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Machine learning is a promising method to model production processes and predict product quality. It is challenging to accurately model complex systems due to data scarcity, as mass customisation leads to various high-variety low-volume products. This study conceptualised knowledge accumulation, extraction, and transfer (KAET) to exploit the knowledge embedded in similar entities to address data scarcity. A sequential cross-product KAET (SeqTrans) is proposed to conduct KAET, integrating data preparation and preprocessing, feature selection (FS), feature learning (FL), and transfer learning (TL). The FS and FL modules conduct knowledge extraction and help address various practical challenges such as changing operating conditions and unbalanced datasets. In this paper, sequential TL is introduced to production modelling to conduct knowledge transfer among multiple entities. The first case study of auxetic material performance prediction demonstrates the effectiveness of sequential TL. Compared with conventional TL, sequential TL can achieve the same test mean square errors with 300 fewer training examples when facing data scarcity. In the second case study, balancing anomaly detection models were constructed for two gas turbines in the same series using real-world production data. With SeqTrans, the F1-score of the anomaly detection model of the data-poor engine was improved from 0.769 to 0.909. [ABSTRACT FROM AUTHOR]

This study investigates the high-impact behaviour of auxetic materials, recognised for their negative Poisson’s ratio and exceptional energy absorption, when combined with shape memory alloys to enhance impact resistance. Using finite element analysis in Abaqus, 42 unique auxetic models were developed with variations in angles, thicknesses, heights, and lengths to examine structural response under high-velocity impacts. The findings reveal that modifications to the height-to-length ratio, thickness-to-length ratio, and cell design angle significantly affect residual projectile velocity – reducing it by up to 17%, fully eliminating it in some cases, or increasing it by 34% depending on the configuration. These adjustments also influence energy absorption rates and specific energy absorption during collision events. Poisson’s ratios, derived through both analytical and numerical methods, showed strong agreement, validating the accuracy of the models. Overall, the study ident ifies optimal design configurations that maximise energy absorption and minimise projectile velocity upon impact. These findings have practical implications for industries requiring durable materials in high-impact applications, and the integration of auxetic structures with shape memory alloys suggests promising directions for innovative material design. [ABSTRACT FROM AUTHOR]

This work introduces a quasi-3D refined theory for assessing the transient dynamic reactions of a sandwich annular sector plate subjected to mechanical shock loading. The sandwich structure has two facesheets composed of graphene origami (GOri)-enabled auxetic metal metamaterials (GOEAMs) and a core composed of carbon fiber reinforced polymer. The auxetic quality of the annular plates is mainly determined by the quantity of graphene and the level of folding in the GOri material. The elements are assessed layer by layer across the thickness of the plates. Micromechanical models supported by genetic programming may be used to predict the position-dependent Poisson's ratio and other material parameters. The concept of Hamiltonian is used to deduce the governing equations of the structure. The equations of motion, which vary with time, are solved using the numerical solution process and the Laplace transform. A comprehensive parametric study is carried out to examine the influence of various geometric and physical parameters on the time-dependent behavior of annular sector plates. The current mathematical modeling results are being compared to the findings of previous works, as well as a machine learning technique. By using this machine learning methodology, it is feasible to computationally solve differential equations at a reduced expense, while simultaneously surmounting the challenge of formulation. To use machine learning techniques, a dependable dataset acquired from either experimental or numerical analysis is necessary. The dataset was created using the quantitative findings of the investigation. Furthermore, the machine learning technique demonstrates its capacity to provide very precise outcomes when predicting the transient behavior of the existing structure under novel loading and boundary circumstances. [ABSTRACT FROM AUTHOR]

Thin-walled tubes are widely used as energy absorbers to increase the crash resistance and safety while maintaining lightness. There has been an increase in interest in the integration of auxetic structures into these tubes. This is due to the better mechanical strength displayed by auxetic structures with negative Poisson's ratio, particularly in terms of compressive behavior and energy absorption. In this study, a group of square-section tubes with different types of cell structures on their side faces was examined. Under quasi-static compression, the behaviors of thin-walled square tubes with reentrant auxetic and conventional honeycomb were examined numerically and experimentally. In addition, geometric optimization of reentrant cell shape was performed to maximize the compressive loading of the square tubes. First, the compression behaviors of thin-walled square tubes made of polylactic acid (PLA) were examined; these tubes' side surfaces have both conventional and reentrant auxetic honeycomb cellular patterns. The reentrant auxetic and conventional honeycomb cell architectures were applied together and separately on the side faces of the thin-walled tube, with the identical cell parameters. In order to better understand the deformations, force-displacement curves were examined for four different types of thin-walled square tubes, including tubes with reentrant auxetic and honeycomb cell structures on all side faces and tubes with these structures on opposite sides and adjacent. Using the ANSYS finite element software package and Digimizer image processing programs, the Poisson's ratio of the reentrant auxetic and conventional honeycomb configurations as well as the maximum compression force of the tubular structures were determined numerically and experimentally. After obtaining the result that the use of the reentrant auxetic structure on the side surfaces of the square tube significantly increased the compression resistance and energy absorption capability of the tube, the optimization of the square tube with the reentrant auxetic structure on all surfaces was examined. The effect of the geometrical parameters such as ligament length, reentrant angle, and cell thickness of the unit-cell on the compression load of the square tube was investigated using an integrated methodology combining numerical simulation and DoE (Design of Experiments) method. The findings show that the tubes combined reentrant auxetic structure exhibits better energy absorption than the conventional honeycomb tubes. It also reveals that the optimum geometric parameters of the reentrant auxetic unit cell are to be the ligament length of 16.358 mm, the ligament angle of 80°, and the ligament thickness of 3 mm. [ABSTRACT FROM AUTHOR]

