Re-entrant Structure Research Articles

Exploring re-entrant auxetic silicone structures to design bra pads

Auxetic materials, known for their negative Poisson's ratio and unique form-fitting deformation, are proposed in this study for designing bra pads to accommodate different bra cup sizes. The deformation elasticity behaviour of re-entrant auxetic structures with a bow-tie shape, made of silicone elastomer, is systematically analysed for size accommodation and shape conformity, and compared with traditional polyurethane foam and spacer fabric used in bra pads. The results indicate that the auxetic structures exhibit desirable mechanical properties, including superior elasticity and stable deformation under tensile loading. Additionally, these structures facilitate 3D shape conformity to breast shapes, thereby improving overall bra fit. Amongst the 4 different unit cell dimensions studied, the auxetic elastomer with a cell size of 9.14 mm is the most promising candidate, which has superior elasticity, linear expansion, and excellent shape conformity. This auxetic elastomer enables increases in area from an A to D cup thus offering the potential to realize a one-size-fits-more concept. The findings provide the grounds for future research endeavours that aim to develop support in different areas of bras and optimize the arrangement of unit cells to enhance the functional aspects of bras.

Non local analytical and numerical modelling of re-entrant auxetic honeycomb

Auxetic materials, characterized by their negative Poisson’s ratio, have been extensively studied for applications in energy absorption and mechanical reinforcement. Re-entrant honeycomb structures, a subtype of auxetic materials, have demonstrated superior mechanical characteristics. However, understanding the mechanical behavior of these structures at the nanoscale remained a significant challenge. To address this gap, the authors explored the influence of size on the deflection behavior of re-entrant auxetic honeycomb structures through non-local continuum mechanics. Their analytical model, incorporating the Euler-Bernoulli beam model and considering four non-dimensional geometrical parameters, was validated through numerical simulations and a comprehensive review of existing literature. The study aimed to provide valuable insights into the design and engineering of re-entrant auxetic honeycomb structures across diverse applications, contributing to the advancement of non-local elasticity theory and deepening the understanding of the mechanical behavior of auxetic structures at the nanoscale. The research laid a foundation for further exploration and optimization of re-entrant honeycomb structures, facilitating their effective utilization in fields such as MEMS/NEMS by leveraging the dimensionless parameters identified in the study.

Mechanical characteristics of auxetic composite honeycomb sandwich structure under bending

Auxetic honeycomb sandwich structures (AHS) composed of a single material generally exhibit comparatively lower energy absorption (EA) and platform stress, as compared to traditional non-auxetic sandwich structures (TNS). To address this limitation, the present study examines the use of aluminum foam (AF) as a filling material in the re-entrant honeycomb sandwich structure (RS). Filling the AHS with AF greatly enhances both the EA and platform stress in comparison to filling the TNS with AF, while the auxetic composite honeycomb sandwich structure effectively addresses interface delamination observed in traditional non-auxetic composite sandwich structures. Subsequently, the positive–negative Poisson’s ratio coupling designs are proposed to strengthen the mechanical features of a single honeycomb sandwich structure. The analysis results show that the coupling structure optimizes the mechanical properties by leveraging the high bearing capacity of the hexagonal honeycomb and the great interaction between the re-entrant honeycomb and the filling material. In contrast with traditional non-auxetic sandwich structures, the proposed auxetic composite honeycomb sandwich structures demonstrate superior EA and platform stress performance, suggesting their immense potential for utilization in protective engineering.

Mechanical properties of an improved flexible auxetic metamaterial and its application in self-expanding vascular stents

Auxetic metamaterials have shown great significance in the field of cardiovascular stents, but improving their applicability remains an issue. Here, we develop a type of improved auxetic metamaterial called the Re-entrant-Arrow-Snake (RAS) structure by adding arrow-shaped and snake-shaped structures to the Re-entrant (RE) structure. We first systematically study its in-plane elastic properties and compression behaviors. It is observed that the RAS structure exhibits improved vertical stiffness, horizontal flexibility, and clear auxetic effect in the vertical direction. The influence of the additional structures on the deformation pattern and the stability is also discussed by the in-plane compression analysis. Furthermore, we propose a new self-expanding (SE) vascular stent named RAS-SE based on the RAS structure. Numerical analysis demonstrates that the RAS-SE stent possesses enhanced dual-plateau radial force, negative foreshortening behavior, and improved bending flexibility, indicating better deployment performance and support in clinical applications. Biomechanical studies also show that axial deformation caused by the auxetic effect of the RAS-SE stent only slightly increases stress damage to plaque without affecting stress damage of the intima. This study further expands the application of metamaterials in SE vascular stents, and the proposed RAS structure shows high applicability on the SE stent, thus warranting further attention.

