Search

The 2D-GDQM (Two-Dimensional Generalized Differential Quadrature Method) and adaptively tuned deep neural network are two computational methods that have been proposed for the frequency analysis of sandwich disks with honeycomb cores. Sandwich disks are commonly used in aerospace and automotive industries due to their lightweight and high strength properties. However, accurately predicting their natural frequencies is crucial for ensuring their structural integrity. The 2D-GDQM is a numerical method that discretizes the equations of motion of the sandwich disk using a grid-based approach. The method has been used to obtain accurate and efficient frequency solutions for various types of sandwich structures. In this study, the 2D-GDQM was applied to analyze the frequency response of the sandwich disk with honeycomb core with first and higher-order deformation theories to model displacement field. Additionally, an adaptively tuned deep neural network was used to predict the natural frequencies of the sandwich disk. This method involves training a deep neural network with a dataset of frequency solutions obtained from the 2D-GDQM simulations. The neural network is then optimized to provide accurate predictions for new cases. The results of this study showed that both the 2D-GDQM and the adaptively tuned deep neural network can provide accurate predictions of the natural frequencies of the sandwich disk with honeycomb core. The 2D-GDQM was found to be more computationally efficient, while the neural network approach can be more flexible and adaptable to new geometries or material properties. [ABSTRACT FROM AUTHOR]

In an unconstrained elastic body, emergence of zero natural frequencies is an expectable outcome on account of the body's ability to purely translate or rotate with no structural deformation. Recent advances in literature have pushed such conventional definition and demonstrated properties transcending typical zero-frequency modes, such as localization of deformation at a structural edge or corner. In this paper, a spring–mass honeycomb lattice with an elastic foundation, referred to here as mechanical graphene, is designed to exhibit zero-frequency corner modes. A central element in the proposed design is the elastic foundation, and the zero-frequency corner modes are enabled by intricate modulation of the elastic-foundation's stiffness. These modes are proven to have their origins from the dynamics of a diatomic chain, made from a single strip of the mechanical graphene with free boundaries. Different shapes of finite mechanical graphene with free boundaries are considered and conditions leading to the manifestation of corner modes are correlated with the angle of corners and stiffness of springs supporting them. Finally, the effect of defects on zero-frequency corner modes is briefly discussed, demonstrating robustness against structural defects that are distant from corners. • The concept of zero-frequency corner modes in a mechanical graphene is introduced. • Elastic foundation of positive-negative springs enables zero-frequency corner modes. • Corner modes origin is connected to edge modes in a comparable diatomic lattice. • Corner modes only occur in mechanical graphene having 60°-angle corners. • Theory is verified numerically using different shapes of mechanical graphene. [Display omitted] [ABSTRACT FROM AUTHOR]

Extensive studies on hexagonal honeycombs under in-plane compression have demonstrated that the structure's symmetry plays a decisive part in the emergence of deformation patterns in post-bifurcated configurations. In this work, the aim is to take advantage of this property by presenting a new group-theoretic approach to list the various attainable post-bifurcated patterns of periodic architectured materials. As of today, some group-theoretic approaches have been elaborated for determining the post-bifurcated paths and thus patterns of a symmetric system submitted to specific loading conditions. However, the application of these approaches requires knowledge of the system's governing equations. By making use of another group-theoretic tool, this work predicts the various possible post-bifurcated configurations of a periodic architectured material a priori of any non-linear computation by simply assessing the symmetry group of its undeformed configuration. This approach is applied, as an example, to the buckling of regular hexagonal honeycombs but can be easily transferred to any periodic architectured material. This work is a first step towards the elaboration of a more general process for the design of architectured materials when harnessing post-bifurcated behaviour is essential. [ABSTRACT FROM AUTHOR]

