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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]

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]

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]

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]

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]