Re-entrant Auxetic Structure Research Articles

Finite element simulations of auxetic structure combined with honeycomb using unidirectional continuous carbon fiber composite properties

Metamaterials have been studied over the last few decades, as they may exhibit peculiar mechanical behavior. An example is the re-entrant auxetic structure, which can display negative Poisson ratio. Likewise, the honeycomb structure has also been widely used, mainly in sandwich-panels. Despite several studies including these geometries, the use of composite as raw material has not been reported in the literature, so this work aimed to perform finite element simulations of combined honeycomb and re-entrant auxetic structures using properties of continuous, unidirectional carbon fiber composite in epoxy matrix. For this, three types of modeling were used: beam, shell and solid and two sets of constraints were applied for each model. By analyzing the total deformation profiles obtained for these three models, it was possible to observe that both beam and shell modeling results were close to the three-dimensional modeling when applying a vertical compression displacement, in which beam modeling showed a better approximation. On the other hand, when applying the compression displacement horizontally, the beam modeling proved to be inadequate, while the shell modeling presented values close to the solid modeling. Therefore, it is concluded that it is possible to model similar structures using shell element instead of solid element.

Machine Learning and Regression Analysis Approaches for Investigation of Mechanical Properties of FDM Manufactured Re-Entrant Auxetic Structures Under Flexural Loading

This paper describes an experimental study on re-entrant auxetic structures manufactured by fused deposition modeling (FDM). The feedstock materials of NPR structures are acrylonitrile butadiene styrene (ABS) and poly-lactic acid (PLA). Experimental study is performed to examine the effect of design factors (angle, width, and length of arm) of unit cell of auxetic structures on three responses namely strength, stiffness, and specific energy absorption (SEA) under flexural loading. From the experimental results, it is found that flexural strength improves with increase in all three design factors of ABS structures; while it improves with increase in angle and reduction in width and length of arm for PLA structures. Furthermore, based on experimental study, regression models of responses are developed using analysis of variance (ANOVA). Also, machine learning (ML) models using neural networks are developed to predict all three responses. Results of regression models are compared with NN models to assess accuracy of prediction. Finally, optimal configuration of auxetic structure is determined using gray relational analysis (GRA) to improve the responses; and reduce weight and fabrication time.

FDM manufactured auxetic structures: An investigation of mechanical properties using machine learning techniques

The present article describes an experimental study on re-entrant auxetic structures manufactured by fused deposition modelling (FDM). The feedstock materials of NPR structures are acrylonitrile butadiene styrene (ABS) and poly-lactic acid (PLA). Experimental study is performed to examine the effect of design factors (angle, width, and length of arm) of unit cell of auxetic structures on three responses namely strength, stiffness and specific energy absorption (SEA) under flexural loading. From the experimental results, it is found that flexural strength improves with increase in all three design factors of ABS structures; while it improves with increase in angle, and reduction in width and length of arm for PLA structures. Further, based on experimental study regression models of responses are developed using analysis of variance (ANOVA). Also, machine learning (ML) models using neural networks are developed to predict all three responses. It is observed that, trained DNN models predicted strength, stiffness and SEA with deviation of 1.62%, 8.33%, and 5.37% for ABS material and 3.056%, 5.56%, and 2.25% for PLA material, compared to SNN models respectively. Further, results of regression models are compared with NN models to assess accuracy of prediction. Finally, optimal configuration of auxetic structure is determined using grey relational analysis (GRA) to improve the responses; and reduce weight and fabrication time.

On the response of re-entrant auxetic structure under dynamic crushing

The present work focuses on the dynamic crushing response of 2D re-entrant auxetic honeycomb. The aim of this work is to propose analytic formulations to predict the crushing strength of the considered structure by including design parameters (specific geometrical ratios and/or material properties). The model for dynamic impact is based on shock waves propagation analogy in a rigid, perfectly plastic, locking (R-P-P-L) material model. The formulations depend on the geometric and the material characteristics of the auxetic but also on the impact velocity. Finite Element simulations of the impact of a plate on an auxetic structure were carried out using the RADIOSS® explicit solver. The impact velocities varies from 35 m/s to 200 m/s. The numerical simulations presented in this study show good accordance between analytical and Finite Element results.