Vibrational behavior of a shear deformable cylindrical shell is studied in this article based on Hamilton's principle. The shell is manufactured by a Copper (Cu) core reinforced with graphene origami auxetic metamaterial and subjected to mechanical and thermal loads. The constitutive relations are developed based on the shear deformable model where the effective modulus of elasticity, Poisson's ratio, and density are evaluated using micromechanical models including volume fraction and folding degree of graphene origami auxetic metamaterial, geometric characteristics of graphene, material properties of matrix, and reinforcement and local temperature. The natural frequencies are obtained based on Navier's and Galerkin's approaches for simply supported, clamped-simply, and clamped-clamped boundary conditions. The formulation, solution procedure, and numerical results are confirmed through comparison with the available results of the literature. The complete numerical results are presented in terms of volume fraction and folding degree of graphene origami auxetic metamaterial, thermal loading, and various types of boundary conditions. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of a sandwich structure featuring an auxetic core, manufactured through Vacuum Assisted Resin Transfer Molding (VARTM) using carbon-aramid hybrid fibers. The core was 3D printed with polylactic acid (PLA). Experimental testing of the structure provided results for validating a cost-effective numerical model. The response surface methodology identified results for different sandwich panel configurations, revealing that auxetic behavior depends on the core's adopted configuration. Increasing the fiber-core contact area induces auxetic behaviors. The structure underwent optimization using the Lichtenberg algorithm, yielding models with 40.32% higher failure load, 36.36% higher natural frequency, and over 20% mass reduction. [ABSTRACT FROM AUTHOR]

This work introduces the novel analysis of the bending behavior of a composite doubly curved panel made of graphene origami (GOri)-enabled auxetic metal metamaterials (GOEAMs) subjected to external mechanical force. The motivation for this study stems from the many applications of such structures in the field of aeronautics. These materials have mechanical and structural properties that continuously vary. This study is the first to examine the effects of an instantaneous external shock on the bending response of a composite doubly curved panel made of GOEAMs due to the extraordinary properties of these advanced materials. The mathematical governing equations are obtained from the higher-order shear deformation theory and are solved using the Laplace transform method (LTM) and the analytical solution procedure (ASP). After solving the equations, the results of the current system are compared to those of a previously published work, revealing a significant level of concurrence between the two sets of data. This study presents a machine learning approach that utilizes a deep neural network (DNN) with input, hidden, and output layers, as well as independent variables and other relevant factors. The aim is to provide an efficient computational technique for solving engineering issues. This is achieved by the use of mathematical modeling and the verification of the current output's outcomes. Additionally, a database is supplied for an in-depth examination of this structure's suitability for aeronautical purposes. The database contains comprehensive bending information, including normal, shear, and displacement fields in various directions, specifically for the GOEAMs subjected to external shock loading. [ABSTRACT FROM AUTHOR]

Proper consideration should be given to the stability of new concrete in order to assure the quality of building engineering, while also demanding its excellent flowability. The inadequate initial state stability negatively impacts the long-term durability of reinforced concrete structures, although this issue has not been well addressed. This work focuses on assessing the aerodynamic response of concrete ceilings reinforced with advanced functionally graded nano-materials. As the reinforcement of the current concrete structure, graphene oxide powders (GOPs) are used with improved material properties than other types of reinforcement. For mathematical modeling of the current structure, Reddy's Higher-order Shear Deformation Theory is used to model the current work's displacement fields. Also, the perturbation aerodynamic force is mathematically described using the Bernoulli equation for potential flow. After that using a method that involves separating variables, we may get the answer for the aerodynamic pressure in its ultimate form. Haber-Schaim foundation made of auxetic material in the Cartesian coordinate system is used to model the foundation of the current work with high accuracy. After obtaining the governing equations and associated boundary conditions, a meshless approach with weighted orthogonal basis and Kronecker delta-based shape functions are used to solve the equations. Finally, some suggestions for improving the aerodynamics and flutter velocity of airflow of the presented concrete plate reinforced by GOPs are presented for related aerodynamics industries. [ABSTRACT FROM AUTHOR]

For the first time, in the current work, the quasi-3D new refined theory (Q3D-NRT) is used to analyze the dynamic reactions of functionally graded (FG) annular sector plates made of graphene origami (GOri)-enabled auxetic metal metamaterials to the mechanical shock loading. The auxetic property of the annular plates is effectively controlled by graphene content and GOri folding degree that is graded across the thickness direction of the annular plates in a layer-wise manner, as Poisson's ratio and other material properties are position-dependent and can be estimated by genetic programming-assisted micromechanical models (MM). Hamilton's concept is used to find the structure's governing equations. The differential quadrature technique and the Laplace transform are used at design sites to solve the time-varying equations of motion. The system response is translated from the Laplace domain to the time domain using a modified version of the Dubner and Abate approach. To investigate the impact of different geometrical and physical factors on the dynamic reactions of the annular sector plates, thorough parametric research is conducted. The findings of the present mathematical modeling are compared with those of the earlier publications and also with those of the machine learning approach. Utilizing this learning strategy, differential equations may be solved with very cheap computer costs while also overcoming formulation complexity. It needs a valid dataset from experimental or numerical analysis to use machine learning techniques. This dataset was compiled using the study's numerical findings. Additionally, the machine learning approach demonstrates the capacity to deliver findings with a high degree of accuracy when predicting the mechanical characteristics of the existing structure under novel loading and boundary circumstances. [ABSTRACT FROM AUTHOR]

Over the years, researchers have investigated active metamaterials because of controllability of their geometry and mechanical properties. However, despite the undeniable appeal and significance of this direction of studies from the perspective of many industries, researchers have struggled to systematically design such structures in an easily reproducible and scalable manner. Herein, it is shown that this can be achieved by harnessing the potential of foldable magnetomechanical metamaterials controlled via the external magnetic field. To this aim, two different configurations of the system with one of them being constrained so that it acts similarly to a linear actuator while the other one allows to fully control its expandability and mechanical properties in all directions are presented. Finally, the possibility of stacking the considered structures to create large systems that may exhibit auxetic properties in multiple planes will be discussed. The magnetomechanical metamaterials discussed are very interesting as they offer multidirectional and finely controlled movement which could be untethered. This is particularly promising for use in actuators, vibration dampers as well as scaffolds in deployable structures and impact resistive materials as the mechanical properties can be fine‐tuned by simply adjusting the external magnetic field and reconfiguring the structure. [ABSTRACT FROM AUTHOR]

