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The main objective of this paper is to evaluate the dynamic behaviour of sandwich toroidal shells composed of a core with negative Poisson ratio (auxetic honeycomb material) and nanocomposite enriched coating layers under impulsive/periodic pressures considering the geometrical nonlinearity. The set of nonlinear equilibrium equations based on the first-order shear deformation theory are and the resultant nonlinear differential motion equations are approximately solved by the Galerkin method and 4th-order Runge–Kutta solution, respectively. The achieved responses show that the amplitude of outward deformations is intensively increased when the proposed sandwich shells are subjected to rectangular periodic and impulsive loadings which shows the destructive effects of this type dynamic loading. The performed parametric studies shows that these destructive effects can be controlled by changing the geometrical properties of the honeycomb cells and the volume fractions of the nanocomposites in the coating layers. It is notable that in the previous studies the nonlinear dynamic response of toroidal shells subjected to various periodic and impulsive pressures was not investigated. However, in the present work, the mentioned dynamic responses were achieved and investigated without spending time-consuming computational. In fact, the novelty of this work is to develop such a robust and efficient tool. [ABSTRACT FROM AUTHOR]

3D printable multi-material honeycombs have attracted increasing interest recently due to the improved elastic moduli, buckling and energy absorption properties. This paper proposes an analytical homogenization for the equivalent in-plane elastic moduli (EIEM) of multi-material honeycombs. First, the axial and bending stiffness of a cantilever beam consist of three sections made of different materials is formulated. Then based on unit cell method and cantilever beam model, the closed-form expressions of EIEM are proposed by fully considering the deformations of both joints and cell walls with arbitrary stiffness, which are sufficiently general to be applied to hexagonal, auxetic and rectangular multi-material honeycombs and validated very well by numerical simulations and experiments. Furthermore, the effects of geometric and material distribution ratios on EIEM are discussed. The results show that the geometric and material distribution ratios of inclined cell wall have a significant effect on all five EIEM while that of vertical cell wall shows a significant effect on shear modulus but only a slight effect on y- direction elastic moduli. Compared with single-material honeycombs, changing joint stiffness has a significant effect on the equivalent Young's moduli and shear modulus but a slight effect on Poisson's ratios. • Closed-form expressions of equivalent elastic moduli for multi-material honeycombs. • Axial and bending stiffness formulated for a dual-material cantilever beam. • Analytical expressions of moduli match well with numerical and experimental results. • Dependency of material and geometric distributions on moduli investigated. • Proposed method applied to multi-material hexagonal and auxetic honeycombs. [ABSTRACT FROM AUTHOR]

Lantern, also known as coloured-lantern making, is known for being an ancient traditional craft in China that can be dated back as early as West Han Dynasty. Inspired by the lantern, the lattice element is built by vertically rotating and duplicating the 2D units, then the 3D auxetic metamaterial is formed by connecting the 8 ligaments of the lattice element on two perpendicular planes. As the elastic behaviors associated with this metamaterial are still almost unknown to a large extent, in this study, an analysis has been conducted to investigate how the geometric parameters related to the lattice design influence its elasticity. For this reason, a novel 3D lantern-shaped honeycomb structure (LSH) has been proposed, the Castigliano's second theorem, energy principle, and Moore's theorem are utilized to solve its Young's modulus and Poisson's ratio in the three main directions. The theoretical results exhibit good agreement with the numerical and experimental results. The results showed that the elasticity of LSH structures can be programmed by adjusting a range of geometric parameters. In addition, LSH features a bidirectional zero Poisson effect and a good stress distribution during compression. It shows potential in terms of load-bearing to meet the requirement of lightweight and high stiffness. This structure shows good promise for applications in aerospace, construction and other fields. [ABSTRACT FROM AUTHOR]

