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In order to achieve the attenuation of low‐frequency sound, in this paper, a hybrid metamaterial structure with a complete band gap below 500 Hz is proposed, which is subjected to second‐order fractal, series fusion, and whether the structure is framed or not to form 8 different structures. Based on the finite element method and Bloch's theorem, the bandgap and transport properties of all model structures are evaluated, and the bandgap and propagation properties of metamaterial structures with different fractal levels are elucidated in terms of band structure and group velocity. In addition, the third‐order fractal structure and the dependence of the band gap on the material are also studied. The results show that the structure has a superior band gap width, and the complete band gap of its tandem fusion structure accounts for up to 45.502% in the range of 500 Hz, and the second‐order fractal has a complete band gap of 45.588% in the range of 1000 Hz. Compared with other structures, it can produce lower and better band gap. The research in this paper provides a new strategy for realizing acoustic metamaterial structures with low frequency band gaps. [ABSTRACT FROM AUTHOR]

Auxeticity of materials improves several of their mechanical properties, especially shear, impact, and bending resistance. It also improves ability of materials to absorb impact energy as well as the overall stiffness of structures. In this research, authors examine synclastic panels made from novel wood‐based composites. The aim is to determine the force–displacement characteristics during uniaxial compression and obtain the stiffness of the panels. These data allow one to predict the behavior of a panel during two‐axial bending with different support scenarios. Finite element method (FEM) analysis is performed, with the use of model material, to determine the impact of varied facings thickness as well as different types of materials and core structures, on the stiffness of synclastic panels. It is demonstrated that proposed multilayer composites allow forming (technologically difficult) spherical shapes, without additional heat and pressure treatment. The type of an outer layer material strictly determines the usability and ease of two‐axial bending process. Presented composites are interesting materials, that can be adopted into the wood industry as a replacement for traditional materials, e.g., bent plywood. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic behavior of a three-layered sandwich beam with a metal foam core is investigated. Outer layers of the sandwich beam are made of AlSi12 alloy and the core is metal porous foam made of AlSi12. Numerical analysis is made for different parameters of the core -- average damping loss factor, densities, Young modulus, and Poisson's ratio of core foam. The simulations are used to determine the mechanical impedance for a sandwich beam with the applied harmonic load. Numerical calculations are made with the use of finite element method. The results imply that the auxetic core of the composite beam can have a great impact on the dynamic behavior (mobility) of the system. Furthermore, it appears that there are ranges of frequencies in which the mobility of the system can be minimized by using the auxetic foam core. [ABSTRACT FROM AUTHOR]

The contact problem between two bodies: plate and semi-cylindrical bar is studied in this paper. The analysis concerns the contact pressure distribution along the contact region, as well as the deflection of the plate. Furthermore, the case of a composite plate covered with the auxetic layer is also considered. The influence of the Poisson's ratio of the layer on the behavior of the plate is studied. The contact pressure distribution along the contact area is analyzed using finite element analysis. [ABSTRACT FROM AUTHOR]

Helical arrangements are very common both in nature and in artificial structures. In this paper, an analysis of a prismatic composite bar is presented. The cross-sectional shape of the bar is described by a regular polygon. The composite is built of two homogeneous isotropic materials characterised by different Poisson's ratios one of which can be negative. Spatial distribution of materials in the composite is based on helical shape. Both materials are connected with the use of a transition zone of assumed width. The bar is subjected to torsional loading and its behavior is investigated by means of FEM method. Both material properties and the parameters of helical shape are investigated and the result of numerical analysis is presented. [ABSTRACT FROM AUTHOR]

We propose in this paper analytical and numerical models that describe the in-plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new numerical method to find the ground state energy of a given physical system within the Kohn–Sham density functional theory. The h‐adaptive finite element method is adopted for spatial discretization and implemented with matrix‐free operator evaluation. The ground state energy is found by performing unconstrained minimization with non‐orthogonal orbitals using the limited memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. A geometric multigrid preconditioner is applied to improve the convergence. The clear advantage of the proposed approach is demonstrated on selected examples by comparing the performance to other methods such as preconditioned steepest descent minimization. The proposed method provides a solid framework toward O(N) complexity for the locally adaptive real‐space solution of density functional theory with finite elements. [ABSTRACT FROM AUTHOR]

