. The special case in which the matrix is rendered auxetic is also evaluated and it is seen that the auxeticity of the matrix may compensate the stiffening introduced by the network, leading to a composite with linear elastic response over a broad range of strains.

Experimental validation of auxetic stent designs: three-point bending of 3D printed Titanium prototypes.

Introduction: Numerical simulations have demonstrated the superior bending flexibility of auxetic stents compared to conventional stent designs for endovascular procedures. However, conventional stent manufacturing techniques struggle to produce complex auxetic stent designs, fueling the adoption of additive manufacturing techniques. Methods: In this study, we employed DMLS additive manufacturing to create Titanium Ti64 alloy stent prototypes based on auxetic stent designs investigated in a previous study. These prototypes were then subjected to experimental three-point bending tests. Result: The experimental results were replicated using a finite element model, which showed remarkable accuracy in predicting the bending flexibility of four auxetic stents and two conventional stents. Discussion: Although this validation study demonstrates the promising potential of DMLS and other additive manufacturing methods for fabricating auxetic stents, further optimization of current stent design limitations and the incorporation of post-processing techniques are essential to enhance the reliability of these additive manufacturing processes.

TPMS-based auxetic structure for high-performance airless tires with variable stiffness depending on deformation.

A novel auxetic structure applicable to airless tire spokes is designed based on the primitive-type triply periodic minimal surface (P-TPMS) to have higher stiffness through deformation under compressive force. For becoming higher stiffness by deformation, an unit cell of auxetic structure is proposed and its characteristics according to design parameters are studied. Based on the parametric study, a rotated primitive-type auxetic structure (RPAS) is designed, and the deformative behaviors of an airless tire with the RPAS spokes are compared with a generally used honeycomb spoke. Simulation and experiment results show that the designed RPAS tire exhibits more stable behavior through higher rigidity depending on the deformation state when compressed on flat ground and obstacles. This variable stiffness characteristic of RPAS tires can be advantageous for shock absorption and prevention of large local deformations. Also, the manufacturability of the designed auxetic structure is evaluated using real rubber-based additive manufacturing processes for practical application in the tire manufacturing industry.

Characterization of Exterior Parts for 3D-Printed Humanoid Robot Arm with Various Patterns and Thicknesses.

Currently, metal is the most common exterior material used in robot development due to the need to protect the motor. However, as soft, wearable, and humanoid robots are gradually being developed, many robot parts need to be converted into artificial skin using flexible materials. In this study, in order to develop soft exterior parts for robots, we intended to manufacture exterior robot arm parts via fused filament fabrication (FFF) 3D printing according to various structural and thickness conditions and analyze their mechanical properties. The exterior parts of the robot arms were manufactured utilizing Shore 95 A TPU (eTPU, Esun, Shenzhen, China), which is renowned for its softness and exceptional shock absorption characteristics. The exterior robot arm parts were modeled in two parts, the forearm and upper arm, by applying solid (SL) and re-entrant (RE) structures and thicknesses of 1, 2, and 4 mm. The mechanical properties were analyzed through the use of three-point bending, tensile, and compression testing. All of the characterizations were analyzed using a universal testing machine (AGS-X, SHIMADZU, Kyoto, Japan). After testing the samples, it was confirmed that the RE structure was easily bendable towards the bending curve and required less stress. In terms of the tensile tests, the results were similar to the bending tests; to achieve the maximum point, less stress was required, and for the compression tests, the RE structure was able to withstand the load compared to the SL structure. Therefore, after analyzing all three thicknesses, it was confirmed that the RE structure with a 2 mm thickness had excellent characteristics in terms of bending, tensile, and compressive properties. Therefore, the re-entrant pattern with a 2 mm thickness is more suitable for manufacturing a 3D-printed humanoid robot arm.

Mechanically Ultra-Robust Fluorescent Elastomer for Elaborating Auxetic Composite.

Fluorescent elastomers are predominantly fabricated through doping fluorescent components or conjugating chromophores into polymer networks, which often involves detrimental effects on mechanical performance and also makes large-scale production difficult. Inspired by the heteroatom-rich microphase separation structures assisted by intensive hydrogen bonds in natural organisms, an ultra-robust fluorescent polyurethane elastomer is reported, which features a remarkable fracture strength of 87.2 MPa with an elongation of 1797%, exceptional toughness of 678.4 MJ m-3 and intrinsic cyan fluorescence at 445 nm. Moreover, the reversible fluorescence variation with temperature could in situ reveal the microphase separation of the elastomer in real time. By taking advantage of mechanical properties, intrinsic fluorescence and hydrogen bonds-promoted interfacial bonding ability, this fluorescent elastomer can be utilized as an auxetic skeleton for the elaboration of an integrated auxetic composite. Compared with the auxetic skeleton alone, the integrated composite shows an improved mechanical performance while maintaining auxetic deformation in a large strain below 185%, and its auxetic process can be visually detected under ultraviolet light by the fluorescence of the auxetic skeleton. The concept of introducing hydrogen-bonded heteroatom-rich microphase separation structures into polymer networks in this work provides a promising approach to developing fluorescent elastomers with exceptional mechanical properties.

3D Tiled Auxetic Metamaterial: A New Family of Mechanical Metamaterial with High Resilience and Mechanical Hysteresis.