A 3D re-entrant honeycomb structure was designed in a simple configuration by introducing a spatial angular design parameter. Mechanical responses under uniaxial compression of it at constant spatial angle (α) and different re-entrant angles (θ) were investigated both experimentally and theoretically. Designed lattice auxetic structures with high shape fidelity were fabricated using selective laser sintering (SLS) of PA 2200 powder. The produced samples exhibited negative, zero, and positive Poisson's ratios depending on a selected θ value, and their mechanical properties varied over a wide range. Bend- and buckling-dominated deformation mechanisms of the struts have been observed under compression. Additionally, the analytical models of re-entrant honeycomb structures effectively illustrated the quantitative relationships between their mechanical properties (Young's modulus (E) and Poisson's ratio) and the design parameter θ. The results presented in this study would provide a reference to the customized design of the porous auxetic structures with unique mechanical properties. [ABSTRACT FROM AUTHOR]

Nonlinear dynamic behavior of double curved shallow shells with negative Poisson’s ratios in auxetic honeycombs on elastic foundations subjected blast, mechanical and damping loads is investigated in the present article. This study considers double curved shallow shells with auxetic core which have three layers in which the top and the bottom outer skins are isotropic aluminum materials; the central layer has honeycomb structure using the same aluminum material. Based on the analytical solution, Reddy’s third order shear deformation theory (TSDT) with the geometrical nonlinear in von Karman and Airy stress functions method, Galerkin method and the fourth-order Runge-Kutta method, the resulting equations are solved to obtain expressions for nonlinear motion equations. The effects of geometrical parameters, material properties, elastic foundations, imperfections, blast loads, mechanical and damping loads on the nonlinear dynamic analysis of double curved shallow shells with negative Poisson’s ratios in auxetic honeycombs are studied. [ABSTRACT FROM AUTHOR]

In the present work, a new design of honeycomb is proposed by embedding the rhombic configuration into the normal re-entrant hexagonal honeycomb (NRHH), in order to enhance the honeycomb’s in-plane mechanical properties. Both theoretical analysis and numerical simulations are employed to calculate the in-plane mechanical properties of the new honeycomb under uniaxial compression, including Young’s modulus, Poisson’s ratio and critical buckling strength. The results show that the new honeycomb can maintain auxetic performance, while both the in-plane Young’s modulus and the critical buckling strength are significantly improved compared to the NRHH. Comparisons between the present design and other exiting enhanced periodic topologies are also carried out. With respect to them, the present design features superior performances. For these outstanding properties, this layout may provide a new concept for the optimization and design of auxetic materials. [ABSTRACT FROM AUTHOR]

• Nonlinear thermo-buckling and postbuckling analysis. • The imperfect eccentrically stiffened FGM double curved shallow auxetic shells. • The shell subjected to uniform external pressure, axial compressive, thermal loads. • Using analytical method, the FSDT, the Galerkin and stress function methods. • Taking account the effect of pores and temperature-dependent material properties. It is the first time the nonlinear thermo-mechanical analysis (buckling and postbuckling) of imperfect eccentrically stiffened (ES) double curved shallow shells made of auxetic material under uniform external pressure, axial compressive and thermal loads has been studied by adopting analytical method. The double curved shallow sandwich shell is constructed by an auxetic honeycomb core layer with negative Poisson's ratio and two isotropic homogeneous skin layers. In the present study, the outer surface of the structure is reinforced by a system of FGM stiffeners and taking the influence of pores in the stiffeners into account to increase the load capacity of the structure. Besides, the material properties of the shells and stiffeners are both temperature-dependent. The first-order shear deformation theory is applied to derive equilibrium and compatibility equations of double curved shallow auxetic shell, considering both the geometrical nonlinearity in the Von Karman sense and initial geometrical imperfections and shells placed on the Winkler – Pasternak foundation. The Galerkin and stress function methods are proposed to determine the critical load value and the deflection– load curve by taking the root form of the two-term rotation angles to give the Galerkin integral an equilibrium equation. Several comparisons with results in other literature are made to examine the reliability and accuracy of the method used in the present study. Finally, the effects of thermal environment, reinforced stiffeners, elastic foundation, pores and parameters of auxetic core layer on the buckling and postbuckling loads are evaluated in this paper. The numerical and graphical results show that the reinforced stiffeners, auxetic core, temperature and porous distribution have significantly influenced on the buckling and postbuckling loads of ES double curved shallow auxetic honeycomb sandwich shells. [ABSTRACT FROM AUTHOR]

