Auxetic materials with the counter-intuitive effect of negative Poisson’s ratio (NPR) have potentials for diverse applications. Typical shape optimization designs of auxetic structures involve ...complicated sensitivity analysis and a time-consuming iterative process, which is not beneficial for designing functionally-graded structures where the auxetics at different locations need to be inversely designed. To improve the efficiency of the inverse design and simplify the sensitivity analysis, we propose a deep-learning-based inverse shape design approach for tetra-chiral auxetics. First, a non-uniform rational basis spline (NURBS)-based parameterization of tetra-chiral structures is developed to create design samples and computational homogenization based on isogeometric analysis is used in these samples to generate a database consisting of mechanical properties and geometric parameters. Then, the database is utilized to train deep neural networks (DNN) to generate a surrogate model that represents the effective mechanical properties as a function of geometric parameters. Finally, the surrogate model is directly used in the inverse design framework where sensitivity analysis can be calculated analytically. Numerical examples with verifications are presented to demonstrate the efficiency and accuracy of the proposed design methodology.
This paper presents an experimental study on impact behaviour and plastic evolution of chiral structure subjected to in-plane impact loading using a Split Hopkinson pressure bar (SHPB). The finite ...element (FE) model developed in ABAQUS/Explicit was validated and utilized for parametric study, and further developed as an extension of experimental work. The impact scenarios from both structure itself and external input are considered, including relative density, topology parameter r/R and initial impact energy. Results indicate that chiral structure exhibits three critical failure modes corresponding to various impact velocities ranging from 5 m/s to 50 m/s. Interestingly, chiral structure occurs with two densification stages induced by ligaments-dominated and nodes-dominated crushing deformation, respectively, proving the capability of independent energy management mechanism. Increasing the value of relative density from 0.19 to 0.39 contributes to a maximum of 250% increase in the specific energy absorption (SEA). Although increasing the value of r/R from 0.04 to 0.2 can dramatically decrease Poisson’s ratio (PR) from 0.07 to − 0.63 (significant negative PR), high strain-rate dependence of PR is also observed. In addition, the impact displacement is mostly influenced by initial impact energy but not by impact velocity and mass. The obtained results of this study provide a new insight into the impact performance of chiral structure, which contributes to the optimal design of auxetic crashworthiness system.
A new auxetic structure was designed with rigid diamonds incorporated to enhance the strength of a star-shaped auxetic structure along with the symmetry in the present work. The new structure was ...fabricated through Multi-Jet Fusion process and subjected to quasi-static compression tests for static analysis. Finite element model was developed using ABAQUS and validated by experimental results in terms of deformation mode, nominal stress-strain curve, and Poisson’s ratio of the auxetic structure. Theoretical model was also developed to predict the Poisson’s ratio of a unit cell of the designed auxetic structure. The theoretically predicted Poisson’s ratio is in tandem with that of obtained from a finite element model, which utilized periodic boundary conditions. Parametric study using the theoretical model revealed that the angle of the inclined members has shown a significant effect on the Poisson’s ratio. The newly proposed structure exhibited 36% better specific plateau stress than a conventional 3D star-shaped auxetic structure of similar geometrical parameters.
Double arrowhead honeycombs (DAHs) are auxetic cellular materials with negative Poisson's ratio (NPR). The quasi-static and impact behaviors of both uniform and functionally graded DAHs are explored. ...Analytical expressions for the in-plane Young's modulus, Poisson's ratio and quasi-static yield stress of uniform DAHs are derived and are found to be consistent with finite element (FE) predictions, showing that the quasi-static yield stress of DAHs is dependent upon the geometrical parameters and NPR. Systematical simulations of uniform DAHs subject to different impact velocities reveal that there exists a critical impact velocity beyond which the dynamic plateau stress is insensitive to the effect of NPR. A semi-empirical expression of the plateau stress is obtained. For functionally graded DAHs, they are shown to only have improved energy absorption capacity under high velocity impacts. Moreover, the results of uniform DAHs are shown to be able to be adopted to interpret the simulated plateau stress of functionally graded DAHs under impact loading. The deformation mechanisms associated with the impact resistance of DAHs are also discussed.
•The impact responses of auxetic double arrowhead honeycombs are simulated.•Analytical expressions for elastic constants and yield stress are derived.•Beyond a critical impact velocity, the plateau stress is insensitive to the auxetic effect.•Functionally graded design is advantageous for energy absorption under high velocity impacts.
•The 3D double-V meta-lattices with auxeticity are further self-adapted to meet the spatial requirement of curved sandwich beams.•The GRC facesheets were designed to have various distributions to ...make the structure possess FG configurations.•Results from full-scale FE modeling and nonlinear analysis have shown the significant effects of structural curvature radii.•FG configurations are found to have distinct effects on fundamental natural frequencies.
The functionally graded (FG) curved sandwich beams with the self-adapted auxetic 3D double-V meta-lattice core and GRC (graphene reinforced composite) facesheets are designed, modeled, and analyzed to reveal their linear vibration and nonlinear dynamic behaviors. The 3D double-V meta-lattices with negative Poisson’s ratio (NPR), developed from the 2D double arrowed honeycombs, are designed that can be self-adapted to meet the spatial requirements of curved sandwich beams. Through micromechanical modeling according to the extended Halpin-Tsai model, the material properties are determined for GRC facesheets, which are further designed to have different distributions of graphene sheets along the structural radial direction, to make the whole sandwich beams possess FG configurations. By linear vibration analysis, the distinct influences of FG configurations on the fundamental natural frequencies are presented. Results from full-scale FE modeling and nonlinear analysis have shown the significant effects of structural curvature radii. The influences of beam lengths, strut radii, thicknesses of the core layer and facesheets, and charge parameters of the blast loadings are followed.
