Temporal transition in parallel-plate waveguides: analysis of scattering and propagation at the temporal interface

In this contribution, we present the analysis and numerical verification of the scattering phenomenon from a temporal interface in a parallel-plate waveguide realized by suddenly modifying the dimensions of the waveguide while the wave is propagating. As it is well known in guided wave theory, at the interface between two different waveguides there exists a change of the effective refractive index and wave impedance perceived by the propagating wave within the device, which inevitably scatters at the interface into a reflected and refracted wave. In analogous way, by suddenly changing the effective material properties within the whole waveguide, it is possible to realize the so-called temporal interface, as well. Here, we theoretically and numerically investigate on the scattering from a waveguide temporal interface induced by the abrupt change of the waveguide dimension, which in turn realize a change of the effective material properties perceived by the wave.

Fast Two-Scale Analysis via Clustering

Both man-made and natural materials exhibit heterogeneous properties at smaller observation scales. The multiscale analysis allows the inclusion of fine-scale information in coarse-scale simulations. One of the commonly used methods is homogenization, replacing the detailed fine-scale structures with their locally homogeneous effective material properties. When fine-scale material structures are stationary, representative volume elements (RVE) are often identified for their effective material properties to be applied over the entire structure. However, in non-stationary material structures, it is inappropriate to assume a single representative material. In this case, homogenization is often required for every individual cell, resulting in significant increases in computational cost. We propose a stiffness-based clustering algorithm that reduces the total number of homogenization computations needed for multiscale analysis. Cells with similar effective stiffness tensors are clustered together such that only a single homogenization is required for each cluster. Specifically, the clustering algorithm is based on the novel concept of Eigenstiffness, which represents the relative directional stiffness of a given material structure. The rotation invariant property of Eigenstiffness allows material structure with similar intrinsic stiffness but different orientations to be clustered together, further decreasing the number of clusters required for the multiscale analysis. Without a priori knowledge of the accurate homogenized material properties, approximated elasticity tensors and Eigenstiffness estimated through FFT-based homogenization methods are used for rapid clustering. The effectiveness of the method is verified by numerical simulations on various multiscale structures, including Voronoi foams and fiber-reinforced composites.

Effects of Shear Deformation of Struts in Hexagonal Lattices on their Effective In-Plane Material Properties

Two-dimensional lattices are widely used in many engineering applications. If 2D lattices have large numbers of unit cells, they can be accurately modeled as 2D homogeneous solids having effective material properties. When the slenderness ratios of struts in these 2D lattices are low, the effects of shear deformation on the values of the effective material properties can be significant. This study aims to investigate the effects of shear deformation on the effective material properties of 2D lattices with hexagonal unit cells, by using the homogenization method based on equivalent strain energy. Several topologies of hexagonal unit cells and several slenderness ratios of struts are considered. The effects of struts’ shear deformation on the effective material properties are examined by comparing the results of the present study, in which shear deformation is neglected, with those from the literature, in which shear deformation is included.

Strong and Weak Formulations of a Mixed Higher-Order Shear Deformation Theory for the Static Analysis of Functionally Graded Beams under Thermo-Mechanical Loads

The strong and weak formulations of a mixed layer-wise (LW) higher-order shear deformation theory (HSDT) are developed for the static analysis of functionally graded (FG) beams under various boundary conditions subjected to thermo-mechanical loads. The material properties of the FG beam are assumed to obey a power-law distribution of the volume fractions of the constituents through the thickness of the FG beam, for which the effective material properties are estimated using the rule of mixtures, or it is directly assumed that the effective material properties of the FG beam obey an exponential function distribution along the thickness direction of the FG beam. The results shown in the numerical examples indicate that the mixed LW HSDT solutions for elastic and thermal field variables are in excellent agreement with the accurate solutions available in the literature. A parametric study related to various effects on the coupled thermo-mechanical behavior of FG beams is carried out, including the aspect ratio, the material-property gradient index, and different boundary conditions.

On Effective Bending Stiffness of a Laminate Nanoplate Considering Steigmann–Ogden Surface Elasticity

As at the nanoscale the surface-to-volume ratio may be comparable with any characteristic length, while the material properties may essentially depend on surface/interface energy properties. In order to get effective material properties at the nanoscale, one can use various generalized models of continuum. In particular, within the framework of continuum mechanics, the surface elasticity is applied to the modelling of surface-related phenomena. In this paper, we derive an expression for the effective bending stiffness of a laminate plate, considering the Steigmann–Ogden surface elasticity. To this end, we consider plane bending deformations and utilize the through-the-thickness integration procedure. As a result, the calculated elastic bending stiffness depends on lamina thickness and on bulk and surface elastic moduli. The obtained expression could be useful for the description of the bending of multilayered thin films.

Thermo-Electro-Mechanical Size-Dependent Buckling Response for Functionally Graded Graphene Platelet Reinforced Piezoelectric Cylindrical Nanoshells

An accurate buckling response analysis for functionally graded graphene platelet (GPL) reinforced piezoelectric cylindrical nanoshells subject to thermo-electro-mechanical loadings is presented by a rigorous symplectic expansion approach. Three types of GPL reinforced patterns are considered, and the modified Halpin–Tsai model is employed to determine their effective material properties. By using Eringen’s nonlocal stress theory and Reissner’s shell theory, new governing equations are established in the Hamiltonian form. Exact solutions are expanded into symplectic series and three possible forms are derived. A comparison with the existing study is presented to validate the solution and very good agreement is observed. The effects of material and geometrical properties of GPLs, electric voltage and temperature rise on critical buckling stresses are investigated and discussed in detail.

Broadband metamaterials and metasurfaces: a review from the perspectives of materials and devices

Metamaterials can possess extraordinary properties not readily available in nature. While most of the early metamaterials had narrow frequency bandwidth of operation, many recent works have focused on how to implement exotic properties and functions over broad bandwidth for practical applications. Here, we provide two definitions of broadband operation in terms of effective material properties and device functionality, suitable for describing materials and devices, respectively, and overview existing broadband metamaterial designs in such two categories. Broadband metamaterials with nearly constant effective material properties are discussed in the materials part, and broadband absorbers, lens, and hologram devices based on metamaterials and metasurfaces are discussed in the devices part.

Vibration of porous functionally graded plates with geometric discontinuities and partial supports

Vibrational study of the porous functionally graded plate with geometric discontinuities and partial supports has been presented in the present paper. The kinematics of functionally graded plate is based on the refined exponential shear deformation theory. The displacement field has been refined by dividing the in-plane and out of the plane displacements into bending and shear components. The theory accounts for the nonlinear transverse shear stress variation along with the thickness with only four unknowns. The closed-form solution (Navier’s solution), as well as FEM-based solution, have been used for the vibration analysis of functionally graded plate. The geometric discontinuities have been incorporated in terms of a circular cut-out of different sizes at the center of the plate. Modified rule of mixtures, modified sigmoid law, and trigonometric law have been used to compute the effective material properties of the functionally graded plate. A C0 continuous iso-parametric FEM formulation has been used to attain the results in the case of FEM solution, and the efficacy of the present solution is demonstrated by comparing the results with the available literature. The results reflect that the porosity inclusion, circular cut-out, and position of the boundary constraints have a notable influence on the fundamental frequency of the functionally graded plate. It is also concluded that after a specific radius of circular cut-out, the vibration response of functionally graded plate exhibits nonlinearity in nature.