Split thickness skin grafting is one of the common skin transplantation techniques employed in treating severe burn injuries. Recent experimental studies have shown that the expansions offered by split thickness skin grafts are much lower than what is claimed by the graft manufacturers. To date, limited studies have investigated the effect of slit patterns on the expansions and the possibility of material innovation. This work has experimentally tested novel auxetic slit patterns on a biofidelic skin simulant to evaluate their effect on skin graft expansion. A wide range of variants of alternating slit (AS), I-shaped (IS), and Rotating Triangle (RT) based auxetic patterns were tested. A biaxial testing device was employed to simulate realistic skin stretching during graft implementation. The deformation, expansion, stress-strain response, void area, and maximum gap size were estimated, and the material behavior was also modeled using hyperelastic curve fit coefficients. The key design parameters were determined, which would produce high expansion with minimal voids. The findings of this study are anticipated to throw light on the possibility of using auxetic slit patterns for generating higher expansions in split thickness skin grafts. [ABSTRACT FROM AUTHOR]

Sandwich structures have been a subject of intense scrutiny and utilization in engineering applications. However, there has been a limited understanding of the mechanical behaviors of novel sandwich structures composed of auxetic metamaterials. This study aims to contribute to the body of knowledge by examining the buckling responses of sandwich beams or wide plates with an orthotropic anti-tetra chiral lattice (ATCL) aluminum cores and symmetric angle-ply carbon-fiber/epoxy face sheets, both of which can exhibit highly negative Poisson's ratios or extreme auxeticity. The linear stability analysis of the sandwich structures under axial compression is conducted by applying the minimum potential energy principle and solving the eigenvalue problem using a numerical method. To achieve an accurate representation of arbitrary two-dimensional buckling morphologies, the first- and fifth-order shear and normal deformation models are employed to simulate the transverse kinematics of the face sheets and cores, while the finite-element model is utilized to discretize the longitudinal displacement of all constituents. The investigation reveals new insights into the interrelationship between global buckling, facial wrinkling, and shear crimping in conventional sandwich structures. The effects of material auxeticity on buckling responses are analyzed across an extensive range of geometrical configurations for the first time, unveiling five unprecedented buckling mode shapes, sophisticated buckling mode landscapes, and Poisson's ratio-sensitive buckling criteria. These findings lay a crucial foundation for designing and optimizing auxetic sandwich structures, bringing diverse possibilities in lightweight constructions, acoustic insulation, energy absorption, and dynamic and shock mitigation. [ABSTRACT FROM AUTHOR]

This study addresses the main challenges in manufacturing large-scale metallic auxetic structures, characterised by a negative Poisson's ratio, focusing on achieving suitable geometry control, surface finish, and structural integrity using Wire Arc Additive Manufacturing (WAAM). Specifically, the research employs the Cold Metal Transfer (CMT) process to fabricate 2D and 3D carbon steel auxetic cells. The primary objective is to address the challenges associated with the production of these structures. A comprehensive experimental and numerical analysis was conducted to investigate the influence of various factors, such as internal defects or geometric irregularities, such as pores and surface waviness, on the mechanical behaviour of the 2D and 3D auxetic cells under tensile and compressive loads, respectively. The compression tests revealed that despite minor defects and geometric imperfections, the manufactured cells consistently exhibit a negative Poisson's ratio. This suggests that the WAAM-produced auxetic structures are viable and capable of maintaining their unique mechanical properties. Furthermore, the study emphasises the significance of parameters such as orientation and the number of auxetic cells in governing the overall auxetic behaviour of the components. [ABSTRACT FROM AUTHOR]

Additive manufacturing is widely used to fabricate metamaterials. The mechanical properties of these are tailored by modifying topological parameters to meet desired performance. Here, an auxetic metamaterial composed of arc-shape elements is presented. The directional dependency of the apparent stiffness was characterized through finite element analysis and tensile and compressive tests on additively manufactured samples with fused filament fabrication in thermoplastic polyurethane. Poisson's ratio was measured with computational vision. The effective Young's modulus resulted with a nonlinear relation to the wall thickness. The orientation sensibility exposed the relevance of rotational symmetry in a lattice architected metamaterial. [ABSTRACT FROM AUTHOR]

This study explores the potential of periodic open cellular structures (POCS) that combine the auxetic and the shape memory effect (SME) with the aim of enhancing heat transfer in catalytic tubular reactors. On the one hand, these structures exhibit a negative Poisson's ratio, contracting perpendicular to the load axis under compression, driven by the rotation of nodes generating complex stress fields. On the other hand, the shape memory alloy (SMA) Nitinol (NiTi) with a reversible strain of up to 8% produced via electron beam powder bed fusion (PBF‐EB) shows extraordinary material properties with a high degree of freedom in structure design. The study conducts finite element method simulations and experiments to design POCS with tailored properties. Compression tests on less expensive Ti‐6Al‐4V POCS compared to NiTi POCS validate the simulative parameter study applied to fabricate novel auxetic hexagonal reentrant structures from NiTi with a unique stacking order and curved struts. The aim of this part of the study is to offer a pathway to design a NiTi auxetic POCS based on validated simulations. Further, it explains the interactions between geometrical parameters and mechanical properties of cellular reentrant NiTi structures. An optimized auxetic NiTi POCS achieved a Poisson's ratio of −1. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the thermal buckling behavior and structural optimization of multi-hybrid nanocomposite-reinforced concrete annular sector plates supported by auxetic foundations. Utilizing the Carrera unified formulation (CUF), a versatile higher-order theory is applied to capture the complex thermo-mechanical interactions in these advanced materials. The multi-hybrid nanocomposites are engineered by combining conventional reinforcement with nanoscale fillers to enhance stiffness, and thermal stability. The CUF framework facilitates the accurate representation of material behavior, geometric, and boundary conditions (BCs), allowing for a comprehensive analysis of the system’s thermal buckling response. An innovative artificial intelligence (AI) algorithm is employed to validate and further refine the results obtained from the analytical models. This AI-based approach ensures robust verification and provides deeper insights into the parameter sensitivities affecting the structural performance. Additionally, the optimization process focuses on minimizing weight and maximizing thermal resistance while adhering to design constraints imposed by the auxetic foundation, known for its unique negative Poisson’s ratio properties. The findings reveal the pivotal role of nanocomposite configurations and auxetic foundation properties in determining the critical buckling temperature and structural integrity. The integration of CUF with AI offers a powerful methodology for exploring complex design spaces, leading to enhanced performance and innovative solutions in engineering applications. This research bridges advanced material science, structural mechanics, and computational intelligence, paving the way for optimized designs in next-generation construction and aerospace systems. [ABSTRACT FROM AUTHOR]

