Multilayered Anisotropic Media Research Articles

An efficient multi-field dynamic model for 3D wave propagation in saturated anisotropic porous media

An efficient multi–field coupled dynamic model for saturated anisotropic porous materials is proposed here. The mathematical formulation of the dynamic deformation–diffusion problem is developed starting from the mixture theory and the definition of the effective stress for anisotropic poro–elasticity, taking into account also the fluid phase compressibility and anisotropic permeability. The effective stress principle is properly extended through the Biot tensor to predict the coupling between the shear stress of the solid skeleton and the pore fluid pressure. Numerical solution of the coupled problem is obtained by inf-sup stable Finite Element spaces. A fundamental issue for the computational efficiency of the coupled model is the numerical solution of the resulting large–size and non–symmetric discrete problem. In this work, we develop a fully implicit monolithic solver based on the Bi–Conjugate Gradient Stabilized (Bi-CGStab) algorithm accelerated via an ad–hoc Multi–Physics Reduction (MPR) preconditioning technique. The proposed advances are implemented in the 3D GeoMatFem research code and several numerical analyses are performed to test the potential and computational efficiency of the proposed tool. In particular, we focus on 3D wave propagation applications in fully saturated single and multi-layered anisotropic media. Numerical results show that our implementation is able to identify the shear wave splitting phenomenon due to the different degree of material symmetry between the solid phase and the whole porous material.

Contraction Integral Equation for Modeling of EM Scattering by 3-D Bodies Buried in Multilayered Anisotropic Medium

Integral equation (IE) is regarded as an efficient method for 3-D modeling of electromagnetic (EM) responses. The main contribution of this article is to develop a contraction integral equation (CIE) algorithm with a high performance for modeling of EM scattering by 3-D bodies buried in multilayered anisotropic medium. The introducing of contraction operator can ensure that the discretized IE will be iteratively convergent in large conductivity contrast between abnormal bodies and background medium. Moreover, the contraction operator can also accelerate the iteration convergence of the IE. During the discretization process of CIE, direct waves are extracted from dyadic Green's functions (DGFs) of multilayered medium, and the singular integrals of direct waves are eliminated using equivalent sphere and ellipsoid methods. By splitting DGF into convolution terms and correlation terms, 3-D FFT can be used to accelerate the product evaluation of DGFs integral and scattering current encountered in each iteration. Validity of the proposed CIE is verified by comparing with the existing finite volume method. Modeling results show that the conventional IE will be iteratively divergent when the conductivity contrast between bodies and background is large, but the CIE is always iteratively convergent even under very large conductivity contrast.

Combined Fourier-wavelet transforms for studying dynamic response of anisotropic multi-layered flexible pavement with linear-gradual interlayers

The objective of this study is to develop an analytical solution for studying dynamic response of anisotropic multi-layered flexible pavement with linear-gradual interlayers under a harmonic moving load. In this study, the flexible pavement structure is simplified as one multi-layered flexible system, which is assumed to be a semi-infinite medium. A new approach combining the Fourier transform with the wavelet transform for solving the dynamic analytical solution. The wavelet transforms for solving inverse Fourier transform, in solving the solution in the physical domain, is superior to the conventional inverse Fourier transform. The linear-gradual interlayer between the adjacent layers is defined using the shear spring model, and the anisotropic property is simplified as transverse isotropy. Also, in the dynamic analytical solving processes, the motion in the transversely isotropic medium is decoupled into in-plane motion and out-of-plane motion because of the propagation of the waves in a transversely isotropic medium with coupling phenomena. The corresponding analytical solution is entered into a MATLAB-based computer program, which can compute the dynamic responses of an anisotropic multi-layered medium at different interlayer conditions. The accuracy of this program is confirmed through comparison with the results from the examples from the references. The influence analyses of linear-gradual interlayers and anisotropic properties of structural layers are illustrated. It is concluded that the proposed analytical solution-based computer program could be used in the multi-layered flexible pavement structural design and risk management in civil engineering.