Investigation of the geometrical nonlinear action of doubly curved shell panels (DCSPs) in micro scale is the main target of this paper. The proposed microshell panels (MSPs) are assumed to be made of an auxetic honeycomb core (AHOC), leading to negative magnitudes of Poisson's ratio, covered by two nanocomposite enriched coating layers (NCECLs). To conduct the size-dependent nonlinear analysis and achieve the corresponding nonlinear equilibrium path (EQP) of the proposed MSPs, the nonlocal strain gradient theory (NLSGT) is utilized. The governing equations containing the equilibrium and compatibility nonlinear partial differential equations in terms of the deformation components are analytically solved based on the Galerkin technique for different types of simply-supported panels. The achieved results of the present solution exhibit the fact that nonlocal and material length scale parameters significantly affect the EQP of the proposed MSPs especially at their post-buckling stage during their snap-through instability. By solving several numerical examples, the effects of various parameters on the size-dependent EQP of the proposed MSPs are investigated. The results indicate that the influences of size-dependency are significantly affected by the curvature and also boundary conditions of the microshells. [ABSTRACT FROM AUTHOR]

The importance of cellular materials continues to increase in lightweight structural applications as more industries realize these materials are becoming more reliable, repeatable and allowing for lower production costs. Among all the common structural applications of cellular architected materials, cores for sandwich panels may perhaps be the most important one, and therefore, were the focus of this work. On the other hand, the fast-paced growth of computational power, in combination with the development of software and numerical methods such as Meshless Methods provide the necessary conditions to study intricate topologies which may offer improved mechanical properties for each different application. In this work, two periodic cellular topologies which are typically used in the cores of sandwich structures were designed, namely conventional honeycombs and re-entrant honeycombs, for 7 different values of relative density, and tested in two different in-plane directions in the linear-elastic domain. The Radial Point Interpolation Method (RPIM) is used in this study, for the first time in the literature, to simulate the elasto-static behaviour of honeycomb structures and provides advantages over the Finite Element Method (FEM) in this field. [ABSTRACT FROM AUTHOR]

In this research, a computational technique is developed for determining effective in-plane properties of hexagonal core honeycombs utilizing homogenization multi-scale technique based on averaging theorems. Purposely associated with engineering constants, specialized unit cells under appropriate boundary conditions are elaborated for two well-known configurations of uniform cell wall thickness and doubled thickness vertical cell walls hexagonal honeycombs. Constant boundary element method (CBEM) are employed for discretizing the boundary integral form of equivalent stress and strain equations and avoiding dependency to the mesh density and elements type selection challenges at cell walls intersection. Comparing with available experimental data for uniform cell wall thickness hexagonal honeycombs, the proposed method validated for a wide range of relative densities. Then comparing with well-defined existing analytical methods which have been previously validated experimentally, the verification of proposed method is done for uniform cell wall thickness and double thickness vertical cell walls. The results show that the proposed methods can present a well approximation of in-plane engineering constants for relative densities lower than 0.3 and also can be applied to higher relative densities by defining proper unit cells where available analytical methods encounter with significant inability. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a study of the mechanical response of hexachiral honeycombs with transversally curved ligaments under planar uniaxial tensile, compressive and shear loads. The impact of the chiral cell design parameters on the resulting macroscopic behaviour is assessed utilising finite elements calculations. It is shown that the presence of ligament curvature permits to attain mechanical responses which are not achievable through conventional chiral honeycomb designs. In addition, the resulting responses exhibit, for all considered load cases, significant tunability through the investigated geometrical design parameters. Two chiral lattices with identical geometries, only differing in their ligament curvature, were manufactured and experimentally tested to validate the finite elements predictions. A connection and assembly strategy is presented and utilised, offering a fast and robust approach to build larger finite lattice structures through 3D printed single basic cells. The hexachiral lattices were tested in tension, compression and in-plane shear, showing good agreement with the numerical predictions. [ABSTRACT FROM AUTHOR]