Impact behavior of auxetic structures: Experimental and numerical analysis

Auxetic materials are structured lattice materials with a negative Poisson’s ratio (NPR) and excellent tensile and impact strength compared to conventional bulk materials. It could be used for crashworthy structural applications in aerospace, automotive, and biomedical sections due to its very high specific energy absorption capacity compared to honeycomb structures. With the advent of additive manufacturing technology, it is possible to fabricate complex auxetic structures using metallic, ceramic, and polymeric materials. The literature on the high-speed impact behavior of auxetic structured thermos plastic polylactic acid (PLA) is limited. Therefore, the present work is focused on studying the impact behavior of S-shaped and re-entrant auxetic structures fabricated using Fused Deposition Modeling (FDM). The drop mass impact tests were conducted on these auxetic structures to estimate their impact resistance and energy absorption capability. FEA was undertaken to simulate and validate the impact behavior with experimental results. Quasi-static compression and Split Hopkinson Pressure Bar (SHPB) tests were conducted to get the bulk material's impact properties and material model. These data were used to model material properties in FEA. It was observed that the S-shaped auxetic structure had shown higher compressive plateau stress and energy absorption capacity compared to the re-entrant structure. These auxetic structures' deformation mode and failure were explored through detailed structural analysis using FEA.

Experimental and numerical analysis of a novel 3D re-entrant auxetic structure

The energy absorption performance during collisions and crushing is one of the critical parameters in the design of vehicle structures. Therefore, researchers are continually trying to improve the energy-absorbing properties of the crash box to reduce the force transmitted to the occupant during an accident. In this research, a novel three-dimensional re-entrant auxetic structure has been proposed to improve energy-absorbing performances. Criteria for evaluating energy absorption including the initial peak crushing force, energy absorption, mean crushing force, crushing force efficiency, and specific energy absorption, were obtained through numerical and experimental methods. The structure showed auxetic behavior in two transverse directions during compressive loading and absorbed more energy. The force-displacement curve showed low initial peak crushing force, and the structure collapsed uniformly during compressive loading. The effects of the angle of the diagonal strut with the vertical axis, the thickness of the struts, and the ratio of horizontal strut length to diagonal strut length on the energy absorption properties of the structure were studied, too.

In-plane compression response of foam filled re-entrant auxetic structure

In-plane compression response of foam filled re-entrant auxetic structure

Fatigue behaviour of re-entrant auxetic structures made of the aluminium alloy AA7075-T651

An investigation of the fatigue behaviour of the re-entrant auxetic structures made of the aluminium alloy AA 7075-T651 is presented in this study. The analysed auxetic structures represent a new class of cellular structures that show anomalous deformation responses such as negative Poisson’s ratio. In the proposed work, the influence of the unit cell orientation on the crack path and fatigue life was studied using experimental and computational approaches. The Low Cycle Fatigue (LCF) tests were performed at load control with the load ratio 0.1 in tension. In the LCF tests five loading levels were selected, and at least two tests were performed at each loading level. The same loading conditions were then applied in the computational model in the framework of the ANSYS software package, where a nonlinear kinematic material model was applied to obtain the stress–strain relationship. The strain-life approach, with consideration of the Morrow mean stress correction, was then used to obtain the fatigue life of the analysed auxetic structures. The experimental and computational results showed that the unit cell’s orientation has a minor influence on the fatigue life of both analysed auxetic structures, but impact on the direction of the fatigue failure path significantly.

Numerical and random forest modelling of the impact response of hierarchical auxetic structures