Honeycombs derived from the combination of multiple kinds of structures have better energy absorption compared with a single structure. A novel bidirectional re-entrant honeycomb (BRH) is designed by ...combining four hexagonal honeycombs with the quadrangular-shaped honeycomb (QSH). The correctness and accuracy of two plateau stress theory are verified by the simulations. The effect of geometric parameters on the plateau stress and negative Poisson ′s ratio (NPR) behavior is studied. The results show that two plateau stress facilitate energy absorption at the low-velocity, and the plateau stress of the BRH is also improved at the medium- and the high-velocity. In addition, the collapsed modes of various velocities and relative density are summarized. These results indicate the BRH has better impact resistance and the energy absorption capacity, and the special energy absorption is adjusted significantly by geometric parameters. Moreover, the NPR effect is more obvious at the low-velocity particularly. Thus, the design method of honeycomb metamaterials can improve the design efficiency for obtaining high performance structures with energy absorption capacity.
•A novel bidirectional re-entrant honeycomb (BRH) with two plateau stress is designed.•The effect of geometric parameters on the plateau stress and negative Poisson’s ratio behavior is studied.•The collapsed modes of various velocities and relative density are summarized.
In this paper, a new kind of chiral three-dimensional honeycomb material was designed by orthogonal assembling based on chiral two-dimensional honeycomb with four ligaments. The analytical formulae ...of equivalent Young’s modulus and Poisson’s ratio are deduced using the beam theory. The calculations of the analytical formulae can be well consistent with those of finite element method. The theoretical and numerical results show that the honeycomb material proposed in this paper is isotropic at the macroscopic scale and its Poisson’s ratio is close to −1, which means the material have larger ratio of shear modulus to Young’s modulus. Furthermore, the influence of geometries on the equivalent elastic parameters are also discussed.
Recent advances in lithography technology and the spread of 3D printers allow us a facile fabrication of special materials with complicated microstructures. The materials are called "designed ...materials" or "architectured materials" and provide new opportunities for material development. These materials, which owing to their rationally designed architectures exhibit unusual properties at the micro- and nano-scales, are being widely exploited in the development of modern materials with customized and improved performance. Meta-materials are found to possess superior and unusual properties as regards static modulus (axial stress divided by axial strain), density, energy absorption, smart functionality, and negative Poisson's ratio (NPR). However, in spite of recent developments, it has only been feasible to fabricate a few such meta-materials and to implement them in practical applications. Against such a backdrop, a broad review of the wide range of cellular auxetic structures for mechanical metamaterials available at our disposal and their potential application areas is important. Classified according to their geometrical configuration, this paper provides a review of cellular auxetic structures. The structures are presented with a view to tap into their potential abilities and leverage multidimensional fabrication advances to facilitate their application in industry. In this review, there is a special emphasis on state-of-the-art applications of these structures in important domains such as sensors and actuators, the medical industry, and defense while touching upon ways to accelerate the material development process.
Novel auxetic tubes (NAT) were designed, fabricated and examined. Their mechanical properties were compared with the original auxetic tube (OAT) by the finite element method and experiments. The ...results show that NAT increases the specific energy absorption (SEA) without sacrificing the auxetic characteristic. Then, the effect of unit cell parameters on the mechanical properties of NAT tubes was explored. The results show that, in a certain range, rib reduction can improve the SEA of NAT without sacrificing the auxetic effect. To further improve the mechanical properties of NAT, three novel ribbed auxetic tubes (NRAT) were proposed and compared with NAT. It is concluded that the SEA of NAT can be improved by adding a straight rib to the inner long axis of the ellipse. In addition, the effect of straight rib width on the mechanical properties of NRAT was investigated. The results show that the larger the straight rib is, the higher the energy absorption is. Finally, the stability of the 3D auxetic tubular metamaterial is greater than that of the 2D auxetic thin-plate metamaterial by investigating. Due to their desirable mechanical properties, the NAT and NRAT have great potential for applications in medical engineering, vehicle crashworthiness and protective infrastructure.
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•Enhancement mechanical properties of the re-entrant honeycomb cell.•Advanced tunable mechanical properties and new derived analytical expressions.•Non-linear behaviour of classical ...and modified re-entrant cells.•Validated analytical and numerical work using literature experiment.
In this paper, a work to improve to the auxetic re-entrant cell is reported. This work aims to conserve the negative or zero Poisson's ratio feature of the classical re-entrant cell with no degradation while amplifying the in-plane elastic moduli. To develop and control the stiffness of the cell a new cell was created using a circular wall element in the middle of the classical re-entrant cell. The analytical expressions of the new re-entrant cell were derived and validated by finite element models. Derived analytical expressions of this work can be used to model the classical cell. Using this feature, validation of analytical and numerical models of this work is also provided with a classical cell's experimental works reported in the literature. In the linear region, both the analytical and the finite element models match very closely with the literature experiments. Because of the highly non-linearity of the re-entrant structures, after the linear examination, this work was expanded to model the non-linear behaviour of both the classical and new cells numerically. Literature experiments also verify the non-linear finite element models of this work in means of the classical re-entrant cell's results. Detailed design graphs are given for tuning the rigidity and negative Poisson’s ratios. The presented new design in this paper grants an extra rigidity while providing the same negative Poisson's ratios with those of the classical cells.
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