The advent of additive manufacturing has enabled the precise manufacturing of lattice materials at different length scales. While honeycombs are usually constructed from a tessellated array of identical unit cells, most structures in nature tend towards stochastic or disordered tessellation. In this work, we explore the effect of disorder properties of honeycombs, in particular, stiffness, strength, fracture toughness, and crack propagation paths using finite element models. The honeycombs are created using Voronoi tessellations with different levels of disorder measured by a regularity parameter δ , where δ = 1 corresponds to a regular hexagonal honeycomb and decreasing values of δ correspond to increasing levels of disorder. We consider three constituent materials: very brittle, quasi-brittle, and very ductile (0.0007–0.25 in failure strain). The results show that pseudo-order realizations with 0.5 ≤ δ ≤ 0.8 show the best strength-toughness trade-off. With increased plasticity, the improvement in fracture toughness compared to regular honeycombs can be as high as 50% at the expense of a 20% decrease in strength. This increase in fracture toughness is achieved both at crack initiation with crack blunting intrinsically and extrinsically during crack growth by a combination of crack deflection and crack bridging. Also, a single mathematical variable δ usually referred to as a "regularity parameter" to control cell stochasticity cannot account for the variability in tensile strength and fracture toughness parameters for brittle or quasi-brittle constituent materials and significantly more for a ductile constituent material. Thus, a local parameter for disorder is required to explain the large statistical variance seen in the mechanical properties of disordered honeycomb structures across the same irregularity value. [ABSTRACT FROM AUTHOR]

Topological edge states form at the edges of periodic materials with specific degeneracies in their modal spectra, such as Dirac points, under the action of effects breaking certain symmetries of the system. In particular, in Floquet topological insulators unidirectional edge states appear upon breakup of the effective time-reversal symmetry due to dynamical modulations of the underlying lattice potential. However, such states are usually reported for certain simple lattice terminations, for example, at zigzag or bearded edges in honeycomb lattices. Here we show that unconventional topological edge states may exist in Floquet insulators based on arrays of helical waveguides with hybrid edges involving alternating zigzag and armchair segments, even if the latter are long. Such edge states appear in the largest part of the first Brillouin zone and show topological protection upon passage through the defects. Topological states at hybrid edges persist in the presence of focusing nonlinearity of the material. Our results can be extended to other lattice types and physical systems, they lift some of the constraints connected with lattice terminations that may not support edge states in the absence of effects breaking time-reversal symmetry of the system and expand the variety of geometrical shapes in which topological insulators can be constructed. • Topological edge states may exist in Floquet insulators with hybrid zigzag–armchair edges. • Such edge states appear in the largest part of the first Brillouin zone and show topological protection. • Topological states at hybrid edges persist in the presence of focusing nonlinearity of the material. [ABSTRACT FROM AUTHOR]

Finite strain numerical solutions are derived for the in-plane, elastic-plastic response of a filled hexagonal honeycomb in uniaxial compression and in uniaxial tension. The cell walls and core are treated as elastic, ideally plastic von Mises solids, but the uniaxial strength of the core material is much less than that of the cell walls. The honeycomb has sides of equal length, and its inclined (but non-vertical) cell walls subtend an angle with respect to the transverse direction that can deviate from the usual value of +/- 30 ° which is characteristic of a regular honeycomb. Two responses of the core are assumed: the fully bonded, 'non-cavitating core' (in the presence of a sufficiently high macroscopic pressure) and a 'cavitating core' that can cavitate or debond freely from the cell walls. When the honeycomb has cell walls that are inclined at 30 ° or less, the unit-cell response in uniaxial compression is stable and displays macroscopic hardening, regardless of whether the core can cavitate or not. In contrast, when the inclination of the cell walls exceeds 30 ° , the honeycomb with a cavitating core displays mild softening in uniaxial compression while the honeycomb with a non-cavitating core has a high initial yield strength, followed immediately by a strongly softening response. The strongly softening, isochoric mode occurs in an inclined shear band by the rotation of inextensional plastic hinges in the cell walls over a wavelength of two cells. A Maxwell construction is adequate for prediction of the propagation stress of the shear band in a finite specimen from a starter defect. Additional insight into the collapse mechanisms of the filled honeycomb (with a cavitating or non-cavitating core) is obtained via analytical solutions for a rigid, ideally plastic honeycomb, whereby the cell walls are treated as slender beams and the core has vanishing deviatoric strength. The full numerical solutions reveal that the filled honeycomb exhibits strong tension-compression asymmetry for both a cavitating core and a non-cavitating core. [ABSTRACT FROM AUTHOR]