In this paper, a novel three-dimensional (3D) cellular structure with negative Poisson's ratio was designed by alternating cuboid surface indents on the vertical ribs of the unit cells. The Poisson's ratio and Young's modulus of structures with different geometric parameters were determined using the finite element method (FEM) as a function of these parameters. Samples with identical geometric variables were fabricated via 3D printing, and their through-thickness direction Poisson's ratios were measured and compared with simulation results. Results showed that the Poisson's ratio of the 3D cellular structures can be tuned from positive to negative and can reach a minimal value of −0.958. Good agreement was found between the experimental results and the simulation. This lattice structure is considerably stiffer than re-entrant negative Poisson's ratio foam with the same solid phase. The design concept developed here can be optimized for specific applications via geometric parameters manipulation. [ABSTRACT FROM AUTHOR]

Herein, based on the finite‐element calculation method, a high‐sensitivity infrared absorption sensor is designed with ZnSe as the substrate, Mo as the waveguide layer and periodic grating, and Ge as the thin film. The absorption performance of the structure is not sensitive to the polarization of the incident light when the transverse‐magnetic light wave is perpendicular to the structure. The thickness of the Ge thin film and the width of the grating column are the main factors for determining its absorption and sensing performance. The optimized structure is sensitive to the refractive index on the grating. Herein, a correspondence between the refractive index change and the position of the peak of the absorbance spectrum is established. When this structure is used as a refractive index sensor, the sensitivity can reach 2300 nm RIU−1 with a high figure of merit of 37.09. In addition, temperature sensing in ethanol shows that the waveguide can quantify the solution temperature by resonance. It is demonstrated in the results that the grating absorber has great potential applications in biomedical sensing. [ABSTRACT FROM AUTHOR]

Auxetics with negative Poisson's ratio (NPR) can expand dimensions along the direction perpendicular to the tensile direction, such as rigid rotation, reentrant and chiral structures, etc. The mechanical performances of chiral metastructures are closely related to internal defects and interactions between defects. In this paper, two types of irregular chiral structures with Gaussian dispersion of circular node positions and missing ligaments are designed, namely: anti‐tetrachiral metastructure and tetrachiral hybrid metastructure. These two types of chiral metastructures are characterized by node radius, ligament thickness, ligament length, the circular node center dispersion range, and missing ligament percentages. Effects of random node distribution range and cell wall missing percentage on the elastic modulus and Poisson's ratio of chiral metastructures are investigated through experimental tests and finite element (FE) simulation systematically. Through dimensionless analysis, it is found that ligament thickness has remarkable influence on the negative Poisson's ratio. Effect of missing ligament on the mechanical properties of the structure is greater than effect of random node center dispersion. With the increase of ligament missing percentage, the resultant modulus of chiral metastructures decreases, and the corresponding NPR increases. [ABSTRACT FROM AUTHOR]

A stiff tubular cellular structure topology is designed by alternatively indenting rectangular contour patterns on the cell ribs. Modified topologies can be obtained by tailoring the geometric parameters. The Poisson's ratios and elastic moduli of the proposed tubular structures with various geometric parameters are determined using finite element method (FEM). Results show that the minimum Poisson's ratio of the proposed structures can reach −0.28. The unit cell topology and orientation can significantly affect the structures deformation behaviors. The structures exhibit mixed mode of bending‐ and stretching‐dominated deformation responses, and show improved specific elastic moduli compared with traditional open‐cell stochastic foams with positive Poisson's ratios. 3D‐printed samples with identical geometric variables to those of the FE models are fabricated, and their Poisson's ratios and stress–strain relationships are determined experimentally, and compared with simulation results. Excellent agreement is achieved between measurements and simulations. The design concept proposed here can be optimized for specific applications via geometric parameters manipulation. [ABSTRACT FROM AUTHOR]

Chiral materials may exhibit negative Poisson's ratio and deformation‐mode coupling phenomena. The finite element numerical method is adopted to analyze a class of 2D chiral and nonchiral materials and to show the effects of microstructural geometry on their effective elastic properties and coupling between tension/compression and bending. With the same area fraction (AF), nonchiral samples show larger effective moduli than chiral ones. The number of unit cells may reduce negativity in effective Poisson's ratio of the chiral samples due to nonuniform lateral deformation under uniaxial straining. Increasing AF in a hierarchical pattern in the chiral samples makes their Poisson's ratio more negative. Bending occurs in the chiral samples when they are under uniform, uniaxial, tensile, or compressive straining due to the coupling of deformation modes. The sensibility of tension–bending coupling may be controlled by the chiral microstructure. Optimization of the coupling sensitivity may help develop novel mechanical sensors. [ABSTRACT FROM AUTHOR]