AbstractIn the field of medical technology, specialized equipment utilizes tubular metastructures with a negative Poisson’s ratio in vascular stents to reduce the risk of embolism. The deliberate incorporation of auxetic structures into stent design offers several benefits over traditional stents. This study examines the nonlinear instability and bending responses of reentrant perfect and imperfect 3D-printed tubular metastructures. First, the governing equations for the auxetic tube with geometric imperfections under transverse and axial mechanical loads are derived using the von-Kármán nonlinear assumption and Timoshenko theory. Then, the equations are derived using the principle of virtual displacement. The physical characteristics of the reentrant structure are derived using Malek-Gibson relations, while tensile tests with digital image correlation (DIC) are used to determine the physical properties of polylactic acid (PLA). Scanning electron microscopy (SEM) images help investigate variations in modulus of elasticity and ultimate tensile strength in dogbone specimens, and the Ritz method with Chebyshev polynomials is employed to discretize the nonlinear equations. Second, two numerical algorithms are used to analyze the static behavior of the metatube within the nonlinear framework. The validation study is conducted for the auxetic tube and the representative volume element (RVE) of the unit cell based on the literature and finite element software Abaqus. Following the validation of the mathematical model, an extensive investigation is conducted to assess how differing parameters impact the mechanical bending and nonlinear instability analysis of the reentrant tube. [ABSTRACT FROM AUTHOR]

The combination of auxetic behavior with concrete offers promising advancements in structural materials, providing unique mechanical properties that enhance impact resistance and energy absorption. The study investigates the mechanical behavior of auxetic concrete cellular structures, focusing on elliptic and peanut-shaped unit cells as well as their modified stiffener configurations, under low-velocity impact loading. To compare their impact performance, traditional and stiffened models were analyzed numerically using finite element solver ANSYS/LS-DYNA. The findings indicate significant differences between traditional and stiffened models. Stiffened models, such as SEC and SPC, exhibit higher maximum impact forces compared to traditional models like TEC and TPC. The introduction of stiffeners delays the zero-force phenomenon, resulting in extended energy absorption periods. The TPC model absorbed the most significant proportion of the initial impact velocity among traditional models, whereas the SPC model exhibited the highest energy absorption in models with stiffeners. The study highlights the potential of stiffened auxetic concrete cellular structures to enhance impact resistance and energy dissipation, making them advantageous for applications requiring high structural resilience. Further research into varying impact velocities and loading directions is recommended to optimize these structures for diverse conditions. [ABSTRACT FROM AUTHOR]

Ferroelastic textures called star patterns are transformable into grilles whose rigid bars replace domain boundaries and are connected with hinges at their junctions. The grilles show several levels of self‐similarity. Exact formulae for the scaling factors as functions of the shape and number N of the arms are provided. The minimal dynamic model of such systems involves force constants at only one level (generation) of self‐similarity. The minimal set of force constants ensures stability of the stars with N = 2 and N = 3. At N = 4 the minimal model exhibits exactly one mode of zero frequency. The reaction of the four‐arm star to a tensile stress applied at the level of the force constants depends on the self‐similarity scaling factor and on the separation between the applied stress and the generation where the observation is made. In some regions of these parameters the reaction is analogous to auxetics but it also shows negative tensile characteristics, that is, a shrinking in the direction of the stress axis. With increasing distance from the external perturbation toward outer generations of self‐similarity the system shows a surprisingly fast restoration of the symmetry broken by the stress. [ABSTRACT FROM AUTHOR]

Rowing is a sport that requires athletes to perform the action of pulling and rotating an oar by hand, applying forces of considerable magnitude. Herein, inspired by the notion that auxetic materials and metamaterials behave differently compared to their conventional counterparts, it is examined how a handle prototype, specifically designed to incorporate the classic re‐entrant motif, behaves and how end‐users perceive it. Physical experiments conducted on such prototype, which measured the contact pressures, suggest that on average, higher pressures are measured when pulling with this reentrant grip compared to its non reentrant counterpart, indicating that this re‐entrant prototype should feel firmer. More importantly, respondents of a survey are asked to give their feedback, and different views on which handle they would prefer to use are provided. The ones who preferred the prototype with the reentrant features report that they preferred it because it felt firmer and allowed for a better grip. This suggests that there is potential for further investigation into whether handles, oar handles in particular, made from auxetic components, re‐entrant cells, or other motifs which are well known for their negative Poisson's ratio characteristics, could provide a better and more secure grip and be used in sports applications. [ABSTRACT FROM AUTHOR]

On‐water rowing is a sport where participants make extensive, powerful, and complex repetitive movements with their wrists to pull and feather (twist) the oar. Herein, the aim is to assess the frequency and perceived causes of wrist and forearm pain in rowers and, in particular, assess whether there are any possible mechanical issues that could be addressed through the use of auxetic technology. Through an online survey of 145 on‐water rowers, it is found that 33.8% of the rowers reported wrist or forearm pain arising from rowing. The majority (67.3%) consider over‐gripping to be the cause while one out of five associated it with periods of tension and anxiety, which also led them to over‐grip. This indicates that rowing handles could benefit from the use of mechanical metamaterials, auxetics in particular, owing to their anomalous manner in how they deform when subjected to mechanical deformations. Moreover, given the rise in popularity of coastal rowing, which will become an Olympic discipline alongside classic rowing as from the 2028 Los Angeles Olympic Games, the potential use of auxetics in the manufacture of protective gear for use in coastal rowing is also discussed. [ABSTRACT FROM AUTHOR]