Abstract: Systems with a negative Poisson’s ratio (auxetic) exhibit the unusual yet very useful property of getting wider rather than thinner when uniaxially stretched. A novel mechanism to generate auxetic behaviour at tailor-made values which may be implemented in composites manufacture using readily available materials is proposed. FEA simulations are used to provide a proof of principle for this concept and an analytical model is proposed so as to elucidate the requirements for auxetic behaviour. It is shown that the simulations and analytical model give comparable results and confirm that this system may reach giant negative values of the Poisson’s ratio. [Copyright &y& Elsevier]

Cellular auxetic materials possess a negative Poisson's ratio (NPR) and attractive mechanical properties; however, these materials are limited by their low stiffness and strength and strong anisotropy. To address these issues, we developed a novel auxetic honeycomb with a fully triangular architecture inspired by the anti-tetra chiral configuration. The new stretch-dominant structure was fabricated using a three-dimensional printing process. The resulting deformation behavior of the triangular auxetic honeycomb structure was compared with that predicted from finite element (FE) simulations; these revealed an NPR and high stiffness, in which the ratio of specific stiffness to specific density was 0.12. The simulations allowed for an NPR in both the longitudinal and transverse directions concurrently. Based on the mechanism revealed by the FE simulations, the novel triangular honeycomb can be tuned to have the same behavior in two orthogonal directions, while retaining high stiffness and an NPR. [ABSTRACT FROM AUTHOR]

This work investigates the effects of cracking on the overall properties of brittle auxetic/non-auxetic honeycombs. The micro numerical model and macro theoretical model are established simultaneously. The analytical expressions of crack opening displacement (COD) are derived and the results agree well with numerical simulations. The fracture toughness of honeycombs is calculated by combining the stress in the numerical model and the stress intensity factor (SIF) in the theoretical model. The reductions in the equivalent stiffness and equivalent thermal stress coefficient (TSC) of the cracked honeycombs are predicted. The negative Poisson's ratio (NPR) effects on those fracture mechanics parameters and equivalent thermomechanical properties are studied. And considering the orthogonal anisotropic properties of honeycombs, the cracking along two orthogonal directions is examined. It reveals that the significant NPR effects can only be detected in a single direction and the effects in another direction are inconspicuous. In addition, the effects of crack length, medium dimensions, and cell-wall angle of honeycomb cells on the overall performance of the cracked medium are also evaluated by parametric studies and the results are displayed graphically. [ABSTRACT FROM AUTHOR]

In this article, a novel re-entrant octagonal honeycomb (ROH) with negative Poisson's ratio (NPR) configuration is proposed owing to its superior energy absorption and lightweight design performances. Regarding the effects of adjacent unit cells, a mechanics-based homogenization approach is put forward and employed to derive static mechanical properties including elastic modulus and Poisson's ratio of two-dimensional (2D) and three-dimensional (3D) ROHs under axial loading. Based on above, the predominant compression failure mode is explored. Then, the static mechanical properties and finite element model of ROH are validated by experiment and demonstrate high accuracy. Subsequently, to obtain dynamic responses of the ROH under dynamic impact loading, the relations among dynamic plateau stress and quasi-static plateau stress, initial density, dense strain and impact velocities are established under the conditions of mass conservation and momentum theorem based on one-dimensional shock wave theory and ideal rigid-perfectly plastic material model. Besides, dynamic energy absorption models of the ROH under dynamic loading are acquired in consideration of the effects of impact velocities on dense strain, the results show that theoretical models agree quite well with simulation results. On this basis, the application of ROH on automotive energy absorber is studied with the purpose of acquiring superior energy absorption and satisfying lightweight requirements simultaneously. Based on the decoupling thought of stiffness and pedestrian protection, a new design method of carbon fiber reinforced plastics (CFRP) hood with ROH is put forward in consideration of energy absorption and lightweight requirements. Of this, ROH is regarded as sandwich structure to meet the demands of energy absorption, CFRP plates are treated as outer and inner skins to satisfy the needs of stiffness. Firstly, multi-objective optimization models are set up under the constraints of reasonable structural parameters and negative Poisson's ratio. Then, the NSGA-Ⅱalgorithm is adopted to achieve the optimal Pareto fronts with the targets for maximum unit mass energy absorption and minimum density. Afterwards, the optimization on thicknesses of CFRP layers is carried out to achieve minimum mass under the constraint conditions that the static stiffness of CFRP hood is larger than that of steel hood. In addition, the layering sequence of inner and lower skins are also optimized. Finally, improved overall stiffness, optimized HIC values and similar lightweight space of CFRP hood with ROH are achieved in comparisons with CFRP hood without ROH. Compared with steel hood, the pedestrian protection performance of CFRP hood with ROH is greatly enhanced, 1st free mode increases by 33.9%, and torsional stiffness and bending stiffness increase by 23.1% and 30.8%, respectively. While the weight decreases by 40.1%. The results indicate that the CFRP hood with ROH presents outstanding advantages of pedestrian protection and lightweight design in terms of HIC and stiffness performance. [ABSTRACT FROM AUTHOR]