Major sources of concern when auxetic protective structures are deployed in service of mission-critical applications encompass the triggering of high impact stress and the weakening of the structures’ elastic strength in response to the impact events. The current prevailing approach to assessing the impact resistance of these structures broadly hinges on mechanics-informed nonlinear finite element (FE) analysis. However, this method is computationally expensive and ill-suited for tackling the implementation of automated condition monitoring schemes. To address these issues, first, this paper proposes a hybrid hierarchical auxetic structure named Hybrid-Hierarchical Re-entrant Honeycomb (HHRH) that is endowed with impact stress-reducing capabilities. Next, using explicit FE, the investigation uncovers the interplay between the key geometric features of this HHRH auxetic structure and the impact performance under low, intermediate, and high crushing velocities. The outcome of the nonlinear explicit FE simulations is then unified with random forests (RF) scheme towards the establishment of intelligent auxetic structural systems. The results revealed that the developed HHRH maintained the auxeticity of the regular re-entrant auxetic and exhibited superior performance in some crushing strain regions. Moreover, the HHRH structure manifests up to an 85 % reduction in peak stress and the proposed reinforcement boosts the auxetic property by up to 23 % when compared to the regular re-entrant auxetic structure under high-velocity applications. Regarding the established data-driven RF-enabled machine learning model, its predictive strength with optimally-tuned hyperparameters is demonstrated to excellently capture the nonlinear multi-modal crushing stress response at various crushing strains, velocities, and geometric variations. Data AvailabilityThe raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Variation of Poisson’s Ratio with Axial Strain for Three-Dimensional Reentrant Auxetic Structures

This study presents numerical investigations of the influence of structural parameters on the variation of the Poisson ratio with axial strain for auxetic structures. Three-dimensional reentrant structures were considered with variable strut thickness to length ratio and reentrance angles. The variation of the volume, relative density, and relative stiffness with axial strain was also studied.

Axial crushing of auxetics tube manufactured by 3D printing of poliamide reinforced with short carbon fibre

Additive manufacturing, and more specifically FFF (Fused Filament Fabrication), makes it possible to manufacture complex designs that are difficult to manufacture using conventional processes that improve the mechanical behaviour of the component. In the present work, the axial impact behaviour of cylindrical tubes with a reentrant auxetic structure has been characterized. The material used is a polyamide 6 reinforced with short carbon fibre. As a reference, a solid thickness tube with the same outer diameter and mass as the tube with the auxentic structure has been designed. The main result is that the auxetic structure not only improves the specific absorption capacity, but also allows a progressive collapse thanks to the design and location of fault initiators. For this reason, 3D printing technologies have very attractive properties for the design of impact absorbers in the transport sector.

Fatigue crack growth in the re-entrant auxetic structure

The investigation of fatigue behaviour of the re-entrant and rotated re-entrant auxetic specimens made of Al-alloy 7075-T651 is presented in this study. In the proposed work, the influence of the orientation of the unit cell on the crack path and fatigue life were studied by using both experimental and computational approaches. In the experimental and computational approach, two geometric layouts of the base unit cell were analysed (re-entrant and rotated re-entrant structure). The Low Cycle Fatigue (LCF) tests were performed at load control with the load ratio 0.1 in tensile. In the LCF tests, five loading levels were selected and at least two tests were performed at each loading level. The same loading conditions were then applied in the computational model in the framework of the ANSYS software package. For the fatigue life calculation, the strain life approach was used, based on the Coffin-Manson model with a Morrow mean stress correction. The comparison between computational and experimental results regarding Fa − N fatigue-life curves and observed fatigue failure path showed a reasonable agreement.

In-plane energy absorption characteristics of a modified re-entrant auxetic structure fabricated via 3D printing

Here, we present the in-plane energy absorption characteristics of modified re-entrant auxetic honeycombs realized via fused filament fabrication in conjunction with parametric analysis and geometry optimization. The influence and interaction effects of the geometrical parameters such as strut-length ratio and joint-angles on the stiffness, strength and energy absorption characteristics of modified re-entrant auxetic honeycombs were evaluated. Subsequently, Finite Element results obtained using ABAQUS/Explicit were corroborated with measured data. Deformation mode, stress-strain response and energy absorption behavior of an optimal re-entrant auxetic honeycomb were studied and compared with conventional re-entrant auxetic structure. Modified auxetic structure reveals an 36% improvement in the specific energy absorption capacity. Our analysis further indicates that due to the introduction of more nodes with low rotational stiffness, the failure strain of the modified re-entrant structure has increased resulting in improved energy absorption capacity.

Blast mitigation using polymeric 3D printed auxetic re-entrant honeycomb structures: A preliminary study

Protection of critical infrastructure in an urban environment is a challenging task, specifically against the vehicle bourne improvised explosive device threat. To design infrastructure to withstand this evolving threat, novel solutions and advanced materials need to be developed. One such material of interest are auxetics. This study experimentally analysed the mitigation of blast response of auxetic re-entrant honeycomb structures, with geometries varying between −ve 30° and +ve 30° using additive manufacturing (3D printing) techniques and non-explosive loading via shock tube. Re-entrant auxetic structures (−ve 15°) exhibited repeatable blast mitigation of 23% and reduced the transmitted pressure and impulse of the blast wave. Further highlighting their potential application as a protective measure to enhance a structures blast survivability.