Materials exhibiting auxetic behavior have garnered significant interest due to their potential applications across various fields, with synthetic auxetic materials being one such group. Theoretical studies have demonstrated the potential for various organic polymeric systems to exhibit auxetic behavior. However, to date, only a few synthesized molecular systems have shown some degree of auxetic behavior. Among the theoretical classes of molecular systems that have attracted attention are calix[4]arene systems in the "egg‐rack" conformation. While the theoretical systems proposed in the literature have been deemed difficult to synthesize, calix[4]arene chemistry has advanced tremendously in recent years. In fact, a number of molecular systems with configurations similar to those predicted to exhibit a negative Poisson's ratio have been synthesized, albeit with different chemical moieties. Consequently, it is deemed valuable to study the potential of these synthesized systems to exhibit a negative Poisson's ratio through force‐field‐based simulations. This study is extended to include theoretical calix[4]arene systems linked by acetylene moieties, which are also potentially synthesizable through known methods. It is suggested that these materials can exhibit auxetic behavior when subjected to on‐axis loading in the [001] direction. A detailed mechanistic study of these systems is also conducted. [ABSTRACT FROM AUTHOR]

Herein, several semianalytical formulae for the optimal distribution of elastic moduli in 2D or 3D domains occupied by nonhomogeneous, least compliant bodies are presented and three different methods for recovering microstructures predicted by the isotropic material design method are proposed, which is a stress‐based variant of topology optimization for isotropic bodies. In all five presented variants of the topology optimization of elastic bodies, the numerical implementation of these formulae requires only the use of any algorithm of searching for the minimum of functional in multidimensions without any constraints, even box constraints on design parameters. For each variant considered, the formulae defining this functional are defined analytically. All results concern the design of composite structures that maximize their stiffness (equivalently minimize their compliance) while satisfying a certain isoperimetric condition introducing the upper limit of the available material resource. The article pays special attention to the fact that the stiffest, heterogeneous isotropic elastic material has almost always auxetic properties. Based on the asymptotic homogenization method and adopted bending‐free lattice model, an algorithm for the numerical recovering of nonhomogeneous isotropic microstructure in the entire domain occupied by the plate is proposed, with a fairly easy‐to‐implement ability to model an auxetic behavior. [ABSTRACT FROM AUTHOR]

This article reports the design of a metamaterial model—made from interconnected units of rotating parallelograms and triangles—in which its Poisson's ratio can range from positive to negative by changing the internal angles between the rotating units. The on‐axes Poisson's ratios are established via geometrical construction while the on‐axes Young's moduli are extracted using energy approach. Results indicate that the metamaterial model manifests auxetic behavior for small and large internal angles, but non‐auxetic properties for intermediate range of internal angle. The results also reveal that a wide range of on‐axes Young's modulus can be adjusted by controlling the internal angle. A sustainable feature of this metamaterial model is its convenient adjustment of the effective mechanical properties over a wide range in order to be redeployed for different applications throughout its entire lifetime. [ABSTRACT FROM AUTHOR]

Cubic lattices based on tetrakaidecahedron cells with re‐entrant ribs are designed and fabricated via additive manufacturing. Poisson's ratio decreased to a negative value as the re‐entrant angle was made smaller. Poisson's ratio decreased as ribs were made more slender. Lattices with convex tetrakaidecahedron (truncated octahedron) cells had a Poisson's ratio near 0.5 in agreement with theory. Rib slenderness had minimal effect on Poisson's ratio in contrast to the re‐entrant lattices. [ABSTRACT FROM AUTHOR]

This study investigates the free vibration behavior of auxetic metamaterial plates using a refined plate theory. The research focuses on the integration of functionally graded graphene origami (GOri) into the plate structures, examining various content levels and folding patterns to enhance dynamic performance. The GOri-reinforced plates are analyzed within the context of a Winkler–Pasternak elastic substrate. Hamilton's principle is applied to derive the kinetic equations governing the auxetic metamaterial plates, facilitating an analytical solution for the governing equations. A comprehensive comparison of numerous parameters is conducted, including graphene content and dispersion type, GOri folding degree and distribution pattern, temperature effects, and elastic foundation coefficients, all of which influence the vibrational characteristics of the plates. The findings identify critical factors affecting natural frequency, providing a thorough understanding of the relationship between the physical configuration of auxetic metamaterial plates and their dynamic response. This study ultimately aims to leverage these insights to optimize the design of auxetic metamaterials for improved vibrational performance in engineering applications. [ABSTRACT FROM AUTHOR]

Materials with a negative Poisson's ratio are known as auxetic materials, which are highly desirable for improved resistance to indentation and impact. Angle-ply composite laminates with high anisotropy exhibit auxetic behavior within a specific range of layup angles. In this research, the influence of negative Poisson's ratio on the mechanical response and the enhancement of the damage behavior of carbon/epoxy composite laminates under low-velocity impact has been numerically investigated. For this purpose, a MATLAB code based on classical lamination theory relationships was developed to determine the range of layup angles to achieve both negative Poisson's ratio in-plane and through-thickness (out-of-plane). Then, the layups with the most negative through-thickness and in-plane Poisson's ratio values were selected. Also, two new stacking sequences were investigated so that both of them partially exhibited the characteristic of negative through-thickness and in-plane Poisson's ratio. The progressive damage model is written and implemented using a computer code in the Abaqus user-material subroutine. The progressive damage model consists of Hashin and Puck failure criteria and the damage evolution model based on the equivalent strain method to predict the initiation and evolution of damage for matrix and fiber. The results indicate that the new laminate configurations have 66% higher effective longitudinal modulus and 173% higher effective transverse modulus compared to the in-plane and through-thickness auxetic ones, respectively. In addition, the proposed configurations showed less overall damage under low-velocity impact loading compared to the auxetic laminates. Based on the investigations, the new configurations with features such as high impact force, low impact time, and low maximum displacement could be suitable for use in structures with a hardwall design approach. [ABSTRACT FROM AUTHOR]

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This research presents a method to convert a conventional Nylon closed cell foam, with a density of 48 kg m−3, into auxetic metamaterials with densities ranging between 68 and 138 kg m−3. The samples are produced by applying vacuum and mechanical compression techniques. The study reports on the effect of processing parameters such as vacuum time, temperature, and mechanical pressure. Under optimized conditions, the resulting auxetic foams exhibit a tensile Poisson's ratio as low as −0.86, while the minimum compressive Poisson's ratio for the same sample reached −0.16. Based on morphological analyses via scanning electron microscopy (SEM), structural changes induced by the treatment are determined to relate with tensile and compressive properties, including modulus and strength, as well as the analysis of the stress level for different strains. The characterizations also include differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) for the Nylon foam before and after conversion. These findings underscore the potential applications of these auxetic foams in sports and military protective gears, as well as energy dissipation systems. [ABSTRACT FROM AUTHOR]

