Orthotropic Medium Research Articles

Rayleigh waves in nonlocal orthotropic thermoelastic medium with diffusion

Rayleigh waves in nonlocal orthotropic thermoelastic medium with diffusion

The propagation of inhomogeneous waves in an orthotropic viscoelastic medium

Abstract The present article deals with the propagation of inhomogeneous waves in an orthotropic viscoelastic medium. For chosen directions of propagation and a real finite inhomogeneity parameter, a complex slowness vector is specified to define the propagation of an inhomogeneous incident wave. Then, the reflection and transmission of plane waves at a plane interface between two orthotropic viscoelastic half-spaces are discussed. In this incidence, horizontal slowness determines the slowness vectors for all reflected and transmitted waves. For each reflected and transmitted wave, the corresponding slowness vector is resolved to define its phase direction, phase velocity and attenuation angle. Appropriate boundary conditions on this wave field determine the amplitude ratios for reflected and transmitted waves relative to the incident wave. The numerical examples are provided to show the effect of the inhomogeneity of the incident wave on the propagation characteristic as well as the reflection and transmission coefficients. The existence of homogeneous, inhomogeneous incident waves also is investigated.

Crack initiation and propagation from a closing flaw with frictional contact in a natural quasi-brittle orthotropic solid

This work considers the frictional closing of a pre-existing flaw in a natural quasi-brittle orthotropic medium (wood) under compression. The effect of the flaw face friction at multiple orientations of the flaw, on the peak load-bearing capacity are investigated. The failure due to crack growth initiation from the periphery of the pre-existing flaw and its propagation was investigated experimentally and modelled numerically. The experimental investigation was carried out using New Zealand Pine wood with a pre-existing flaw under a quasi-static compression test. In the numerical investigation, an eXtended Finite Element Method (XFEM)-based cohesive zone model (CZM) is employed in the modelling of the local crack initiation and propagation. The onset of the crack initiation is modelled using a stress-based criterion and the progressive degradation due to crack propagation is traction-separation based damage evolution. The XFEM-based CZM captures the crack initiation and propagation consistent with the experimental results. The numerical results also show the influence of flaw face friction on the peak load bearing capacity as well as the local stress response.

Analysis of reflection of wave propagation in magneto-thermoelastic nonlocal micropolar orthotropic medium at impedance boundary

PurposeThis study aims to examine the plane wave reflection problem in micropolar orthotropic magneto-thermoelastic half space, considering the influence of impedance as a boundary in a nonlocal elasticity.Design/methodology/approachThis study presents the novel formulation of governing partial differential equations for micropolar orthotropic medium with impact of nonlocal thermo-elasticity under magnetic field.FindingsThis study provides the numerical results validation for a particular numerical data and expression for the amplitude ratios of reflected waves and identifies the existence of four different waves, namely, quasi longitudinal displacement qCLD-wave, quasi thermal wave qCT-wave, quasi transverse displacement qCTD-wave and quasi-transverse micro-rotational qCTM-wave. The study derives the velocity equation giving the speed and phase velocity of these waves. The study also shows that the small-scale size effect gives significant impact on phase velocity.Research limitations/implicationsThe graphical analysis examines the variation of speeds and coefficients of attenuation of these waves due to frequency, magnetic field and nonlocal parameters. Also, significant conclusions on the variation of reflection coefficient against nonlocal parameter, frequency, impedance parameter and angle of incidence are provided graphically.Practical implicationsThe creation of more effective micropolar orthotropic anisotropic materials which are very useful in the daily life and their applications in earth science are greatly impacted by the findings of this study.Originality/valueThe authors of the submitted document initiated and produced it collectively, with equal contributions from all members.

An adaptive dynamic phase-field modeling with variable-node elements for thermoelastic fracture in orthotropic media

In this work, a novel adaptive algorithm integrated into a dynamic phase-field method is developed to model the fracture of orthotropic materials under thermoelastic loading. The procedure of local refinement is synchronized with crack tip advancement, with the phase-field value serving as the criterion for marking elements. To address mesh refinement inconsistencies, variable-node elements are employed. Hughes–Hilbert–Taylor (HHT) and backward difference method are utilized for time discretization of displacement and temperature, respectively. A penalized structural matrix is incorporated into crack surface density to realize the orthotropy of crack growth. The performance of the proposed method is validated through several numerical benchmarks, i.e., the proposed method can effectively simulate the dynamic crack propagation of orthotropic materials under thermoelastic loading, and can assuage computational overhead while keeping acceptable accuracy.