Analytical solution for the effect of anisotropic layers/interlayers on an elastic multi-layered medium subjected to moving load

The intent of this study was to develop an analytical solution for the mechanical behaviors associated with a three-dimensional anisotropic multi-layered medium when it is subjected to a moving load. However, for simplicity, a planar model (two-dimensional model) was used as a substitution. The anisotropic property of the structure layers was approximated as transverse isotropy. Both the interlayer conditions (bonded and sliding) between the adjacent layers and load properties including load velocity and frequency were considered in the mathematical derivation of the analytical solution. Following the mathematical derivation, implementation and verification, the analytical solutions obtained were able to successfully evaluate the mechanical behaviors of an anisotropic elastic multi-layered medium subjected to a moving load. Subsequent numerical results revealed that both the anisotropic properties and the interlayer conditions have a significant impact upon the mechanical behaviors of an elastic multi-layered medium. In contrast, due to the conditions/assumptions considered in the computations, the load velocity and frequency were found to have a negligible impact on the mechanical behavior.

Fast Calculation of Scattering in Planar Uniaxial Anisotropic Multilayers

In this paper, the generalized recursive formulations of the finite difference time domain (FDTD) for updating the electric and magnetic fields in the multi-layer anisotropic media are derived with a uniaxial perfectly matched layer. The stability condition of the proposed method is clearly analyzed and verified. Then this method is used to calculate the three-dimensional complex scattering fields in planar multilayered anisotropic microstructures with optical axis perpendicular to the layered interface and the scattering fields of arbitrary shape scatters in the anisotropic layered structures. The electric field induced by the sine dipole source is calculated in the spatial domain and the corresponding spectral domain results are achieved through Fourier transform. The scattering field of composite materials with submillimeter thicknesses used in the industrial engineering is calculated using a terahertz wave with operation frequency of 0.3 THz. Robustness of the derived formulations for the complex uniaxial anisotropic media is verified by comparing with the COMSOL software, which is based on FEM analysis. The comparison of memory and CPU time shows the efficiency of the proposed FDTD method. Finally, the scattering fields of different scatters buried in multilayer anisotropic media are studied. So it is expected to become an effective simulation tool for dealing with complex electromagnetic environment in the future, such as abnormal detection of aircraft coating materials and detection of hidden target and so on.

Assessing the mechanical responses for anisotropic multi-layered medium under harmonic moving load by Spectral Element Method (SEM)

• An analytical solution for analyzing the mechanical behavior of multi-layered medium under moving load is proposed. • A more realistic harmonic moving load is applied in the multi-layered medium model. • The impact of the anisotropic property changes with the variety of load properties. • The impact of interlayer condition and top layer thickness are investigated. The article is concerned with the mechanical responses of anisotropic multi-layered medium under harmonic moving load. An analytical solution for two-dimensional anisotropic multi-layered medium subjected to harmonic moving load is devoted via Spectral Element Method (SEM), while the anisotropic property is approximated as transverse isotropy. Starting with the constitutive equations of transversely isotropic body and the governing equations of motion based on the loading properties. The analytical spectral elements in the wavenumber domain are obtained according to the principle of wave superposition and Fourier transformation. Then, the spectral global stiffness matrix of the multi-layered medium is derived by assembling the nodded stiffness matrices of all layers depended on the different interlayer conditions between the adjacent layers, i.e. sliding and bonded. The corresponding analytical solutions are achieved by taking the Fourier series and Inverse Fast Fourier Transform (IFFT) algorithm. Finally, some examples are given to validate the accuracy of the proposed analytical solution, and to demonstrate the impact of both anisotropy, top layer thickness, interlayer conditions, and loading properties (velocity and natural frequency) on the mechanical response of the multi-layered medium.

An efficient ray-tracing method and its application to Gaussian beam migration in complex multilayered anisotropic media

We have developed a fast ray-tracing method for multiple layered inhomogeneous anisotropic media, based on the generalized Snell’s law. Realistic geologic structures continuously varying with embedded discontinuities are parameterized by adopting cubic B-splines with nonuniformly spaced nodes. Because the anisotropic characteristic is often closely related to the interface configuration, this model parameterization scheme containing the natural inclination of the corresponding layer is particularly suitable for tilted transverse isotropic models whose symmetry axis is generally perpendicular to the direction of the layers. With this model parameterization, the first- and second-order spatial derivatives of the velocity within the interfaces can be effectively obtained, which facilitates the amplitude computation in dynamic ray tracing. By using complex initial conditions for the dynamic ray system and taking the multipath effect into consideration, our method is applicable to Gaussian beam migration. Numerical experiments of our method have been used to verify its effectiveness, practicability, and efficiency in memory storage and computation.