AbstractThe lightweight design of thin-walled curved structures as spherical shells are frequently implemented in architecture, aerospace, mechanical, automotive, nuclear, and defense structures. Under the transverse loads, shells may largely deform and hence snap from one equilibrium position to the other. Thus, this work aims to develop a mathematical model and computational solution to investigate the nonlinear bending and snap-through behavior of doubly curved auxetic metamaterial shell subjected to transversal loading, for the first time. The shell is composed of several layers through the shell thickness, each layer is manufactured from a copper (Cu) matrix reinforced with a specified weight fraction of graphene origami auxetic metamaterial (GOAM). The mechanical properties of the GOAM shell panel are presented and described by functions of the GOAM volume fraction and folding degree. Three types of GOAM-distributions are considered, which are U-type, X-type, and O-type. The theoretical framework of Kirchhoff–Love hypotheses for thin shells and von Karman type nonlinearity are used to derive the governing equations. The differential quadrature method (DQM) is implemented to discretize the space domain and convert the nonlinear partial differential equation to nonlinear algebraic equations in terms of displacement field. An efficient incremental iterative procedure is developed to solve the nonlinear equations and predict the snap-through behavior. A model conversion and validation with isotropic spherical shell is considered. Several numerical results are conducted considering the effects of changing GOAM content, distribution pattern, folding degree, and shell curvature and thickness. For panels exhibiting snap-through behavior, increasing the shell curvature leads to higher snap-through limiting load; however, the instability gap is enlarged. [ABSTRACT FROM AUTHOR]

AbstractAuxetic materials and structures have been largely regarded because of their superior mechanical properties compared to other structures. These materials and structures contract (expand) laterally under uniaxial compression (tension). In this study, we have investigated different types of auxetic cells such as reentrant, chiral and non-chiral, rotating polygonal, and etc. Also, we have described their mechanical properties in a separate section. The applications of these cells were also investigated in various fields of automotive, medical and etc. In this study, in addition to previous works, recent works have also been introduced. Being a comprehensive reference for different types of auxetic cells, this study helps researchers design various auxetic structures. [ABSTRACT FROM AUTHOR]

To obtain materials or metamaterials with desired elastic properties that are tailor-made for a particular application, it is necessary to design a new material or composite (which may be cumbersome) or to modify the structure of existing materials in order to change their properties in the desired direction. The latter approach, although also not easy, seems favourable with respect to parameters like costs and time-to-market. Despite the fact that elastic properties are one of the oldest studied physical parameters of matter, our understanding of the processes at the microstructural level, that are behind these properties, is still far from being complete. The present work, with the help of Monte Carlo computer simulations, aims to broaden this knowledge. The previously studied model crystal of hard spheres, containing a combined nanolayer and nanochannel inclusions, is revisited. This periodic model crystal has been extended to include a degree of disorder in the form of degenerate crystalline phase by introducing a degenerate crystalline phase within its structure. The inclusion has been transformed (without changes to its shape, size, or orientation) by randomly connecting the neighbouring spheres into di-atomic molecules (dumbbells). The impact of this modification on elastic properties has been investigated with the help of the Parrinello–Rahman approach in the isothermal–isobaric ensemble ( N p T ). It has been shown, that the presence of the degenerate crystalline phase of hard dumbbells in the system leads to a significant decrease in the Poisson's ratio in [ 110 ] -direction ( ν = − 0.235 ) and an overall enhancement of the auxetic properties. [ABSTRACT FROM AUTHOR]

AbstractThe many mechanical properties of the negative Poisson’s ratio structure and its connection to additive manufacturing have made them useful in a variety of fields. Information regarding the negative Poisson’s ratio (NPR) structures utilized in applications in daily life. Many studies have been carried out based on its applications and testing by changing its parameters on a single auxetic structure. Nonetheless, comparatively little study has been done on the behavior, significance for applications, and comparison of various auxetic structural types. Furthermore, the majority of research papers, articles, or papers addressing subjects about negative Poisson’s ratio structure have not discussed the advantages and disadvantages of the various NPR structures that have emerged recently. The goal of this study is to analyze various uses for negative Poisson’s ratio structures as well as many varieties of these structures. The tasks related to this project are specifically focused on designing, finite element analysis, 3D printing, and mechanical testing of various forms of negative Poisson’s ratio structures including a novel structure designed and 3D printed using both flexible and rigid materials to examine their mechanical characteristics and behavioral patterns. These findings may aid in the development of structures using materials for various applications by their specifications. [ABSTRACT FROM AUTHOR]

Unusual negative longitudinal piezoelectric effect (NLPE) and electric auxetic effect (EAE) have essential implications for designs of piezoelectric sensors and actuators. The emerging ferroelectric HfO2 is recently discovered to have both effects, while the underlying physical mechanisms remain elusive. To understand and regulate these intriguing effects, it is crucial to investigate the piezoelectricity in ferroelectric HfO2 and related fluorite-structure ferroelectrics. Here, we corroborate using first-principles calculations that all twelve fluorite-structure ferroelectrics covered in this study possess the NLPE. A chemical tendency of piezoelectricity is demonstrated, i.e., the larger the "iconicity," the stronger the NLPE. The structural origin is attributed to the predominant influence of the triple-coordinated anion displacement, namely, the more "ionic" fluorite-structure ferroelectrics exhibit larger anion displacement under a pressure or strain, which gives rise to a more negative internal-strain contribution dominating over the positive clamped-ion contribution and hence a stronger NLPE. Moreover, we confirm several electric auxetic materials in fluorite-structure ferroelectrics with finite electric field calculations. We find that the piezoelectricity of electric auxetic materials is suppressed by the external electric field along the polar direction, since it weakens the bonding heterogeneity. The unraveled fundamental understanding of the NLPE and EAE in this study may profoundly benefit the design and application of fluorite-structure ferroelectrics. [ABSTRACT FROM AUTHOR]