Abstract: Meshes are widely used topologies for Networks on Chip (NoC). Honeycomb meshes have better topological properties than Meshes. In order to communicate efficiently in a linear or cyclic manner, it is benefited that there is a Hamiltonian path or Hamiltonian cycle in NoC. In this paper, we give a necessary and sufficient condition for the existence of Hamiltonian path between any pair of vertices in a honeycomb mesh and for the existence of Hamiltonian path in a honeycomb mesh with one faulty vertex. Besides, we give a systematic method to construct a Hamiltonian path in Honeycomb meshes. [Copyright &y& Elsevier]

Abstract: In this study we investigate the effect of imperfect (not perfectly bonded) interfaces on the stiffness and strength of hierarchical polycrystalline materials. As a case study we consider a honeycomb cellular polycrystal used for drilling and cutting tools. The conclusions of the analysis are, however, general and applicable to any material with structural hierarchy. Regarding the stiffness, generalized expressions for the Voigt and Reuss estimates of the bounds to the effective elastic modulus of heterogeneous materials are derived. The generalizations regard two aspects that are not included in the standard Reuss and Voigt estimates. The first novelty consists in considering finite thickness interfaces between the constituents undergoing damage up to final debonding. The second generalization consists of interfaces not perpendicular or parallel to the loading direction, i.e., when isostress or isostrain conditions are not satisfied. In this case, approximate expressions for the effective elastic modulus are obtained by performing a computational homogenization approach. In the second part of the paper, the homogenized response of a representative volume element (RVE) of the honeycomb cellular polycrystalline material with one or two levels of hierarchy is numerically investigated. This is put forward by using the cohesive zone model (CZM) for finite thickness interfaces recently proposed by the authors and implemented in the finite element program FEAP. From tensile tests we find that the interface nonlinearity significantly contributes to the deformability of the material. Increasing the number of hierarchical levels, the deformability increases. The RVE is tested in two different directions and, due to different orientations of the interfaces and Mixed Mode deformation, anisotropy in stiffness and strength is observed. Stiffness anisotropy is amplified by increasing the number of hierarchical levels. Finally, the interaction between interfaces at different hierarchical levels is numerically characterized. A condition for scale separation, which corresponds to the independence of the material tensile strength from the properties of the interfaces in the second level, is established. When this condition is fulfilled, the material microstructure at the second level can be efficiently replaced by an effective homogeneous continuum with a homogenized stress–strain response. From the engineering point of view, the proposed criterion of scale separation suggests how to design the optimal microstructure of a hierarchical level to maximize the material tensile strength. An interpretation of this phenomenon according to the concept of flaw tolerance is finally presented. [Copyright &y& Elsevier]

Abstract: Electronic, magnetic, and structural properties of graphene flakes depend sensitively upon the type of edge atoms. We present a simple software tool for determining the type of edge atoms in a honeycomb lattice. The algorithm is based on nearest neighbor counting. Whether an edge atom is of armchair or zigzag type is decided by the unique pattern of its nearest neighbors. Particular attention is paid to the practical aspects of using the tool, as additional features such as extracting out the edges from the lattice could help in analyzing images from transmission microscopy or other experimental probes. Ultimately, the tool in combination with density-functional theory or tight-binding method can also be helpful in correlating the properties of graphene flakes with the different armchair-to-zigzag ratios. Program summary: Program title: edgecount Catalogue identifier: AEIA_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 66 685 No. of bytes in distributed program, including test data, etc.: 485 381 Distribution format: tar.gz Programming language: Fortran 90/95 Computer: Most UNIX-based platforms Operating system: Linux, Mac OS Classification: 16.1, 7.8 Nature of problem: Detection and classification of edge atoms in a finite patch of honeycomb lattice. Solution method: Build nearest neighbor (NN) list; assign types to edge atoms on the basis of their NN pattern. Running time: Typically ∼second(s) for all examples. [ABSTRACT FROM AUTHOR]

Abstract: Micro-pillars of anodic aluminium oxide with nano-sized honeycomb channels along the pillar axis exhibit compressive stress–strain response with large excursions corresponding to discrete, inhomogeneous deformation events. Each excursion is found to associate with the severe distortion of a material layer at the pillar’s head, whereas the remaining of the pillar remains intact. The stresses at which these excursions occur do not exhibit any significant dependence on the pillar size. A simple model is proposed to describe the response of pillars under compression, which energetically, as well as kinetically, explains as to why the localized deformation always takes place at the pillar head. Predictions on the occurrence of instability events from this model also quantitatively agree with the experimental observations. [ABSTRACT FROM AUTHOR]