Auxetic fixation devices can achieve superior pullout performances compared to standard fixation concepts

Despite bone screws being the most commonly inserted implant in orthopaedic surgery, 10% of fracture fixation failure is a result of screw migration or pullout. In this study, the effect of four auxetic structures on the pullout performance of a novel unthreaded bone fastener was investigated through experiments and numerical simulations. The auxetic fasteners included the re-entrant, rotating squares, missing rib, and tetrachiral structures. Parametric CAD models were developed for each, and polymer samples manufactured using a stereolithography process. Pullout testing using bone analogue material found the rotating squares fastener to achieve superior pullout resistance 2.5 times that of the non-auxetic control sample. With a pullout to push-in force ratio of 33.7, this fastener achieved high pullout resistance with a low insertion force improving ease of installation. The Poisson’s ratio of the structure was determined using image analysis to be −1.31, similar to the missing rib and re-entrant types. The low axial stiffness of 12.1 N mm−1 for the rotating squares fastener was the reason for superior performance, allowing axial and resulting transverse strain to be initiated at relatively low load. The effect of increased diametral interference was investigated, and the re-entrant structure found to be superior with pullout resistance improved by 342%. This work provides a foundation for further development of unthreaded auxetic bone fasteners, which have the potential to replace screws for some orthopaedic applications and significantly reduce the prevalence of pullout as a failure mode.

3D novel zero Poisson’s ratio metamaterials with programmable thermal expansion and Young's modulus

The shape stability of the structure plays a very important role in deep space exploration engineering. This paper presents 3D novel zero Poisson’s ratio metamaterial (ZPRM) with programmable thermal expansion and Young's modulus through the combination of bi-material triangles and re-entrant hexagonal structures. The coefficient of thermal expansion (CTE) and Young's modulus of the ZPRM-1 are predicted by establishing theoretical analysis models based on the classical beam theory. The mechanical response behavior of the ZPRM −1 under small deformation is simulated by finite element analysis (FEA). 3D printing is adopted to design and prepare experimental specimens, and compression experiments are carried out to certify the accuracy of the theories and FEA of Young's modulus. The results of parameter analysis show that the ZPRM-1 can tune the CTE and Young's modulus in a wide range when the geometric parameters and material combination are changed. In addition, the mechanical properties of the ZPRM-1 under the combined field of temperature and mechanical loads are investigated to achieve the tunable Young's modulus from positive to negative. This study provides a feasible reference for temperature and mechanical sensitivity instruments.

The dynamic response of composite auxetic re-entrant honeycomb structure subjected to underwater impulsive loading

The researches on dynamic responses of underwater impulsive loading have been conducted. However, the previous study mainly concentrated on metal sandwich structure and fixed supported boundary. The relative research on composite auxetic re-entrant honeycomb structure and simply supported boundary are rarely. In this paper, the effect of the gradient form and relative density on impact resistance performance of composite auxetic re-entrant honeycomb structure was experimentally and numerically investigated. The one-stage light gas gun was applied to provide initial kinetic energy of the fly plate, and the diffuser-type shock tube was utilized to generate and propagate exponential decaying shock wave. The pressure–time curve was respectively amplified and recorded by the charge amplifier and oscilloscope. The response speed, final deflection of rear panel and failure mode of cores and panels were used to evaluate impact resistance of composite auxetic re-entrant honeycomb structures. Moreover, acoustic-structure interaction algorithm was applied to simulate impact course of specimens in Abaqus/Explicit. The results between experiment and numerical simulation exhibited good consistency. The results indicated that the positive gradient form could excessively slow down response speed of rear panel by dissipating energy of shock wave, and the average gradient demonstrated smaller final displacement of rear panel and less failure compared with graded structures.

Mechanical behavior of graded combined auxetic-honeycomb structures

Various methods such as geometry changes can improve the energy absorption of auxetic structures. In this article, the mechanical behavior of graded combined auxetic-honeycomb structures is investigated through various models of grading. In the graded angle method, the best samples are selected for construction and experimental after performing numerical simulations, and this method comprises both the all-auxetic and honeycomb-auxetic graded angle techniques. Additionally, it is proven that energy absorption can be further increased by adding a reinforced core to the cells of the re-entrant structure. Finally, optimal models for energy absorption are developed by combining the best models of graded angle, graded thickness, and reinforced core. The best of them is the all-auxetic unilateral graded angle with rhombic core auxetic (UGA-A)+(RCA) sample with energy absorption that is three times higher than HAR, which can be utilized in various industrial and sports applications.