Impact of interlayer on the anisotropic multi-layered medium overlaying viscoelastic layer under axisymmetric loading

• An analytical solution for analyzing the mechanical behavior of multi-layered medium is proposed. • Computational efficiency of proposed solution is higher than ABAQUS . • Interlayer condition and anisotropic property significantly affected on the mechanical behavior of multi-layered medium. Multi-layered media is the most common structure in artificial and natural surroundings, and it is considered as a good candidate for mathematical model. The anisotropic properties and viscoelastic properties of layer materials have been widely used in multi-layered medium. Furthermore, the interlayer condition between the layers also plays an important role in the mechanical behavior of multi-layered medium. Despite many numerical approaches having been applied in these analyses, only few analytical solution were developed to analyze the effects of these three issues at the same time. The objective of this study is to develop an analytical solution that can be used for analyzing the impact of interlayer conditions on the mechanical behavior of anisotropic multi-layered medium overlaying viscoelastic layer subjected to axisymmetric loading, but the anisotropy property was approximated as transversely isotropy. The interlayer condition between the adjacent layers will also be considered. Details of the mathematical derivation, implementation and verification of the proposed analytical solution were presented. Subsequent numerical results demonstrate that both viscoelastic, transverse isotropy and interlayer condition could substantially contribute to the mechanical behavior of the multi-layered medium.

Multiple scattering analytical method for apparent characteristics in multilayer media

A multiple scattering analytical method is developed to analyze the apparent characteristics of multilayer isotropic and anisotropic media in this work. The model to calculate the apparent directional radiative intensity in multilayer media is established. A monolayer infinite slab with different scattering phase functions is considered as an example to examine the accuracy of the proposed method. The results are compared with data calculated by a Monte Carlo method. Moreover, the radiative intensity as a function of apparent direction, under the assumption that rays are obliquely incident on the surface of participating media, is obtained. The influence of optical thickness on the apparent directional radiative intensity in multilayer anisotropic media is analyzed. The forward and backward scattering energy, which is not involved in the attenuation in the incident direction of light, dependence on optical thickness for different scattering orders is studied. These results advance the theory of multiple scattering, especially with respect to the total energy of forward and backward scattering. We provide theoretical and experimental data relevant for atmospheric research and target detection.

Analytical relations for achieving zero reflection in anisotropic materials

Complete transparency and zero reflection condition in anisotropic materials are investigated, and are undertaken in an analytical study. First, the relations related to multilayer anisotropic media in linear structures are stated, and then, through these relations, zero reflection from layered structures composed of conventional materials and/or metamaterials are studied. The authors have formulated a rule for zero reflection from anisotropic media, and have presented various aspects of such structures from the viewpoints of frequency and the angle of incidence, and have created complete transparency in them.

Electro-elastic coupled fields of the general line source in infinite multilayered piezoelectric medium

Electro-elastic coupled fields excited by a general line source in a multilayered anisotropic piezoelectric medium are expressed in an analytical form. The general line source represents a combination of a straight 4D dislocation with the force and charge, distributed along the same line. The results are obtained in the form of well-convergent Fourier integrals. They can be considered as Green’s functions describing electro-elastic fields created in the given medium by arbitrary 2D bulk distributions of dislocations, forces, charges and electro-potential. The analysis is accomplished in terms of the propagator matrix which is equally applicable to both the stratified and graded layered media.

