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This study aims to analyse the behaviour of plane waves within a nonlocal transversely isotropic visco-thermoelastic medium having variable thermal conductivity.

The concept of enunciation is used in the generalized theory of thermoelasticity in accordance with the Green–Lindsay and Eringen’s nonlocal elasticity models. The linear viscoelasticity model developed by Kelvin–Voigt is used to characterize the viscoelastic properties of transversely isotropic materials.

It has been noticed that three plane waves, which are coupled together, travel through the medium at three different speeds. The derivation of reflection coefficients and energy ratios for reflected waves is carried out by incorporating suitable boundary conditions. Numerical computations are performed for the amplitude ratios, phase speeds and energy partition and displayed in graphical form.

The outcomes of the numerical simulation demonstrate that the amplitude ratios are significantly influenced by variable thermal conductivity, nonlocal parameters and viscosity. It is further observed from the plots that the phase speeds in a transversely isotropic medium depend on the angle of incidence. In addition, it has been established that the energy is preserved during the reflection phenomenon.

The purpose of this paper is to establish a two-dimensional model of Green–Lindsay theory for micropolar magneto-thermoelastic medium to study the photothermal effect. The model is used to study the coupling between elastic waves and plasma waves generated due to thermal changes in a micropolar elastic medium.

Normal mode analysis is used to obtain the analytical solutions of the governing equations.

Effects of magnetic field, micropolarity, photothermal and time are highlighted on various physical fields such as stresses, temperature, displacement and carrier density. The above physical fields also conform to the boundary conditions. It is further observed that all the physical quantities become zero outside some bounded region of space, thus confirming the notion of generalized theory of thermoelasticity.

The values of physical fields are computed numerically using MATLAB software considering material constants for silicon. Furthermore, the effects are depicted graphically and analyzed accordingly. The study is valuable for the analysis of thermoelastic problems involving magnetic field, micropolarity and elastic deformations.

The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks.

With the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained.

The expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases.

As observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium.

To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method.

The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium.

A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

The purpose of this article is to investigate the propagation characteristics (such as particle motion, attenuation and phase velocity) of a Rayleigh wave in a nonlocal generalized thermoelastic media.

The bulk waves are represented with Helmholtz potentials. The stress-free insulated and isothermal plane surfaces are taken into account. Rayleigh wave dispersion relation has been established and is found to be complex. Due to the presence of radicals, the dispersion equation is continuously computed as a complicated irrational expression. The dispersion equation is then converted into a polynomial equation that can be solved numerically for precise complex roots. The extra zeros in this polynomial equation are eliminated to yield the dispersion equation’s roots. These routes are then filtered for inhomogeneous wave propagation that decays with depth. To perform numerical computations, MATLAB software is used.

In this medium, only one mode of Rayleigh wave exists at both isothermal and insulated boundaries. The thermal factors of nonlocal generalized thermoelastic materials significantly influence the particle motion, attenuation and phase velocity of the Rayleigh wave.

Numerical examples are taken to examine how the thermal characteristics of materials affect the existing Rayleigh wave’s propagation characteristics. Graphical analysis is used to evaluate the behavior of particle motion (such as elliptical) both inside and at the isothermal (or insulated) flat surface of the medium under consideration.

The purpose of this paper is to examine the impact of moisture and temperature changes on the behavior of a semi-infinite solid cylinder made of T300/5208 composite material. This study aims to provide analytical solutions for temperature, moisture and thermal stress through the de-coupling technique and the method of integral transforms. Both coupled and uncoupled cases are considered.

This study investigates the hygrothermo-elastic response of a semi-infinite solid circular cylinder using an integral transform technique that includes Hankel and Fourier transforms. The cylinder is subjected to prescribed sources, and a numerical algorithm is developed for the numerical computation of the results. The goal is to understand how the cylinder responds to changes in temperature and moisture.

The paper presents an analytical solution for temperature, moisture and thermal stress in a semi-infinite solid cylinder obtained through the use of an integral transform technique. The study focuses on a graphite fiber-reinforced epoxy matrix composite material (T300/5208) and discusses the coupled and uncoupled effects of temperature, moisture and thermal stress on the material. The results of the transient response hygrothermo-elastic field are presented graphically to provide a visual representation of the findings.