Dynamic bandgap responsiveness of modified re-entrant metamaterials in thermal-mechanical field

This paper introduces a nested sinusoidal re-entrant (NSR) metamaterial characterized by tunable complete bandgaps (CBGs) and dynamic responsiveness in thermal-mechanical dual fields. NSR comprises shape memory polymer and features a sinusoidal modification with nested re-entrant hexagonal and star-shape re-entrant structure. Dynamic response of NSR is studied using the representative volume element method, specifically focusing on the effective modulus and Poisson's ratio and CBGs under varying average strains. The findings indicate that both the mechanical properties and CBGs exhibit dynamic responses to mechanical field, demonstrating interrelation between mechanical adjustments and functional performance. Moreover, the study examines how temperature fluctuations influence the NSR's elastic modulus, thereby altering its CBGs. Hence, manipulating both compression and temperature variations presents a viable approach to control and adjust the CBGs of NSR effectively. These results are validated by computations of the frequency response function under various average strains. Overall, this design presents a promising approach for developing mechanical metamaterials with tunable functionality.

3D printed auxetic metal stiffener for lightweight metal–composite T-joints with high strength and toughness

A novel auxetic structure-based stiffener for stainless steel–carbon reinforced polymer (CFRP) T-joints with outstanding strength and toughness improvement is proposed. The stiffener was composed of a bulk web and re-entrant structure flange that was 3D printed using a selective laser melting 3D printer. The stiffener was bonded to a CFRP skin, and a pull-off test was performed to evaluate the pull-off strength, stiffness, and toughness of the joint. The results demonstrated that the proposed structure has specific strength and toughness that were 3.4 and 77 times greater than those of the baseline joint, respectively. The improvement in strength was due to the delayed damage initiation caused by the mismatch between the bending stiffness of the bulk web and the stiffener under the first re-entrant structure. However, the damage initiation in the baseline joint was located at the stiffener edge. Moreover, the negative Poisson's ratio of the re-entrant structure arrested the delamination growth after damage initiation, which enhances the toughness of the joint. By optimizing the structure of the stiffener, a joint with 2.66 and 38.2 times larger specific strengths and toughness compared to the baseline joint with the same specific stiffness was achieved.

Experimental and simulation study on effects of material and loading direction on the quasi-static compression behavior of re-entrant honeycomb structure

The re-entrant honeycomb structure has a strong energy absorption capacity because of its auxetic characteristics. The energy absorption capacity of the re-entrant honeycomb structure is closely related to the material and loading direction. In this paper, the Selective Laser Sintering(SLS) 3D printing technology was used to print the re-entrant honeycomb structure with commonly used FS3300PA and Glass Fiber reinforced FS3300PA. A quasi-static compression finite element model was developed for the re-entrant honeycomb structure printed with two materials when loaded along three directions. The influence of material and loading direction on the quasi-static compression performance of re-entrant honeycomb structures was systematically studied through simulation and experiments. The deformation mode and energy absorption index of the simulation results are in good agreement with the experimental results, verifying the effectiveness of the finite element model. The results show that the deformation mode and energy absorption performance of the structure are affected by the material and loading direction. The quasi-static compression performance in the Y direction is optimal for both materials. However, when loading along the Y direction, the specific energy absorption of FS3300PA printed re-entrant honeycomb structure is 18.3 % higher than that of FS3300PA + 30 % Glass Fiber printed re-entrant honeycomb structure, ηCFEis 83.3 % higher. Therefore, when the re-entrant honeycomb structure of the two materials is loaded in different directions, the structure printed with FS3300PA has the best quasi-static compression performance when loaded in the Y direction.

Experimental and simulation study of the crashworthiness behavior of thickness-graded auxetic structures of ductile and brittle materials

This article examines the compressive behavior of re-entrant auxetic structures to optimize its energy absorption. The unique properties of auxetic structures have made them popular in various industries, especially for sports equipment. This study aims to create different types of structures using an FDM 3D printer. First, an appropriate raster angle for 3D printing of tensile test samples is examined for PLA and PLA+ materials. Next, three types of structures are constructed using brittle PLA and ductile PLA+ materials, and their energy absorption is compared. These structures are homogeneous auxetic re-entrant (HAR), unilateral graded thickness (UGT), and bilateral graded thickness (BGT). Changing from brittle (PLA) to soft material (PLA+) increases energy absorption in all structures. Likewise, grading the thickness of the structure, especially on BGT, increases energy absorption. Simulation results are validated by modeling the structures in two ways for brittle and ductile materials using Abaqus software. Finally, based on the simulation results, the most appropriate step of the bilateral graded thickness is recognized as 0.8-1-1.2.