The far-field scattering response of a side drilled hole in single/layered anisotropic media in ultrasonic pulse-echo setup

Ultrasonic testing for defects in anisotropic material is one of the difficult problems in non-destructive testing (NDT) with elastic waves. Even though a series of studies have been performed on the waves interacting with flaws, however, only a small portion was on anisotropic materials. In this paper, an analytical solution for the far-field scattering response of a side drilled hole (SDH) in anisotropic media in an ultrasonic pulse-echo setup with its incident wave normal to the axis of cylindrical hole is presented. The solution is based on the Kirchhoff approximation, and validated upon several numerical examples, yielding satisfactory results in the comparison to the results achieved by different methods. Also, an attempt is made to extend the use of this solution from homogeneous anisotropic media to weld, which is considered as the multi-layer anisotropic media.

Analytical solution for the electric potential in arbitrary anisotropic layered media applying the set of Hankel transforms of integer order

ABSTRACTThe analytical solution and algorithm for simulating the electric potential in an arbitrarily anisotropic multilayered medium produced by a point DC source is here proposed. The solution is presented as a combination of Hankel transforms of integer order and Fourier transforms based on the analytical recurrent equations obtained for the potential spectrum. For the conversion of the potential spectrum into the space domain, we have applied the algorithm of the Fast Fourier Transform for logarithmically spaced points. A comparison of the modelling results with the power‐series solution for two‐layered anisotropic structures demonstrated the high accuracy and computing‐time efficiency of the method proposed.The results of the apparent‐resistivity calculation for both traditional pole‐pole and tensor arrays above three‐layered sequence with an azimuthally anisotropic second layer are presented. The numerical simulations show that both arrays have the same sensitivity to the anisotropy parameters. This sensitivity depends significantly on the resistivity ratio between anisotropic and adjacent layers and increases for the models with a conductive second layer.

Theoretical analysis of screw dislocations and image forces in anisotropic multilayered media

The elastic field induced by a screw dislocation embedded in an anisotropic elastic multilayered medium is presented in this study. A linear coordinate transformation is introduced in this study to simplify the problem. The explicit complete solutions of shear stresses and displacement for this problem consist only of the simplest solutions for a screw dislocation in an infinite homogeneous medium. The physical meaning of the solution is the image method and the magnitudes and locations of image screw dislocations are determined automatically from the mathematical method presented in this study. With the aid of the Peach-Koehler equation, the explicit forms of image forces exerted on screw dislocations are easily derived from the full-field solutions of stresses. Numerical results for full-field stress distributions in multilayered media subjected to a screw dislocation are presented. The image forces and equilibrium positions of a screw dislocation, two screw dislocations, and an array of screw dislocations are presented by numerical calculations and are discussed in detail.

Hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media

This paper presents the hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media. The method utilizes the hybrid matrix of each layer in a recursive algorithm to deduce the stack hybrid matrix for a multilayered structure. Like the stiffness matrix method, the hybrid matrix method is able to eliminate the numerical instability of transfer matrix method. By operating with total stresses and displacements, it also preserves the convenience for incorporating imperfect or perfect interfaces. However, unlike the stiffness matrix, the hybrid matrix remains to be well-conditioned and accurate even for zero or small thicknesses. The stability of hybrid matrix method has been demonstrated by the numerical results of reflection and transmission coefficients. These results have been determined efficiently based on the surface hybrid matrix method involving only a subset of hybrid submatrices. In conjunction with the recursive asymptotic method, the hybrid matrix method is self-sufficient without hybrid asymptotic method and may achieve low error level over a wide range of sublayer thickness or the number of recursive operations.

Transient Reflection Properties of a Dispersive and Lossy Bi-Isotropic Slab With an Anisotropic Laminated Composite Backing

This paper presents a detailed analysis of the transient reflection from a general bi-isotropic slab backed by a laminated composite. Either a nonreciprocally Tellegen medium or a reciprocally dispersive chiral medium with losses is considered as the bi-isotropic slab. The laminated composite is a graphite-fiber-reinforced-plastic composite (GFRPC), which has been widely used as a replacement for metals and may be treated as a multilayered anisotropic medium from the electromagnetic point of view. For the analysis, a theoretical model is developed based on a state-equation approach. On the basis of this model, both the time-domain and the frequency-domain plane-wave reflection results are obtained and studied. The factors affecting the results, such as the material parameters of the bi-isotropic slab and the fiber-orientation pattern of the GFRPC, are investigated in detail. Some special reflection properties, such as the twist-polarizer reflection and the antireflection, are observed based on this investigation. The properties may lead to a novel transient absorber technology for electromagnetic compatibility (EMC) applications.