The research presented in this article is primarily hypothetical and focused on the analysis of mathematical models.

To the authors' best knowledge, this study is the first to investigate the hygrothermal effect in a semi-infinite circular cylinder. Additionally, the material properties used in the analysis are both homogenous and isotropic and independent of both temperature and moisture. These unique aspects of the study make it a novel contribution to the field.

This paper aims to study the impact of pyro-electricity, moisture and temperature diffusivity on the energy distribution of plane waves at the free surface of an orthotropic piezo-hygro-thermo-elastic medium.

This study presents the novel creation of governing equations for an anisotropic piezothermoelastic medium with moisture impact, which is a significant contribution of this paper.

In addition to providing numerical data for the amplitude ratios and energy ratios of reflected waves, this study identifies five different kinds of coupled reflected plane waves, namely, quasi-longitudinal P wave, quasi-thermal wave, quasi-transverse wave, quasi-moisture wave and electric potential wave.

The graphical analysis examines the impact of various factors, such as the angle of incidence, moisture and temperature diffusivity, pyro-electricity and frequency, on energy distribution.

This paper's results significantly impact the development of more efficient piezoelectric materials and their applications in geophysics.

The authors of the submitted document initiated and produced it collectively, with equal contributions from all members.

This paper aims to study the energy ratios of plane waves on an interface of nonlocal thermoelastic halfspace (NTS) and nonlocal orthotropic piezothermoelastic half-space (NOPS).

The memory-dependent derivatives (MDDs) approach with a hyperbolic two-temperature (HTT), three-phase lag theory is used here to study how the energy ratios change at the interface with the angle of incidence.

Plane waves that travel through NTS and hit the interface as a longitudinal wave, a thermal wave, or a transversal wave send four waves into the NOPS medium and three waves back into the NTS medium. The amplitude ratios of the different waves that are reflected and transmitted are used to calculate the energy ratios of the waves. It is observed that these ratios are affected by the HTT, nonlocal and MDD parameters.

The energy ratios correspond to four distinct models; nonlocal HTT with memory, nonlocal HTT without memory, local HTT with memory and nonlocal classical-two-temperature with memory concerning the angle of incidence from 0 degree to 90 degree.

This model applies to several fields, including earthquake engineering, soil dynamics, high-energy particle physics, nuclear fusion, aeronautics and other fields where nonlocality, MDD and conductive temperature play an important role.

The authors produced the submitted document entirely on their initiative, with equal contributions from all of them.

This 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.

The 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.

The 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.

Specific cases are also discussed in detail, offering the potential to advance the creation of precise models and facilitate future simulations.

The 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.

This manuscript is the result of the joint efforts of the authors, who independently initiated and contributed equally to this study.

The purpose of this study is to further advance the multiple space/time subdomain framework with model reduction. Existing linear multistep (LMS) methods that are second-order time accurate, and useful for practical applications, have a significant limitation. They do not account for separable controllable numerical dissipation of the primary variables. Furthermore, they have little or no significant choices of altogether different algorithms that can be integrated in a single analysis to mitigate numerical oscillations that may occur. In lieu of such limitations, under the generalized single-step single-solve (GS4) umbrella, several of the deficiencies are circumvented.

The GS4 framework encompasses a wide variety of LMS schemes that are all second-order time accurate and offers controllable numerical dissipation. Unlike existing state-of-art, the present framework permits implicit–implicit and implicit–explicit coupling of algorithms via differential algebraic equations (DAE). As further advancement, this study embeds proper orthogonal decomposition (POD) to further reduce model sizes. This study also uses an iterative convergence check in acquiring sufficient snapshot data to adequately capture the physics to prescribed accuracy requirements. Simple linear/nonlinear transient numerical examples are presented to provide proof of concept.

The present DAE-GS4-POD framework has the flexibility of using different spatial methods and different time integration algorithms in altogether different subdomains in conjunction with the POD to advance and improve the computational efficiency.

The novelty of this paper is the addition of reduced order modeling features, how it applies to the previous DAE-GS4 framework and the improvement of the computational efficiency. The proposed framework/tool kit provides all the needed flexibility, robustness and adaptability for engineering computations.