Compressive properties of a modified re-entrant chiral auxetic structure (MRCA) under uniaxial quasi-static loading

Auxetics are a unique class of innovative materials/structures. Auxetic material/structures possess a negative value of Poisson’s ratio owing to the distinguished deformation behavior represented by the transvers expansion or contraction when they experience uniaxial stretching or compression, respectively. The aim of this manuscript is to show contributions of the structural modification on an auxetic hybrid structure. The in-plane properties of an auxetic structure, called the modified re-entrant chiral auxetic (MRCA) structure under quasi-static compression were experimentally and numerically explored. The experimental specimens were 3D printed using fused deposition modeling technique. The commercial ABAQUS/Explicit solver was used to develop the simulated models. Results showed that the structural modification have led to effectively improve deformation coordination (i.e. uniform deformation patterns) and the compressive properties of the modified structure. Young’s moduli were 1.75 and 12.7 higher than those of the original geometry, while values of plateau stress were 3.1 and 1.23 higher than those of the original geometry when they were compressed along the X and Y axes, respectively. The specific energy absorptions per unit mass were 4.7 J g−1 and 3.9 J g−1 when the MRCA specimens were compressed along the X and Y axes, respectively. However, the added cylinders limited the auxeticity (i.e. the transvers contraction) of the specimens during the compression tests.

Facile design of amphiphobic PVDF membranes utilizing synergy of pore structure and surface fluorination: A demonstration in membrane distillation

Amphiphobic membranes have attracted much attention in membrane distillation (MD) applications, due to its potential in simultaneously resisting membrane wetting and fouling when treating complex wastewater. The current amphiphobic membranes often require non-trivial design of multilevel re-entrant structure. Here we proposed a new class of amphiphobic membranes without multilevel re-entrant surface, by creating a composite poly(vinylidene fluoride)/polyvinyl alcohol/SiO2 membrane with asymmetric structure and well-controlled small surface pores via the NTIPS method, followed by direct fluorination via chemically binding the –OH of polyvinyl alcohol and low surface energy moieties 1H,1H,2H,2H-perfluorodecyl-triethoxysilane, assisted by 3-aminopropyltriethoxysilane and trimesoyl chloride. The amphiphobic membrane showed superior liquid entry pressure above 5 bar with various simulated saline feeds containing surfactants and organic pollutants. The amphiphobic membrane demonstrated robust anti-wetting and anti-fouling performance through a series of 24-h direct contact MD experiments using the above feeds, presenting stable water flux and high rejection, e.g., flux of 50.6 kg/(m2·h) and rejection >99.9 % with feed containing 3.5 wt% NaCl, 1 mM FA, and 2 mM SDS. The results demonstrated the fabrication of robust amphiphobic membrane through simple procedure utilizing the synergy between pore structure and surface chemistry, inspiring more efforts to design adequate membranes for treating complex wastewater.

Effect of production angle on low cycle fatigue performance of 3D printed auxetic Re-entrant sandwich panels

This study explores the static and fatigue behavior of re-entrant sandwich structures fabricated via 3D printing to assess their energy dissipation capability and durability. Various core structures of sandwich panels with different angles are considered for analysis. The shells, cores, and the entire sandwich structures are manufactured using polylactic acid (PLA) material. A combination of numerical simulations and experimental tests were employed to evaluate the energy absorption capacity and stiffness of re-entrant sandwich structures. Initial mechanical properties of the core structures were obtained through static tensile testing and the experimental fatigue analysis was carried out by using an Instron 8871 servo hydraulic test device, following the principles of the three-point bending test. The results of both static and fatigue analyses evaluated and the energy absorption capacity of the structures increases with increase in production angles. FEM and experimental results are compared and both results are in good agreement with eachother. Additionally, affect of changes in the geometry of re-entrant sandwich panels evaluated in terms of Young's Modulus and Poisson's ratio. The improved structures characterized by a negative Poisson's ratio hold significant innovation potential, especially in the defense and automotive industries, through the integration of various topological research findings.

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.