Propagation of plane waves at the initially stressed surface of an orthotropic nonlocal rotating half space under dual-phase-lag model

PurposeThe purpose of the current manuscript is to investigate the reflection of plane waves in a rotating, two-dimensional homogeneous, initially stressed, nonlocal orthotropic thermoelastic solid half-space based on dual-phase-lag model.Design/methodology/approachThe reflection phenomenon has been utilized to study the effects of initial stress, rotation and nonlocal parameter on the amplitude ratios. During the reflection phenomenon three coupled waves, namely quasi displacement primary wave (qP), quasi thermal wave (qT) and quasi displacement secondary wave (qSV) have been observed in the medium, propagating with distinct velocities. After imposing the suitable boundary conditions, amplitude and energy ratios of the reflected waves are obtained in explicit form.FindingsWith the support of MATLAB programming, the amplitude ratios and energy ratios are plotted graphically to display the effects of rotation, initial stress and nonlocal parameters. Moreover, the impact of anisotropy and phase lags is also observed on the reflection coefficients of the propagating waves.Originality/valueIn the current work, we have considered rotation and nonlocality parameters in an initially stressed orthotropic thermoelastic half-space, which is lacking in the published literature in this field. The introduction of these parameters in a nonlocal orthotropic thermoelastic medium provides a more realistic model for these studies. The present work is valuable for the analysis of orthotropic thermoelastic problems involving rotation, initial stress and nonlocality parameters.

Response of Moisture and Temperature Diffusivity on an Orthotropic Hygro-thermo-piezo-elastic Medium

This research explores the complex interaction between piezoelectric waves and heat-moisture diffusion within a semi-infinite piezoelectric material under hygro-thermal conditions. By employing a two-dimensional Cartesian framework, novel governing equations for a thermo-piezoelectrically orthotropic medium influenced by moisture effects are developed. Accurate representations for key parameters are obtained by utilizing normal mode analysis. The investigation examines the influence of critical factors like moisture content, diffusivity, and temperature diffusivity on the spatial distribution of various physical fields. Additionally, a particular scenario of significance is highlighted. These results have the potential to improve sensor, actuator, and energy-harvesting device performance and dependability.

Axisymmetric torsion of rigid disc parallel to penny shaped crack at the interface of layer bonded by two orthotropic half spaces

Two half-spaces and a layer of finite height of linear elastic orthotropic medium containing a penny-shaped crack and a circular rigid disk are considered such that the crack surface is parallel to the rigid disk, where both are situated at two different interfaces of layer and half-space and perpendicular to the axis of symmetry. The rigid disk is agitated by an axisymmetric torsion. The equations of equilibrium are solved with the use of Hankel’s integral transform method. Then, the tangential displacement components and shear stress components are determined. With the help of mixed-type boundary conditions, a system of integral equations is derived. After that, by utilizing a trial solution, these integral equations are transformed into a pair of simultaneous Fredholm integral equations of the second kind. The numerical results of the Fredholm integral equations are evaluated by converting it into a system of algebraic equations to interpret the physical quantity, like the stress intensity factor (SIF), which is demonstrated graphically. The obtained results are compared to the previously published article to ensure its accuracy.

Separation of fast and slow shear waves and prediction of fracture parameters based on non-orthogonal assumptions

SUMMARY Natural fractures play a significant role in oil and gas reservoirs. Accurate predictions of fracture parameters are vital in reservoir prediction and oil and gas development. The birefringent phenomenon of shear waves in fractured media makes shear wave splitting (SWS) analysis an important tool in formulating fracture predictions. The traditional SWS analysis method is based on an orthogonal assumption of fast and slow shear waves. However, in an orthotropic medium composed of a background vertical transversely isotropic medium and a set of vertical fractures, fast and slow shear waves are not necessarily orthogonal. This causes the traditional SWS analysis method to fail. To solve this problem, we proposed an SWS analysis algorithm with a non-orthogonal assumption of fast and slow shear waves in this study. First, we introduced a parameter (difference angle) to characterize the angle between slow shear waves and the normal polarization directions of the fast shear waves. Subsequently, based on the traditional two-parameter scanning algorithm, a parameter was added to facilitate three-parameter scanning. In addition, we derived an expression for the two-parameter scanning objective function using the non-orthogonal assumption. Two-parameter scanning can accurately extract fast and slow wave time delay data, but it cannot determine an accurate fast shear wave polarization direction. Therefore, we optimized the three-parameter scanning algorithm as follows: first, we used two-parameter scanning to obtain the fast and slow wave time delays and then performed further scanning to determine the polarization direction of the fast shear wave and difference angle. The optimization algorithm significantly improved the computational efficiency. Subsequently, we tested the accuracy of this method using synthetic single-trace and three-component vertical seismic profile data. We demonstrated the implementation process of the three-parameter scanning method using actual data, separated fast and slow shear waves, and predicted fracture parameters. The final fracture parameters were verified.