For artificial materials, desired properties often conflict. For example, engineering materials often achieve high energy dissipation by sacrificing resilience and vice versa, or desired auxeticity by losing their isotropy, which limits their performance and applications. To solve these conflicts, a strategy is proposed to create novel mechanical metamaterial via 3D space filling tiles with engaging key-channel pairs, exemplified via auxetic 3D keyed-octahedron-cuboctahedron metamaterials. This metamaterial shows high resilience while achieving large mechanical hysteresis synergistically under large compressive strain. Especially, this metamaterial exhibits ideal isotropy approaching the theoretical limit of isotropic Poisson's ratio, -1, as rarely seen in existing 3D mechanical metamaterials. In addition, the new class of metamaterials provides wide tunability on mechanical properties and behaviors, including an unusual coupled auxeticity and twisting behavior under normal compression. The designing methodology is illustrated by the integral of numerical modeling, theoretical analysis, and experimental characterization. The new mechanical metamaterials have broad applications in actuators and dampers, soft robotics, biomedical materials, and engineering materials/systems for energy dissipation.

Modeling of single-lap joints with auxetic adhesive utilizing homogeneous and heterogeneous bondline microstructures.

Producing lightweight structures can be effectively achieved using adhesive bonding that incorporates a high-performance adhesive, eliminating the mechanical joints (rivet, bolts). Here, the proof-of-concept of tailoring the high-performance adhesive using microstructures exhibiting a negative Poisson's ratio (auxetic) is investigated using two single lap joint (SLJ) models developed in ABAQUS/Standard. The SLJ models consist of two rigid adherends that are bonded using either homogeneous or heterogeneous adhesive that produces auxetic response. In homogeneous adhesive, a negative value of Poisson's ratio is defined in the adhesive part of the models. In heterogeneous adhesive, the negative Poisson's ratio is obtained by explicitly building orthogonally-arranged elliptical voids in the adhesive part of the models. In addition, the adherend-adhesive interface is represented by cohesive elements with bi-linear traction-separation rule. The effects of using two different adhesive models and thickness on peel and shear stresses, as well as failure mechanism and joint strength, are evaluated. We found that the effect of auxetic adhesive on SLJ response is more profound in the model using heterogeneous adhesive rather than the homogeneous one, where the joint strength enhancement could achieve 45 % in reference to the baseline model. The heterogeneous adhesive embedded between adherends is able to activate ligaments, the mechanism that could not be obtained using merely homogeneous adhesive. Our proposed modeling strategy can be a starting point to further the modeling approach of bonded joints utilizing auxetic adhesive.

Auxetic Photonic Patterns with Ultrasensitive Mechanochromism.

Photonic crystals with mechanochromic properties are currently under intensive study to provide intuitive colorimetric detection of strains for various applications. However, the sensitivity of color change to strain is intrinsically limited, as the degree of deformation determines the wavelength shift. To overcome this limitation, auxetic photonic patterns that exhibit ultra-sensitive mechanochromism are designed. These patterns have a regular arrangement of cuts that expand to accommodate the strain, while the skeletal framework undergoes torsional deformation. Elastic photonic crystals composed of a non-close-packed array of colloidal particles are embedded in the cut area of the auxetic patterns. As the cut area amplifies the strains, the elastic photonic crystals show significant color change even for small total strains. The degree of local-strain amplification, or sensitivity of color change, is controllable by adjusting the width of cuts in the auxetic framework. In this work, a maximum sensitivity of up to 60 nm/% is achieved, which is 20 times higher than bulk films. It is believed that the auxetic photonic patterns with ultra-sensitive mechanochromism will provide new opportunities for the pragmatic use of mechanochromic materials in various fields, including structural health monitoring.

Computational Comparison of the Mechanical Behavior of Aortic Stent-Grafts Derived from Auxetic Unit Cells.

PURPOSE: Inappropriate stent-graft (SG) flexibility has been frequently associated with endovascular aortic repair (EVAR) complications such as endoleaks, kinks, and SG migration, especially in tortuous arteries. Stents derived from auxetic unit cells have shown some potential to address these issues as they offer an optimum trade-off between radial stiffness and bending flexibility. METHODS: In this study, we utilized an established finite element (FE)-based approach to replicate the mechanical response of a SG iliac limb derived from auxetic unit cells in a virtual tortuous iliac aneurysm using a combination of a 180° U-bend and intraluminal pressurization. This study aimed to compare the mechanical performance (flexibility and durability) of SG limbs derived from auxetic unit cells and two commercial SG limbs (Z-stented SG and circular-stented SG models) in a virtual tortuous iliac aneurysm. Maximal graft strain and maximum stress in stents were employed as criteria to estimate the durability of SGs, whereas the maximal luminal reduction rate and the bending stiffness were used to assess the flexibility of the SGs. RESULTS: SG limbs derived from auxetic unit cells demonstrated low luminal reduction (range 4-12%) with no kink, in contrast to Z-stented SG, which had a kink in its central area alongside a high luminal reduction (44%). CONCLUSIONS: SG limbs derived from auxetic unit cells show great promise for EVAR applications even at high angulations such as 180°, with acceptable levels of durability and flexibility.