Two-photon polymerized wetting morphologies for tunable external and internal electrode micropatterning

Numerous existing and emerging microsize technologies operate by utilizing electrical circuits on surfaces and within solid objects, i.e., external and internal electrodes, respectively. While current micropatterning techniques have achieved extensive progress on current systems via pattern resolution and discretization on simple surfaces, the introduction of new applications relies on the complexity of the parts on which these patterns are fabricated. Additionally, many state-of-the-art applications utilize novel materials for functional systems, which further complicates their fabrication. This paper introduces innovative electrode micropatterning and microchannel filling approaches that support complex 3D designs and reduce the number of fabrication steps. The approaches leverage microsize hydrophobic and hydrophilic morphologies fabricated using the two-photon polymerization (2PP) additive manufacturing (AM) process, in conjunction with the target part. Once fabricated, the part is dipped into a conductive solution or other functional liquids, forming patterns on the surfaces and filling the channels based on the pre-designed wetting morphologies. These morphologies incorporate additional structures beyond the conventional hydrophilic and reentrant hydrophobic structures to facilitate the dipping process. This paper demonstrates the efficacy of the tunable electrode micropatterning approach to fabricate various microsystems utilizing 2PP, wetting morphologies, and the developed dipping process.

Improving Energy Harvesting from Cantilever-like Structures Based on Beam Geometry

Abstract Purpose Power gain from piezoelectric harvesters depends on several parameters and one of them is to design the substructure as to increase the mechanical strain occurred in the piezoelectric material. In this study, the effect of geometrical modification of the beam on the harvested power was investigated and new geometries were offered for increased power response from cantilever type energy harvesters. Method First, the effectiveness of auxetic structures on harvested power was investigated to see the effect of the negative Poisson’s ratio on harvested power. These structures are very popular in recent years on energy harvesting applications; however, their performances were generally compared to plain structures which is not a fair comparison. Rather, in this study, their performances were compared to non-auxetic nonlinear structures as well as plain geometry. Then, three new shapes inspired by re-entrant auxetic structure were presented for increased power response, and harvested power from these structures were evaluated under different conditions. Results It was shown that the power gain from auxetic structures is very high compared to plain structures; however, this increase in power could also be achieved using a non-auxetic simple rectangular structure in some cases. On the other hand, new geometries offered in this study performed better than the auxetic and non-auxetic geometries in most cases.

A new three-dimensional re-entrant negative Poisson's ratio metamaterial with tunable stiffness

Re-entrant structure, as a branch of mechanical metamaterial, has attracted attention due to its excellent mechanical properties. However, this structure suffers from the defect that the initial stiffness and load capacity are not customizable, which limits its practical application in engineering. Therefore, it is important to study a new type of three-dimensional re-entrant negative Poisson's ratio (NPR) structure that can tailor mechanical features like stiffness, load capacity, and energy absorption, and is suitable for practical engineering applications. In this work, a re-entrant unit with different sizes of γ (re-entrant column clearance) was designed, manufactured, and tested to achieve the adjustability a function of original stiffness and capacity for load by adjusting the size of γ. The accuracy between the finite element results and the actual results was verified through experiments and numerical analysis. In addition, the mechanical properties of the new re-entrant structure were compared with those of the conventional re-entrant structure. Using the verified finite element model, the influence of different structural parameter ratios on the initial stiffness, load capacity, energy absorption, and Poisson's ratio of the new re-entrant structure was analyzed. The results show that different sizes of γ can change the structure's mechanical attributes, realizing the adjustability of mechanical properties and providing a new method for the study of mechanical properties of NPR metamaterial.

Multi-objective optimization and theoretical analysis of re-entrant structure with enhanced mechanical properties

In response to the challenge of low stiffness and energy absorption capacity, various designs of negative Poisson's ratio (NPR) structures have emerged. However, these designs often lack a comprehensive analysis of other mechanical properties, leading to subpar mechanical performance. Previous studies have explored the mechanical properties response of enhanced re-entrant honeycombs (ERH) under impact conditions, revealing limitations in optimizing the structure's performance with a single objective. Therefore, this study aims to enhance ERH structural parameters to achieve superior mechanical performance through theoretical derivations and geometric optimizations. The results demonstrate that the proposed theoretical model is consistent with finite element analysis and response surface (RS) predictions. Expressions for Young's modulus, specific energy absorption, and compressive strength are proposed, facilitating the identification of structural parameters that meet specific requirements during reverse design. Furthermore, a multi-objective optimization approach optimizes the geometric parameters based on maximum energy absorption and compressive strength. The mechanical behavior of the optimized ERH is investigated using the finite element method, revealing the energy absorption capacity of 13.78 J/g while maintaining Poisson's ratio at -1.06. Additionally, the deformation mode of the optimized structure showcases enhanced stability compared to traditional honeycomb structures. The theoretical model and RS method were used to guide the design of ERH and promote the application of NPR structures.