This study derives the constitutive relationships between stress resultants and strain measures for 4-star auxetic structures using force-moment analysis of a representative unit cell and the Castigliano strain energy method. To validate the accuracy of the constitutive model, bending analysis is performed for a 4-star auxetic rectangular plate under Levy boundary conditions. The analytical and numerical results show excellent agreement, confirming the validity of the constitutive relations extracted from the generic 4-star unit cell. This work establishes a theoretical framework for designing 4-star auxetic metamaterials and demonstrates their potential for diverse engineering applications. [ABSTRACT FROM AUTHOR]

This experimental study delves into the vibration response and energy absorption characteristics of three distinct auxetic tubular structures under quasi-static compression: the Reentrant, Double-V, and Anti-Trichiral designs. Notably characterized by their negative Poisson's ratio, these structures exhibit superior mechanical properties in comparison to conventional tubular structures with a positive Poisson's ratio. For consistency, all samples were standardized in terms of diameter and height, while variations due to unit cell geometry were parameterized based on the structure's weight. The samples were fabricated using Fused Deposition Modeling (FDM) with both PLA and PLA-Carbon filaments. Modal testing was conducted to evaluate structural damping, providing insights through time domain plots and frequency response functions. Subsequent compression testing facilitated the assessment of force-displacement relationships, thereby enabling the quantification of energy absorbed, specific energy absorption, and peak crushing force metrics. The analysis revealed that Reentrant unit cells constructed from PLA exhibited a 5% higher damping efficiency compared to Double-V and 4% higher than Anti-Trichiral units. Similarly, Reentrant units in PLA-Carbon demonstrated an 8 and 30% increase in damping relative to Double-V and Anti-Trichiral, respectively. During quasi-static compression, Double-V units in PLA showcased a 66 and 13% superior energy absorption capacity over Reentrant and Anti-Trichiral units, respectively. With PLA-Carbon, Double-V units exhibited a 28 and 116% enhanced energy absorption capacity compared to Reentrant and Anti-Trichiral units, respectively. This comprehensive evaluation offers insightful revelations into the damping and energy absorption capabilities of varying auxetic cell structures when composed of different materials, highlighting their potential in engineering applications. [ABSTRACT FROM AUTHOR]

This paper dealt with the vibration characteristics of an auxetic rectangular plate under in-plane compression. Firstly, the equivalent bending stiffness matrix of a star-shaped auxetic plate was obtained using Castigliano's theorem and the homogenization technique. Then, employing the classical plate theory (CPT) in conjunction with the Rayleigh–Ritz method, the natural frequencies of auxetic plate were extracted. The chebyshev polynomial series has been selected to define the assumed displacement fields of the plate. Convergence study for the Rayleigh–Ritz method was conducted. The accuracy of the proposed mathematical model for the star-shaped auxetic plate was validated using the results from a finite element analysis (FEA). Effects of unit cell geometric parameters on the natural frequencies of the plate were examined. The auxeticity angle of star-shaped pattern had a significant effect on the natural frequencies. The present approach can be extended into other auxetic patterns, such as re-entrant bowtie auxetics. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of a blast-resistant design of reinforced concrete panels with a novel auxetic reinforcement layout inspired by auxetic materials, which have a negative Poisson's ratio, i.e., shrink under compression and expand under tension. A series of two-way supported panels reinforced with re-entrant auxetic-shaped rebars were numerically tested under a TNT explosion. The high-fidelity multi-physics explicit solver of LS-DYNA was utilized to analyze the efficiency of the proposed design. Firstly, the incident pressure of a TNT explosion data and the structural response of a conventional reinforced concrete panel under a TNT explosion were successfully validated by comparing with the experimental and empirical results. Secondly, the blast-resistant capacity of the proposed model was evaluated in comparison to two different conventional designs. Moreover, a parametric study was carried out to reveal the driving parameters of the newly proposed auxetic-shaped reinforcement design. It has been proved that the proposed auxetic reinforcement layout significantly reduces the spalling radius and increases the energy absorption capacity of panels. As a result of the parametric study, the increased reinforcement volume ratio was ineffective on the spalling radius, although the cell size of auxetic reinforcement was found to be quite effective for the blast-resistant design of concrete panels. Overall, the proposed re-entrant auxetic reinforced panel performed far better than conventional designs under blast load. With the recent developments in 3D printing technology, the proposed auxetic reinforcement layout is a strong candidate to deal with blast-resistant designs of concrete panels. [ABSTRACT FROM AUTHOR]

Auxetic metamaterials, characterized by their negative Poisson's ratio, have garnered significant interest in various fields due to their unique mechanical properties. This article presents a pioneering approach to the development of auxetic smart metamaterials using shape memory alloy (SMA) as the core material. As SMAs can be Joule heated to change between their low‐ and high‐temperature phases to trigger the actuation of the structure, the auxetic smart metamaterial can actively modify its shape and stiffness to produce bidirectional actuation with a single power input and using a single bias mechanical element. The proposed active auxetic metamaterial consists of an SMA plate patterned with auxetic cuts, creating hinges that modulate the deformation of the structure to produce an auxetic behavior. This work looks at the impact of different geometric parameters on the behavior of the structure, including its generated force, its maximum strain, and its Poisson's ratio. The study also investigates the effect of the number of segmented units, revealing that designs with more segmented units suffer from stress concentrations near attachment points, limiting their advantages. This article shows that smart materials can help imbue metamaterials such as auxetic metamaterials with active properties to facilitate their implementation in future robotic applications. [ABSTRACT FROM AUTHOR]

AbstractThis study presents a comprehensive thermal buckling analysis of sandwich plates composed of functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) face sheets on an auxetic concrete foundation, using Carrera’s unified formulation (CUF) as the theoretical framework. FG-GOEAM materials are emerging as advanced composites, combining exceptional mechanical resilience, tunable auxetic behavior, and high thermal stability, making them suitable for extreme environments. By employing CUF, a powerful and adaptable modeling approach, this work accurately captures the complex mechanical interactions within the FG-GOEAM sandwich structure under thermal loads, incorporating both material gradation and auxetic properties. To further enhance the precision and efficiency of this thermal buckling analysis, a deep neural network (DNN) is developed as a machine learning algorithm to predict critical temperature differences, based on a dataset generated through mathematics simulation. The DNN model demonstrates excellent predictive capability, validated by close alignment between its estimates and CUF results, thus reducing computational costs while maintaining high accuracy. Parametric studies are conducted to assess the effects of material gradation, aspect ratios, and foundation properties on thermal buckling performance. The results highlight the superior thermal stability of FG-GOEAM structures and the potential of DNNs to serve as reliable, computationally efficient tools for advanced structural analysis. This study provides a novel, integrated framework for high-fidelity thermal buckling prediction in complex auxetic composites, paving the way for broader applications in engineering fields requiring lightweight, thermally stable structures. [ABSTRACT FROM AUTHOR]