Thermoelastic diffusion in nonlocal orthotropic medium with porosity

The present article investigates the linear theory of nonlocal thermoelasticity in homogeneous orthotropic porous medium with diffusion in the context of dual-phase-lag model. The focal point of the present study involves an examination of Fick’s mass diffusion law and the generalized Fourier’s law within the context of the dual-phase-lag model of hyperbolic thermoelasticity. The incorporation of voids, mass diffusion with phase lagging in the diffusion flux is the basis for establishing the void diffusion-elasticity models. Furthermore, the new dual-phase-lag diffusion model introduces the consideration of nonlocal effects in mass transfer. The resolution of the problem involves the utilization of normal mode analysis, employed for solving, and encompasses the application of thermal shock at the surface boundary. Numerical calculations of stress components, displacement components, voids, temperature, and concentration of the diffusive material are performed for various distances and time intervals.

In situ stress prediction method for decoupled overburden pressure under tectonic constraints

Abstract The prediction of in situ stress based on azimuthal seismic data has extensive use in horizon crushability evaluation. Nonetheless, existing in situ stress seismic prediction models do not consider overburden pressure and tectonic strain, which limit the prediction accuracy. To this end, we propose a decoupled overburden pressure in situ stress prediction method under tectonic constraints. The key to this method is to consider that the overburden pressure could act on the rock skeleton and pore fluid, i.e. generating effective pressure and pore pressure; the pore pressure can be estimated using Eaton's method, and then the effective stress can be obtained. The relationship between tectonic strain and effective pressure is constructed based on Hooke's law, where tectonic strain can be calculated from curvature attributes extracted from seismic data. Introducing pore pressure and deriving a model for calculating the maximum and minimum horizontal stresses and the difference in horizontal stress ratio for orthotropic media (OA). When the Thomson anisotropy parameters and the pore pressure are neglected, the proposed model can be degraded to a conventional horizontal transverse isotropy medium in situ stress prediction model, which proves the validity of the model. The results of sensitivity analysis experiments affirm the need to decouple overburden pressure and account for tectonic strain when predicting in situ stress reasonably. Finally, single-well and azimuthal seismic prediction were carried out by using the a priori information from well logging and seismic data.

Reflection of quasi plasma wave in photo-piezo semiconductor medium with distinct higher order fractional derivative two temperature models

This article investigates the reflection of thermo-photo-piezo-elastic plane waves from a homogeneous, orthotropic, and piezo semiconductor medium during the photo-thermal process. A novel higher-order fractional dual-phase lag hyperbolic two-temperature model is employed to tackle this study. The analytical solution to the problem in the xz plane reveals the existence of five interconnected waves. The derivation of formulas for reflection coefficients and their corresponding energy ratios is performed for an incident quasi-plasma wave. Numerical computations determine the energy ratios for different angles of incidence. These energy ratios are visually represented in graphs, demonstrating the influence of higher-order parameters, two-temperature effects, fractional order derivatives, and various heat conduction models.

A fast, rapidly convergent Nyström solver for electromagnetic scattering from orthotropic media

This article presents a simple, efficient, and high-order numerical scheme for the approximation of the convolution integral of the form(1)∫R2∇x′Φ(x,x′)⋅U(x′)dx′, where Φ(x,x′)=i4H0(1)(κ|x−x′|) and U is smooth and compactly supported vector function on R2. Moreover, we employ this integration scheme to obtain a Nyström solver for the numerical solution of the electromagnetic wave scattering problem by inhomogeneous orthotropic media, that is, media with refractive index of the form[n11(x)n12(x)0n21(x)n22(x)000n33(x)], where nij(x1,x2,x3) are independent of x3 coordinate. On a uniform grid of size n×n, the suggested approach has computational complexity O(n2log⁡n) and displays high-order convergence when the material properties are smooth. When the material attributes are real analytic, the approach actually converges exponentially. We demonstrate the performance of our integration scheme and the Nyström solver through several numerical experiments.

Mode-III external circular crack in an infinite orthotropic medium under torsional loading

This paper contains an investigation of interaction of torsional wave with a mode-III outer circular crack in an infinite orthotropic elastic medium. Using mixed boundary condition, the problem reduced into a dual integral equation. After some manipulation and use of Abel’s singular integral equation, the dual integral equation transformed into the Fredholm second kind integral equation, which is solved numerically. The obtained solution has been adopted to interpret the physical quantities like Crack Torsional Displacement (CTD) and mode-III Stress Intensity Factor (SIF) which are shown graphically.

Adaptive PD-FEM coupling method for modeling pseudo-static crack growth in orthotropic media

In this study bond-based peridynamic formulation is developed and coupled with the finite element method (FEM) to simulate crack growth in orthotropic materials. The coupled PD-FEM formulation gives an opportunity to use both peridynamic and finite element method advantages simultaneously. The Legendre functions are implemented to define varying bond properties according to the material orientation. Pseudo-static crack propagation in the composite materials is simulated and it is shown that the proposed method is able to predict crack growth in orthotropic materials faster than the conventional PD methods. Accuracy of the proposed method is demonstrated through comparison of the results against those of numerical studies which are available in the literature.