Abstract: The macroscopic mechanical behavior of elliptical cell honeycombs are characterized using couple-stress elasticity theory. General expressions for the couple-stress elastic constants are obtained through a combination of non-dimensional analysis and numerical analysis. The expressions for the six in-plane orthotropic couple-stress compliances are derived in terms of the honeycomb cell size, cell wall thickness, cell ellipticity and the linear elastic properties of the cell wall material. The derived expressions are validated through numerical analyses. [ABSTRACT FROM AUTHOR]

Abstract: Examples of chiral materials include some auxetic materials, bones, some honeycomb structures, as well as composites with inclusions. The chiral effects cannot be described within classical elasticity. In the context of the linear theory of Cosserat elastic solids, we investigate the deformation of a chiral rod subjected to tractions on the lateral surface, to body loads, and to resultant forces and moments on the ends. The work is motivated by the recent interest in the using of the Cosserat elastic solid as model for auxetic composites, carbon nanotubes and bones. The three-dimensional problem is reduced to the study of some generalized plane strain problems. New chiral effects are presented. In the case of cylinders of arbitrary cross-section, the flexure produced by a transversal force, in contrast with the case of achiral materials, is accompanied by extension and bending by terminal couples. The body loads and the tractions on the lateral surface produce extension, flexure, torsion, bending by terminal couples and a plane strain. It is shown that a uniform pressure acting on the lateral surface of a chiral circular cylinder does not produce bending effects. [ABSTRACT FROM AUTHOR]

Abstract: Detailed mathematical derivation and simple closed form results for the size-dependent elastic properties of micro- and nano-sized honeycombs are presented in this paper. The results indicate that at micrometer scale, strain gradient has a dominant effect and at nano-meter scale, surface elasticity dominates the effect on the honeycomb elastic properties. The in-plane elastic properties of a nano- or micro-honeycomb could be controlled to vary over a range of around 10% by adjusting the initial stress in the cell walls by applying an electric potential. In addition, the bending and shear rigidities of some commonly used micro- and nano-structural elements have been obtained and presented in this paper, which could be of important applications in the design of MEMS and NEMS. [Copyright &y& Elsevier]

Abstract: Wave propagation and its frequency bandgaps in a parametrically modulated composite laminate are reported in this paper. The modulated properties under considerations are due to periodic microstructure, for example honeycomb core sandwich composite, which can be parameterized and homogenized in a suitable scale. Wave equations are derived by assuming a third-order shear deformation theory. Homogenization of the wave equations is carried out in the scale of wavelength. In-plane wave and flexural–shear wave dispersions are obtained for a range of values of a stiffness modulation coefficient . A clear pattern of stop-bands is observed for . To validate the band-gap phenomena, we take recourse to time domain response obtained from finite element simulation. As predicted by the proposed analytical technique, a distinct correlation between the chosen frequency band and the simulated wave arrival time and amplitude reduction is found. This promises practical applications of the proposed analytical technique to designing parametrically modulated composite laminate for wave suppression. [Copyright &y& Elsevier]

Abstract: Equations for calculating the shear modulus of non-isotropic, open cell foams in the plane perpendicular to the rise direction and in a plane parallel to the rise direction are derived using an elongated Kelvin foam model. This Kelvin foam model is more general than that employed by previous authors as the size and shape of the unit cell are defined by specifying three independent cell dimensions. The equations for the shear compliances are derived as a function of three unit cell dimensions and the section properties of the cell edges. From the compliance equations, the shear modulus equations are obtained and written as a function of the relative density and two unit cell shape parameters. The dependence of the two shear moduli on the relative density and the two shape parameters is demonstrated. [Copyright &y& Elsevier]