Deviation of a monochromatic Lamb wave beam in anisotropic multilayered media: asymptotic analysis, numerical and experimental results

The aim of this paper is threefold: to describe the physical phenomenon of the excitation of modal waves such as Lamb waves, in anisotropic multilayered media, by a monochromatic incident beam, using an asymptotic approach; to present a three-dimensional model using the decomposition of the incident beam into monochromatic plane waves (the formalism is applied to the particle displacement vector); to illustrate the phenomenon both numerically and experimentally. Numerical and experimental maps of the reflected field of pressure are presented, and the reradiation of the Lamb wave beam in an oblique plane is theoretically and numerically illustrated.

Waves in stratified anisotropic poroelastic media: a transfer matrix approach

The problem of propagation of waves in multilayered anisotropic poroelastic medium is studied using the technique of transfer matrix. The model consists of a stack of anisotropic poroelastic solid layers overlying an anisotropic elastic solid layered half-space. The whole layered medium is lying under fluid half-space. The transfer matrices for anisotropic poroelastic layer and anisotropic elastic solid layer are derived. Using these matrices, reflection and transmission coefficients for the waves propagating in considered multilayered model are evaluated. The interface between the two stacks is considered to be imperfect and modified boundary conditions are applied thereat. Numerical computations are done for a particular model. The effects of porosity, anisotropy of the layers, thickness of the layers and imperfect bonding are studied on the wave propagation through the considered model. The results indicate that anisotropy of half-space is a very dominant property influencing the reflection–refraction phenomenon. Also, it is noticed that the imperfection of interface is accompanied by the dissipation of energy and the interface acts as an absorbing boundary.

Full-wave 2D and 3D spectral domain analysis of HTS multistrip multilayer lossy structure

The 2D and 3D CAD tools for modeling planar microwave devices are developed. The full-wave 2D analysis based on Method of Moments (MoM) is used for calculation of propagation characteristics of slot- and stripmulticonductor lossy lines embedded in multilayer lossy media. The 3D analysis based on MoM allows considering an arbitrary conductor structure embedded in a multilayered anisotropic media. Two examples of simulation are given. The modeling of the structure consisting of four coupled slots in HTS film based on a bilayered substrate with a tunable upper ferroelectric layer was performed by 2D-analysis. The results of simulation are analyzed for estimation of the insertion loss for each propagation mode. The simulation by 3D-analysis of the HTS microstrip resonator based on ferrite-MgO substrate has been done. The comparison of the HTS microstrip line current distribution simulated by 2D and 3D approaches is implemented and a high accuracy of used models is demonstrated.

Time-resolved line focus acoustic microscopy of layered anisotropic media: application to composites.

This paper presents theoretical and experimental studies of the time-domain response of line focus acoustic microscopy from a layered anisotropic medium. A method for elastic constant reconstruction from acoustic microscopy signatures also is presented. The microscopy response is complicated by multiple reflections in the layers and by the anisotropic nature of the material. The model is based on a new, stable recursive stiffness matrix algorithm developed for a multilayered anisotropic medium, which is applied to the interpretation of the time-resolved acoustic microscopy signature. Specific examples are given for unidirectional and multidirectional graphite epoxy composites. It is shown that the fluid load has a significant effect on the leaky surface waves in these composites, increasing surface wave speed above that for the slow transverse wave. This results in its absence from the microscopy signature of the surface wave. The theoretical results are compared with experiments carried out using a line focus PVDF transducer developed at National Institute of Standards and Technology (NIST). Time-resolved acoustic microscopy has been applied to the determination of elastic constants of a unidirectional composite or of one lamina in a cross-ply composite. The lateral waves and multiple reflections of bulk waves appearing in the microscopy signatures are used for the elastic properties reconstruction. The reconstruction results are compared to data obtained by the self-reference double-through-transmission ultrasonic bulk wave method.