Hybrid Trefftz finite element method for heat conduction in cylindrical composite laminates

Laminated composites are made of continuous fibers and matrix which can provide required engineering properties. This paper proposed a hybrid Trefftz finite element method for the analysis of conductive heat transfer in cylindrical composite laminates by assuming two independent temperature fields. The non-conforming intra-element field which is approximated by a linear combination of T-complete solutions satisfying the governing equation and undetermined coefficients is defined within the element domain, while the auxiliary conforming frame field which is interpolated by standard one-dimensional shape functions is defined on the element boundary. Due to the fabrication characteristics of laminates, each layer can be treated as an orthotropic medium for which the hybrid functional is employed to enforce the continuity of temperature and heat flux across the interface of adjacent elements. The proposed method is tested on three numerical examples and compared with exact or ABAQUS solutions. It was found that the proposed method exhibits low sensitivity to mesh distortion and achieves more acceptable results compared with ABAQUS.

Anisotropy and magnetoelasticity effects on the propagation of the SH-wave-induced semi-infinite crack in a magnetoelastic orthotropic medium

The crux of the present study is to investigate semi-infinite crack propagation in magnetoelastic strip influenced by propagating SH-wave under orthotropic geometrical configurations. The Wiener-Hopf (WH) technique and two-sided Fourier integral transforms (FIT) are applied in the proposed analytical model. A closed-form expression of the stress intensity factor (SIF) has been established for the constant concentrated force. The SIF in a magnetoelastic orthotropic strip is shown to be significantly affected by the crack length and crack speed, medium anisotropy, and magnetoelastic parameter. The proposed model is compared to the case of a magnetoelastic isotropic strip in order to demonstrate the effect of orthotropy as well as other anomalies. Among other observations, it is noted that regardless of whether orthotropy exists in the strip or not, the value of the SIF rises along with the crack speed until it reaches its maximum, at which point it rapidly declines.

Photo-thermo-piezo-elastic waves in semiconductor medium subject to distinct two temperature models with higher order memory dependencies

PurposeThis study aims to examine the impacts of higher memory dependencies on a novel semiconductor material that exhibits generalized photo-piezo-thermo-elastic properties. Specifically, the research focuses on analyzing the behavior of the semiconductor under three distinct temperature models.Design/methodology/approachThe study assumes a homogeneous and orthotropic piezo-semiconductor medium during photo-thermal excitation. The field equations have been devised to encompass higher order parameters, temporal delays and a specifically tailored kernel function to address the problem. The eigenmode technique is used to solve these equations and derive analytical expressions.FindingsThe research presents graphical representations of the physical field distribution across different temperatures, higher order plasma heat conduction models and time. The results reveal that the amplitude of the distribution profile is markedly affected by factors such as the memory effect, time, conductive temperature and spatial coordinates. These factors cannot be overlooked in the analysis and design of the semiconductor.Research limitations/implicationsSpecific cases are also discussed in detail, offering the potential to advance the creation of precise models and facilitate future simulations.Practical implicationsThe research offers valuable information on the physical field distribution across various temperatures, allowing engineers and designers to optimize the design of semiconductor devices. Understanding the impact of memory effect, time, conductive temperature and spatial coordinates enables device performance and efficiency improvement.Originality/valueThis manuscript is the result of the joint efforts of the authors, who independently initiated and contributed equally to this study.

Reflection of plane waves in an orthotropic micropolar thermoelastic diffusive medium with two-temperature

Reflection of plane waves in an orthotropic micropolar thermoelastic diffusive medium with two-temperature

A peridynamic model for coupled thermo-mechanical-oxygenic analysis of C/C composites with SiC coating

The oxidation induced by coating cracking is a general failure mode of high-temperature composites such as C/C and C/SiC. However, this failure mode has not been fully investigated due to the lack of a method suitable for both crack simulation and oxidation interface capture. In this paper, a coupled thermo-mechanical-oxygenic peridynamic model is proposed for SiC-coated C/C composites in an oxidizing environment. The ordinary state-based peridynamics is extended to plane strain thermoelastic problems for orthotropic media to calculate the crack distribution. Cracks in the coating are modeled as oxygen diffusion channels and the peridynamic oxidation equation is developed to simulate the oxidation of the C/C substrate. Furthermore, the peridynamic non-Fourier heat transfer equation is employed to consider the finite thermal propagation speed and the model is validated by experimental results. Numerical examples are presented to investigate the oxidation failure after thermal shock, non-Fourier thermal shock fracture, and stress oxidation failure of SiC-coated C/C composites.