Fabrication and testing of re-entrant auxetic samples and sensor: Numerically and experimentally

Auxetic structures (negative Poisson’s ratio) are a group of materials that expand (contract) under tensile (compression) longitudinal loading. In this work, the effect of re-entrant auxetic structure geometry on Poisson’s ratio was investigated under large tensile loading experimentally and numerically and showed that the location and stiffness of rotation joints are two new important parameters affecting the value of Poisson’s ratio. Poisson's ratio increases as the rotation joints tighten and move away from the center of the structure. Therefore, by changing the location and stiffness of the rotation joints, it will be easy to obtain re-entrant auxetic structures with different Poisson's ratios, which makes it possible to build piezoresistant auxetic sensors with different sensitivities. A highly sensitive, stretchable piezoresistant auxetic sensor made of silicon rubber and chopped carbon fibers is proposed for low strain values. The main feature of this sensor is its high sensitivity for strains less than 6%, which previous works have been unable to detect this range of strains. Shifting strain is the value of strain in which the Poisson's ratio of the structure changes from negative to positive. The provided auxetic sensor performs exceptionally well until the shifting strain and then performs as conventional sensors. This improvement in sensing performance is about 150% (in terms of gauge factor).

Simulation-based assessment of coupled frequency response of magneto-electro-elastic auxetic multifunctional structures subjected to various electromagnetic circuits

This article deals with the modeling of magneto-electro-elastic auxetic structures and developing a methodology in COMSOL Multiphysics® to assess the free vibration response of such structures when subjected to various electromagnetic circuit conditions. The triple energy interaction between elastic, magnetic, and electric fields are established in the COMSOL Multiphysics® using structural mechanics and electromagnetic modules. The multiphase magneto-electro-elastic material with different percentages of piezoelectric and piezomagnetic phases are used as the material. In the solid mechanics module, the piezoelectric and piezomagnetic materials were created in stress-charge and stress-magnetization forms, respectively. The electric and magnetic fields are defined in COMSOL Multiphysics® through electromagnetic equations. Further, the customized controlled meshing constituted of free tetrahedral and triangular elements is adapted to trade-off between the accuracy and the computational expenses. The eigenvalue analysis is performed to obtain the natural frequencies of the MEE re-entrant auxetic structures. Also, the efficiency of smart auxetic structures over conventional honeycomb structures is presented throughout the manuscript. In addition, the discrepancy in the natural frequencies of the structures considering coupled and uncoupled state is also illustrated. It is believed that the modeling procedure and its outcomes serve as benchmark solutions for further design and analysis of smart auxetic magneto-electro-elastic structures.

In-plane elasticity of a novel vertical strut combined re-entrant honeycomb structure with negative Poisson’s ratio

In this study, a new vertical strut combined re-entrant auxetic structure was designed and its mechanical behaviors have been studied. An analytical model was established based on energy theorems considering bending, shearing and stretching. Numerical simulations and experiments were both carried out to confirm the validity of the analytical model based on beam theory. Results exhibited a good agreement between the refined analytical model, the numerical simulation and experimental study. Four deformation mechanisms were analyzed and the effect of deformation on the effective Poisson’s ratio (EPR) and elastic module were investigated. A parametric study was further performed to quantitatively illustrate the influences of the geometrical parameters on the effective elasticity properties of the designed structure. The results showed that the lightweight structures can significantly enhance the auxetic behavior and achieve a high degree of anisotropy with wide vertical strut lengths and internal angles compared with conventional re-entrant honeycomb configurations.