Exact solutions are derived for the small-strain, in-plane, elasto-plastic response of a hexagonal honeycomb using slender beam theory; incompressibility of the honeycomb is enforced by filling its voids with an incompressible, inviscid fluid. The honeycomb has sides of equal length, but its inclined struts subtend an angle that can deviate from 120° with respect to the vertical side walls. The relative density is sufficiently small that the struts are slender and can be treated as Euler-Bernoulli beams. Exact solutions are obtained for the elastic moduli and macroscopic yield surface of the rigid, ideally plastic lattice under general in-plane loading: the solutions satisfy equilibrium, compatibility and the constitutive response of each elastic, ideally plastic beam. Prior to conducting an elastic analysis, and a rigid, ideally plastic analysis, initial insight is gained by exploring the vector space of inextensional collapse mechanisms of the pin-jointed, compressible version of the hexagonal truss. Two inextensional collapse mechanisms of the compressible honeycomb are identified from the null space of the kinematic matrix. The presence of an incompressible, inviscid fluid in the voids of the honeycomb locks-up one mechanism but the other mechanism survives and generates macroscopic shear strain. Consequently, the incompressible hexagonal honeycomb with rigid joints has a high shear compliance and a low shear strength, with values equal to that of the unfilled, compressible honeycomb. In contrast, macroscopic tensile straining of the incompressible honeycomb requires the stretching of bars in addition to bar-bending, and the tensile modulus and strength of the incompressible honeycomb are thereby elevated. Explicit analytical formulae are derived for the macroscopic tensile modulus and strength of the incompressible honeycomb. [ABSTRACT FROM AUTHOR]

The mechanics of cellular honeycombs—part of the rapidly growing field of architected materials—in addition to its importance for engineering applications has a great theoretical interest due to the complex bifurcation mechanisms leading to failure in these nonlinear structures of high initial symmetry. Of particular interest to this work are the deformation patterns and their stability of finitely strained circular cell honeycomb. Given the high degree of symmetry of these structures, the introduction of numerical imperfections is inadequate for the study of their behavior past the onset of first bifurcation. Thus, we further develop and explain a group-theoretic approach to investigate their deformation patterns, a consistent and general methodology that systematically finds bifurcated equilibrium orbits and their stability. We consider two different geometric arrangements, hexagonal and square, biaxial compression along loading paths, either aligned or at an angle with respect to the axes of orthotropy, and different constitutive laws for the cell walls which can undergo arbitrarily large rotations, as required by the finite macroscopic strains applied. We find that the first bifurcation in biaxially loaded hexagonal honeycombs of infinite extent always corresponds to a local mode, which is then followed to find the deformation pattern and its stability. Depending on load path orientation, these first bifurcations can be simple, double or even triple. All bifurcated orbits found are unstable and have a maximum load close to their point of emergence. In contrast, the corresponding instability in square honeycombs always corresponds to a global mode and hence the deformation pattern will depend on specimen size and boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract: The magnetic correlation in the Hubbard model on a honeycomb lattice is systematically studied by quantum Monte Carlo method. It is found that the magnetic order is qualitatively different in two filling regions separated by the Van Hove singularity around . A short-ranged ferromagnetic correlation is found in the low filling region, which is enhanced slightly by the on-site Coulomb interaction. The ferromagnetic fluctuation depends sensitively on the filling but is strengthened markedly as the next-nearest hoping integral increases. [Copyright &y& Elsevier]

• Both Kerr and saturation nonlinearities can cause triangular deformation of conical diffraction pattern. • Asymmetric conical diffraction with a dark notch appears by adjusting rotation angle θ of the three vectors. • By employing both nonlinearity and vector rotation simultaneously, triangular breakage occurs. We investigate the generation and destruction of asymmetric conical diffraction in honeycomb lattices by adjusting rotation angle θ of the three vectors and considering nonlinearities. For θ = 0° and 60°, the modes of the Dirac cone of the honeycomb lattice are excited, symmetric conical diffraction are obtained. When 0 < θ < 60°, asymmetric conical diffraction with a dark notch appears and the dark notch moves clockwise or anti-clockwise around the outer edge of the bright ring. In addition, it is also demonstrated that both Kerr and saturation nonlinearities can cause triangular deformation of conical diffraction pattern. Under the same nonlinearity, two identical wave centered around different Dirac points can evolve to identical triangular rings pointing in opposite directions. The dark notch at a point of triangular appears and moves in a clockwise or anti-clockwise way for self-focusing and self-defocusing nonlinearity, respectively. [ABSTRACT FROM AUTHOR]