AbstractAuxetic materials are characterized by a negative Poisson’s ratio (NPR), which expands when stretched and shrinks when compressed. Due to the synclastic curvature of auxetics, they have good formability. These properties make them useful in applications requiring formability, such as composites, fashion and clothing, medical, protective, and sports fields. In this research, auxetic weft-knitted fabrics based on foldable structures were knitted. The effect of structural parameters including fabric pattern, yarn count, and loop length on the formability of auxetic weft-knitted fabrics was investigated and compared to plain weft-knitted fabric (Jersey). Auxetic fabrics with three distinct patterns and three different loop lengths were knitted using polyester yarns of varying three counts. Then, the formability experiment was conducted using the hemisphere mold, and the forming energy of fabric samples was obtained. The results demonstrated that auxetic fabrics exhibit superior formability to conventional (non-auxetic) fabrics, attributed to their synclastic curvature. Among the auxetic fabrics, those with larger zigzag angles, finer yarn counts, and larger loop lengths showed higher formability. These findings enhance the potential applications of auxetic fabrics in various industries such as medical and protective, emphasizing their ability to conform to complex shapes with minimal wrinkling. [ABSTRACT FROM AUTHOR]

Speculative negative Poisson's ratio (NPR) materials exhibit an auxetic response to strain in a predetermined direction due to their unusual morphologies, making them highly suitable for various specialized applications. For the rationale, these materials have immense potential in various specialized contexts. In weft-knitted auxetic fabrics, uneven tension in the purl loops leads to the distinctive curling architecture. Due to their inherent curly structure and adaptability, weft-knitted fabrics are an excellent choice for emulating NPR materials. In this study, 3D weft-knitted auxetic fabrics were created using flatbed purl knitting technology. Two distinctive patterns, comprising knit and tuck stitches, were employed. The number of stitches per repeat (SPR) was varied to assess the impact of grid size on NPR behavior. Additionally, the variation in measurement points within standard-sized characterization specimens was analyzed, revealing slight differences in auxeticity. Increasing the SPR size initially enhanced NPR behavior, up to a certain limit, beyond which the trend declined. A significant shift in NPR was observed due to material variation and inter-yarn friction, with a 27% and 28% shift of Poisson's ratio was experienced above and below the mean, respectively. Poisson's ratio was also positively correlated with energy absorption, suggesting that the designed materials could be effective for protective and energy-absorbing applications. [ABSTRACT FROM AUTHOR]

This work aims to study the influence of the material and geometric parameters that characterize re-entrant hexagonal honeycomb auxetic structures in the maximum transverse static deflection of beams. In addition, this study considers the composition of the material through the thickness results from the mixture of a metallic phase and one of four different selected ceramics, using the exponential volume fraction law. The first-order shear deformation theory within an equivalent single-layer approach is used to assess the material and geometric parameters' influence on the structures' deflection. Considering this theoretical approach, the impact of the material and geometric parameters on the shear correction factors, calculated for each specific case, is also analyzed. The results allow us to conclude how the shear correction factors and the structures' maximum static deflection are affected by the re-entrant hexagonal honeycomb auxetic cells' aspect ratios, by the angle associated with the direction of the inclined members of the hexagonal cells and the use of materials with differentiated Poisson's ratios. [ABSTRACT FROM AUTHOR]

This study explores a new nanoplate design's thermal and mechanical properties, including an auxetic core with a negative Poisson ratio. The core is between face plates made of barium–cobalt, which possess magnetoelectroelastic properties. The analysis centers on the parameters θ, β1, and β2 to clarify their influence on the nanoplate's performance. The evaluations of the nanoplate's thermal, electrical, and magnetic properties showcase its remarkable versatility and sensitivity. Incorporating magnetoelectroelastic face plates improves the multifunctionality of the nanoplate, making it a highly promising option for use in smart technologies. The findings offer valuable insights into the distinctive features of auxetic core structures, significantly enhancing the comprehension of these materials. This research emphasizes the potential for creating groundbreaking applications in fields like aerospace engineering and advanced electronics, where versatile and adaptable materials play a vital role. This study contributes to the broader knowledge of auxetic materials and their practical implementation in cutting‐edge technological solutions by exploring the interplay between thermal, mechanical, and magnetoelectroelastic properties. [ABSTRACT FROM AUTHOR]

AbstractThe present work investigates stress, strain and deformation analyses of a shear deformable cylindrical shell manufactures by a Copper (Cu) core reinforced with graphene origami auxetic metamaterial subjected to mechanical and thermal loads. The cylindrical models can be used in sport equipment especially in expander component. The effective material properties of the graphene origami auxetic reinforced Cu matrix are developed using micromechanical models cooperate both material properties of graphene and Cu in terms of local temperature, volume fraction and folding degree. The principle of virtual work is used to derive governing equations with accounting thermal loading. [ABSTRACT FROM AUTHOR]

Auxetic materials are mostly known for their negative Poisson's ratio, a parameter used to describe the deformation behavior of structures. This ratio serves a similar role as a material constant, detailing behavior on a microscopic scale. However, the deformation behavior of complex auxetic structures cannot be described completely using the classical Poisson's ratio approach. While it may suffice to describe auxetic behavior in foams or crystals, it fails for larger scales like the auxetic lattice structures, discussed in this study. To address this limitation, an extension to the classical Poisson's ratio is proposed to better describe the behavior of such structures. The developed method shows the different dependencies, namely the directional dependency, the frequency dependency and the position dependency of auxetic unit cells. [ABSTRACT FROM AUTHOR]