Numerical and experimental investigation of FDM fabricated re-entrant auxetic structures of ABS and PLA materials under compressive loading

Purpose Auxetic structures are one type of mechanical meta-materials mainly used for energy absorption applications because of their unique negative Poisson’s ratio. This study is focused on numerical and experimental investigations of fused deposition modeling (FDM) fabricated re-entrant auxetic structures of acrylonitrile butadiene styrene (ABS) and poly-lactic acid (PLA) materials under compressive loading. Influence of geometric parameters, namely, re-entrant angle, height and arm-length on strength, stiffness and specific energy absorption (SEA) of auxetic structures under compressive loading. Optimization of significant parameters is also performed to maximize these responses and minimize weight and time of fabrication. Further, efforts have also been made to develop predictive models for strength, stiffness and SEA of auxetic structures. Design/methodology/approach A full factorial design of experiment is used for planning experiments. Auxetic structures of ABS and PLA are fabricated by FDM technique of additive manufacturing within the constrained range of geometric parameters. Analysis of variance is performed to identify the influence of geometric parameters on responses. To optimize the geometric parameters Gray relational analysis is used. Deformation of auxetic structures is studied under compressive loading. A numerical investigation is also performed by building nonlinear finite element models of auxetic structures. Findings From the analysis of results, it is found that re-entrant angle, height and arm-length with their interactions are significant parameters influencing responses, namely, strength, stiffness and SEA of the auxetic structures of ABS and PLA materials. Based on the analysis, statistical nonlinear quadratic models are developed to predict these responses. Optimal configurations of auxetic structure of ABS and PLA are determined to maximize strength, stiffness, SEA and minimize weight and time of fabrication. From the study of deformation of auxetic structures, it is found that ABS structures have higher energy absorption, whereas PLA structures have better stiffness. Results of finite element analysis (FEA) are found in good agreement with experimental results. Research limitations/implications The present study is limited to re-entrant type of auxetic structures of ABS and PLA materials only under compressive loading. Also, results from the present study are valid within the selected range of geometric parameters. The findings of the present study are useful in maximizing strength, stiffness and SEA of auxetic structures that have wide applications in the automotive, aerospace, sports and marine sector. Originality/value No literature is available on studying the influence of geometric parameters, namely, re-entrant angle, height and arm-length of auxetic structure on strength, stiffness and SEA under compressive loading. Also, a comparative study of feedstock materials, namely, ABS and PLA, is also not reported. The present work attempts to fulfill the above research gaps.

Experimental approximation of the sound absorption coefficient (∝) for 3D printed reentrant auxetic structures of poly lactic acid reinforced with chicken keratin materials

In this research, auxetic composites of polylactic acid (PLA) reinforced by keratin materials (barbs and rachis), were developed through 3D printing manufacture to induce diverse acoustic properties. To evaluate the coefficient of sound absorption, an electro-acoustic experiment was implemented. The capacity of sound absorption for the composites was superior to conventional (honeycomb) and auxetic PLA geometries without reinforcement. Reduction of the free space in cavities (achieved by keratin materials) triggered an increment in the resistance in air flow, improving the sound absorption. Also, increasing the interconnectivity of the cavities provides sound waves with irregular transmission routes, which reduce the wave’s energy. Thus, in this work, acoustic properties are associated with 3D geometry of auxetic composites, shape, and concentration of reinforcements; considering the synergistic effect due to this combination, a range of metamaterials with acoustic capabilities were generated.

Re‐entrant auxetic structures fabricated by fused deposition modeling: An experimental study of influence of process parameters under compressive loading

AbstractThe present article is focused on investigating the influence of process parameters under compressive loading in case of reentrant auxetic structures fabricated by fused deposition modeling (FDM). Auxetic structures of acrylonitrile butadiene styrene (ABS) and poly‐lactic acid (PLA) materials are fabricated. Three process parameters of FDM namely layer thickness, raster angle, and number of contours are considered to investigate their influence on compressive strength, stiffness, and specific energy absorption (SEA). Experiments are performed on the basis of central composite design and analysis is performed using ANOVA. It is found that compressive strength of auxetic structure improves with increase in layer thickness. But with increase in raster angle, it increases first and then decreases. Compressive stiffness of structures initially decreases and then increases with increase in raster angle, while it increases with increase in number of contours. SEA of structures increases with decrease in layer thickness. Based on the analysis of experimental results, regression models are developed to predict these responses. Also, multi‐response optimization is performed to optimize strength, stiffness, and SEA. Auxetic structures failed under compressive loading are also examined using scanning electron microscope.