Honeycombs or foams with reentrant microstructures exhibit effective negative Poisson's ratio. Although they are light weight due to inherently empty space, their overall stiffness and damping are somewhat limited. With judiciously chosen filler material to fill the voids in star‐shaped honeycomb, it is numerically demonstrated its auxeticity may be enhanced. By combining the filler and skeleton, the hierarchical composite materials are constructed. The magnitude of the enhancement depends on inner and outer filler's modulus mismatch, as well as the types of filling. Filler's auxeticity also largely enhances overall auxeticity of the outer‐ and all‐filled honeycomb. In addition, for outer‐filled honeycomb, its effective viscoelastic modulus and damping are significantly increased, while maintaining relatively light weight, due to local stress concentration. [ABSTRACT FROM AUTHOR]

A chiral 3D lattice is designed, made by 3D printing, and studied experimentally. The lattice exhibits squeeze–twist coupling and a Poisson's ratio near zero. Squeeze–twist coupling does not occur in classical elasticity which makes no provision for chirality. By contrast, chiral effects are allowed in Cosserat elasticity. An experimental squeeze–twist coupling strain ratio on the order of unity and a Poisson's ratio near zero are in reasonable agreement with prior finite element analysis of a lattice with similar structure, for which negative Poisson's ratio is anticipated for a sufficient number of cells. [ABSTRACT FROM AUTHOR]

The folded geometry has successfully been transformed into auxetic woven fabric in the literature. However, the influences of the microgeometric parameters on the macroscopic behavior have not been addressed yet. Herein, several key microgeometric parameters for the folded geometry are identified and the mechanical behaviors of the folded structure are preliminarily studied using the finite element method. The results show that the folded structure can be unfolded in both longitudinal and transverse directions when stretched and thus achieve a negative Poisson's ratio. More interestingly, another fantastic property of tension–bending coupling effect is found in the folded structure and a competition exists between the auxeticity and the tension–bending coupling effect. This is the first time to report a structure that can stimulatingly have the auxeticity and the tension–bending coupling effect. Due to the unique properties, the folded geometry is very promising in some important fields; for example, the textiles, civil engineering, and auto industry. The present work may provide a good guide for the design and application of the folded structure. [ABSTRACT FROM AUTHOR]

An extensive investigation is carried out on the missing rib square grid structure using finite element simulations. This showed that, in the cases considered in this study, the type of deformation is primarily dependent on the ratio of the thickness of different ribs with the structure behaving like an anti-tetrachiral at particular ratios. The analysis also showed that the ability of the structure to deform predominantly through the bending of the ligament allows it to achieve much more negative values of the Poisson's ratio than previously reported. Confirmation of the numerical results is obtained through experimental methods involving the 3D printing of representative structures which are subsequently subjected to compression. [ABSTRACT FROM AUTHOR]

The electron states in a holey elliptically shaped GaAs quantum dot are investigated within the effective mass scheme with the use of the adiabatic approximation and the finite element method. The effects of a donor impurity center and an applied electric field are particularly taken into account. Electron‐impurity energies are reported as functions of both the geometry of the quantum dot and the applied field intensity, whereas temperature effects are also included. The analysis of electron‐impurity intersubband transitions allows the investigation of the light absorption response of the system. [ABSTRACT FROM AUTHOR]

Auxetic cellular materials show great potential for improved properties in case of impact loading. Due to this potential, auxetic structures made from inverted tetrapods are extensively analyzed experimentally and computationally. The built samples are compressed in two orthogonal directions to determine their base mechanical properties and deformation mechanisms. The lattice computational model is developed and validated using the experimental results. A new shape optimization procedure to develop new auxetic structures with functionally graded geometry is proposed and tested in a case study. With introduction of the functionally graded geometry the response of the auxetic structure can be tailored to a particular loading condition, which is especially important in impact or ballistic performance of modern composite materials. [ABSTRACT FROM AUTHOR]

Microstructured plates, consisting of various conventional and re-entrant cells, are numerically constructed and analyzed for their effective elastic properties under in-plane deformation. The finite element numerical method is adopted. The calculated effective Poisson's ratios of the plates are found to be in the range between −1 and 1, in consistency with the theory of two-dimensional elasticity. Auxetic angles need to be greater than about 20° in order to obtain negative Poisson's ratio. Increasing the auxetic angles reduces the effective pure shear modulus. Elastically anisotropic characteristics of the homogenized plate are analyzed with the calculated effective Young's modulus, Poisson's ratio, and pure shear modulus. [ABSTRACT FROM AUTHOR]