Nowadays, sandwich plates with cellular core structures are gaining the attention of researchers owing to their outstanding features. For a better insight into auxetic structures, in this study, we propose an excellent computational approach based on polygonal meshes to comprehensively examine the free vibration, buckling and dynamic instability behaviors of the auxetic honeycomb sandwich plate structures. A generalized C 0 -type higher-order shear deformation theory ( C 0 -HSDT) in conjunction with both Laplace and quadratic serendipity shape functions is employed to approximate the strain fields for polygonal plate elements. The sandwich plate structures are constituted by an auxetic honeycomb core layer with negative Poisson's ratio and two skin layers reinforced by graphene nanoplatelets (GNPs). Ultra-light features of the plate structures can be obtained by using the auxetic honeycomb cells with negative Poisson's ratio while the GNPs are embedded into skin layers to enhance the structural stiffness. In order to determine the dynamic instability region of the sandwich plate, Bolotin's approach is utilized in the current research. Several numerical examples are carried out to investigate the influences of geometrical parameters of auxetic cell and GNPs reinforcement on the structural behaviors. The results obtained in the current research can be considered as benchmark ones to investigate auxetic sandwich plate structures. [ABSTRACT FROM AUTHOR]

• The mechanical properties and failure stress of re-entrant honeycombs is formulated analytically. • The stretching, flexing and hinging mechanisms of the auxetic honeycomb are considered. • Using the Euler buckling and Tsai-Wu criterion, the critical stress of the honeycomb is obtained. • Effects of geometric parameters and loading conditions on the mechanical properties are studied. In the present study, a novel theoretical model is developed, based on classical laminate theory, to predict the equivalent mechanical properties of the re-entrant lattice structures, which composed of continuous fiber reinforced composite struts. Three main mechanism of stretching, flexing and hinging are considered and a general closed-form formulation is derived to estimate the auxetic honeycomb's elastic and shear modulus as well as Poisson's ratios. In spite of previous studies in which the response of honeycomb structures is modeled using beam theory, here, each strut of unit cell is expressed as a composite laminate with orthotropic mechanical properties and classical laminate theory is implemented to calculate the mechanical constants. In addition, using the available relations, the elastic buckling stress and failure load of the auxetic unit cell is evaluated. The proposed model is validated using experimental results, which are available from the previous studies as well as FE simulations. A parametric study is also conducted on the model to study the effects of cell angle and honeycomb's density on the mechanical properties and failure stresses of the re-entrant structure. The results show that, the proposed analytical model can finely predict the equivalent and failure properties of the auxetic honeycomb structures. Furthermore, it is observed that, for the considered re-entrant composite structures with the cell angles between −25 to 25, the vertical strut fails due to the damage evolution and for the unit cells with other cell angles, the buckling failure is determinative. [ABSTRACT FROM AUTHOR]