Spin transport properties of graphene non-local spin valve devices are typically determined from Hanle spin precession measurements by using a simplified solution of the one-dimensional Bloch-Torrey equation which assumes infinitely long transport channels and uniform spin transport parameter. We investigate the effects of a finite graphene size and explore the influence of spatially-varying transport parameters on the measured Hanle curves by finite element simulations. We assume enhanced spin dephasing in the contact-covered graphene areas with additional Fermi level pinning and explore the influence of non-magnetic reference electrodes which are not properly decoupled from graphene. In experiments, it is typically observed that the spin lifetime increases with increasing charge carrier density. None of our simulations can reproduce this trend indicating that this dependency originates from spin transport through graphene areas which are not covered by contacts. We find that the extracted spin lifetime might be overestimated in flakes which are shorter than the spin diffusion length. Moreover, contact-induced spin dephasing leads to an overall reduction of the extracted spin lifetime. Additionally, we show that non-magnetic reference electrodes may also influence the measured spin lifetime even though they are not part of the transport area under investigation. [ABSTRACT FROM AUTHOR]

The optical absorption response of an elliptical quantum-dot-type nanostructure is investigated by numerically determining the electron states within the effective mass and parabolic approximations via the finite element method, taking into account the effect of an externally applied electric field. Validation of the numerical procedure is discussed through the comparison with analytical results of previous works for zero external field conditions. For finite field, the comparison is made with the outcome of degenerate perturbation theory. The calculated electron energies and wavefunctions are used to evaluate the linear and nonlinear light absorption and refractive index change coefficients in the system. Their corresponding expressions are those typically derived within a perturbative approach for solving the density matrix equation of motion. It is shown how the electric field and the change in the elliptical geometry affect the optical response of the considered structures. The extension of the treatment to consider the properties of elliptic nanoparticles under external field influences is briefly discussed. [ABSTRACT FROM AUTHOR]

The article describes the design, manufacturing, modelling and testing of a hybrid composite support made from auxetic open cell foam liners and curved thermoplastic plates with rhomboidal perforations for human body support. Both the foam and the curved perforated plate have in-plane negative Poisson's ratio behaviour. The static bending stiffness of the hybrid auxetic composite support is modelled using an analytical and Finite Element approach benchmarked against experimental results from three-point bending tests. The benchmarked Finite Element models are used to develop a map of optimised static stiffness versus the geometry of the rhomboidal perforations. A Design of Experiment testing campaign is also carried out on 16 hybrid auxetic composite plates to understand the interaction and correlation of the static bending versus the geometry of the perforations and the contribution given by the auxetic foam liner. [ABSTRACT FROM AUTHOR]

The dynamic mechanical responses of the ferroelastic materials under uniaxial straining and temperature cycling are studied via the Landau-type phase field model in two dimensions. The model may exhibit a single-well (doublewell) energy profile when temperature is greater (less) than the critical temperature. Effective negative stiffness in the vicinity of the temperature-induced solid-solid phase transformation is numerically demonstrated through monotonic uniaxial straining on a single-domain ferroelastic under temperature cycling around the Curie temperature. Under sinusoidal uniaxial straining, the effective Young's modulus and damping, as indicated by the enclosed area of the stress-strain curve, may be largely increased due to the phase transition. Our calculated responses here are consistent with experimental data reported in the literature, as well as theoretical results based on the composite theory with inclusions assumed to have negative modulus. No negative stiffness values are directly assigned in our phase field model as the underlying physics of the order parameters, i.e., spontaneous strains, provides effective negative stiffness into the systems. [ABSTRACT FROM AUTHOR]

A two phase, fibrous composite subjected to bending nonuniform load is studied in this article. The composite is built of two constituents: the matrix is built of conventional material characterised by constant positive Poisson's ratio, whereas the Poisson's ratio of fibres is changed from positive (common materials) to negative values (auxetics). The influence of the arrangement of fibres, the volume fraction of fibres' materials and the distribution of loading force is studied by means of FEM. The behaviour of the composite is investigated in order to determine if auxetic reinforcement improves rigidity and indentation resistance of the composite. The results obtained confirm that auxetics can be used in composites to decrease deformation in the direction of acting force. [ABSTRACT FROM AUTHOR]

Chiral three-dimensional isotropic cubic lattices with rigid cubical nodules and multiple deformable ribs are developed and analyzed via finite element analysis. The lattices exhibit geometrydependent Poisson's ratio that can be tuned to negative values. Poisson's ratio decreases from positive to negative values as the number of cells increases. Isotropy is obtained by adjustment of aspect ratio. The lattices exhibit significant size effects. Such a phenomenon cannot occur in a classical elastic continuum but it can occur in a Cosserat solid. [ABSTRACT FROM AUTHOR]

From periodically cutting off rods in two-dimensional lattice grids, we find an easy and feasible way to control elastic bandgaps (BGs) in them. Due to the periodical cut-off (PCO) operations, the exposed cantilevers lose the static load-supporting ability; however, their mass distribution and inertia significantly affect the propagation of elastic waves. We first give several PCO types for square and triangular lattice grids. Then a detailed finite-element method for the calculation of elastic BGs is described. The BGs in the hexagonal-type PCO triangular lattice grid are studied for example. Localized resonant BGs are found and predicted. Frequency responses of the finite specimen are also analyzed to support our conclusions. Sketches of three kinds of PCO lattice grids: the PCO square lattice grid (left), the hex-type PCO triangular lattice grid (center), and the Kagomé-type PCO triangular lattice grid (right). [ABSTRACT FROM AUTHOR]

Composite materials containing negative-stiffness inclusions embedded in positive-stiffness matrix may exhibit unconventional (anomalous) effective coupled-field properties through interactions of the two phases. Effective coupled-field properties are calculated with the finite element methods under the quasi-static assumption. Stability boundaries are determined by applying 10 Hz sinusoidal loading on boundary surfaces, and the system is unstable if its energy becomes divergent for a chosen inclusion Young's modulus ratio ( λE) or bulk modulus ratio ( λK). Effective viscoelastic properties and their stability are studied for negative λE at 10 Hz, while the Poisson's ratio of the purely elastic inclusion is kept constant. For small inclusion volume fractions, their stability boundary is at λE ∼ -0.3, and extreme large effective damping and viscoelastic modulus are in the unstable regime. Furthermore, in the viscoelastic case, inclusion shapes have no effects on stability. As for the effective coupled-field properties, all anomalous peaks are in the unstable regime for negative λE or λK, except for an anomalous peak in effective thermal expansion coefficient with electrically insulated inclusions. Insulated inclusions may cause charge accumulation at the inclusion-matrix interface and boundary surface effects may serve as stabilizing agents to the composite system. [ABSTRACT FROM AUTHOR]

A composite structure with tunable mechanical properties is introduced. The composite consists of matrix material and a stack of inclusions. The specific hollow re-entrant shell inclusions could exhibit 'expansion effect' and 'closure effect' as responses to tensile and compressive loadings, respectively. Due to the special deformation mechanism of the inclusions, the global structure exhibits unusual properties over a wide range of applied deformations. The overall Poisson's ratio of the composite is significantly reduced comparing with its constituents, and an overall hardening effect is achieved. Moreover, according to the results of a parametric finite element analysis, the specific properties of this composite structure can be tailored by controlling the geometry features and density of the inclusions. [ABSTRACT FROM AUTHOR]

There exist several honeycomb networks exhibiting zero Poisson's ratio (ZPR). Applications of these networks can be found in different fields. The ZPR properties of these structures have been mechanically modeled and tested. However, the underlying mechanism driving the ZPR behavior has not been paid much attention. The present work focuses on the deformation mechanism of the ZPR networks. Through the discussion and comparison of the deformation process of the ZPR, auxetic and common honeycomb networks, the strain-isolation mechanism is proposed to explain the ZPR behavior. Then, according to this mechanism, the reversed semi-re-entrant (RSRE) honeycomb is created. With experimental measurements and finite-element analysis (FEA), the ZPR properties of the RSRE can be proven. The strain-isolation mechanism can not only explain the ZPR behavior but also be used in the design of new ZPR honeycomb networks. 3D ZPR structures are also derived from the 2D honeycomb networks. Their Poisson's ratios in 3D space are also discussed based on FEA results. The model of the 3D RSRE structure showing ZPR behaviors in three orthogonal planes. [ABSTRACT FROM AUTHOR]

An investigation of Poisson's ratios and band gap behaviors of 2D hierarchical re‐entrant lattice structures is conducted using finite element method (FEM). The structure with a hierarchy order n (n≥1) is constructed by replacing each outmost vertex of the re‐entrant octagons of a hierarchical structure of hierarchy order n−1 with a smaller self‐similar re‐entrant octagon. The dispersion relation and transmission spectrum of the proposed hierarchical structures are analyzed based on the Bloch's theorem. The effects of geometrical parameters, order of rotational symmetry and orientation angle of some types of re‐entrant polygon cores on the lattice Poisson's ratio and band gap structures are also investigated. Results show that the re‐entrant structures with first order hierarchy exhibit a wider band gap and a stronger attenuation effect compared with structures without structural hierarchy. The first order 2D hierarchical re‐entrant structure with a negative Poisson's ratio of −0.032 exhibits the widest band gap, 17.8% wider than that of the zeroth order 2D re‐entrant structure. The order of rotational symmetry and the orientation angle of the re‐entrant polygon cores of the lattice have a strong impact on the lattice Poisson's ratio and band structures. [ABSTRACT FROM AUTHOR]