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In this paper we approach the linear mixed problem with initial and boundary values for a Cosserat body which is elastic and has pores. We coupled the equations characterizing the pores evolution with basic equations that describing the elastic deformations of the Cosserat body. The coupling is done by means of predetermined coefficients. To prove the continuous dependence of the solutions, we introduce an adequate measure which is useful in obtaining of some estimations with respect to the gradient of elastic deformations and regarding the gradient of a specific the application, introduced to characterize the behavior of the pores. [ABSTRACT FROM AUTHOR]

The investigation of the reflection issue in a hygrothermal medium in nonlocal elasticity is the focus of the current research project. The velocity equation is created by formulating and solving the governing equations of a hygro-thermoelastic material. The solution for plane waves predicts three incorporated plane waves, including longitudinal displacement, P-wave, thermal diffusion TD-wave and moisture diffusion mD-wave and shear vertical SV wave propagate in the medium. The velocity of P, TD, mD and SV waves are computed for the hygrothermal medium. Expressions for the energy ratio and reflection coefficient are developed for the incidence of a hygrothermal plane wave. The effect of hygrothermal parameters and nonlocal parameter on velocity, the reflection coefficient and energy ratio are displayed on a graph. [ABSTRACT FROM AUTHOR]

Our paper deals with a mixed initial-boundary value problem in thermoelasticity of piezoelectric bodies with dipolar structure. It is considered the general case of a thermoelastic body which inhomogeneous and also anisotropic and we add the effect of piezoelectricity. We take into account the main equations and basic conditions of a temperature rate dependent theory which predict the waves propagation with a finite speed. Using some middle conditions imposed on the boundary conditions and initial data, we obtain that our mixed problem admits one solution. A generalized form of the Hamilton's principle is obtained to cover this context. [ABSTRACT FROM AUTHOR]

In our article, we deduce a reciprocal relation in the context of dipolar porous materials. As an application, we analyze the effect of the dipolar structure on bodies charges which are similar to a dislocation of seismic type. Our results appear as generalizations of equivalent statements from the simpler theory of classical elastic bodies and they cover the more complicated theory of thermoelastic bodies with a dipolar structure. [ABSTRACT FROM AUTHOR]

Our study is dedicated to a composite, which, in fact, is a mixture of two thermoelastic micropolar bodies. We formulate the mixed initial boundary value problem in this context and define the domain of influence for given data. For any solution of the mixed problem we associate a measure and prove a second-order differential inequality for it. Based on the maximum principle for the heat equation and on the second-order differential inequality, we establish an estimate which proves that the thermal and the mechanical effects, at large distance from the domain of influence, are dominated by an exponential decay. [ABSTRACT FROM AUTHOR]

In our study, we formulate the boundary value problem in the context of the nonlinear theory of dipolar, porous, and elastic materials. For this problem, some existence and uniqueness results are proven. The results are natural generalizations of the results obtained by Langenbach for the classical elastic bodies. [ABSTRACT FROM AUTHOR]

Abstract In order to describe the photothermal dynamic behavior of viscoelastic semiconductor materials, the authors of this work propose a fractional modification of the Kelvin-Voigt type. The generalized Mittag-Leffler function method with two parameters was utilized as the non-local, nonsingular kernel of the Goufo-Caputo fractional operator, which is similar to the AB fractional derivative. Also, a new concept of photovoltaic heat transfer has been developed to describe the process of photothermal heating in semiconductors, in which light energy is converted into thermal energy by absorption. This unique model is grounded in the theoretical framework of the Moore-Gibson-Thompson (MGT) equation, and it offers additional insights into the underlying process of light sensitive heat transfer, as well as the intricate interaction between heating signals, elasticity, and plasma. As a direct application of the proposed model, the photothermal interactions that occur when an infinitely rotating semiconductor material with a cylindrical hole is subjected to a laser thermal flux and immersed in a constant axial magnetic field have been investigated. These findings may have implications for developing optically absorbent nanostructures and their use in photothermal energy generation. For this reason, the comparison of modified photoelasticity models with spherical derivatives and classical models applied to semiconducting materials seems interesting. [ABSTRACT FROM AUTHOR]

AbstractThis study employs a novel mathematical formulation of temperature-dependent thermoelastic diffusion with multi-phase delays (TDMT). The TDMT model, which is assumed, is obtained by converting the fundamental rules of Fourier’s and Fick’s laws into higher order time derivatives of the heat flow vector, the temperature gradient, diffusing mass flux, and the chemical potential gradient. Fundamental theorems such as energy, uniqueness, reciprocity theorems, and variational criterion are established using the fundamental equations for the assumed model TDMT. The reciprocity theorem is applied to a particular scenario by using instantaneous concentrated body forces, heat sources, chemical potential sources, and moving heat sources as examples. It is noted that both the variational criterion and these theorems depend on the field variables’ susceptibility as well as the fluctuations in the higher order temporal derivatives’ parameters. Additionally, the assumed model’s two-dimensional (2D) plane wave propagation is described. Three longitudinal waves are identified: the longitudinal (P) wave, the thermal (T) wave, the chemical potential (CP) wave, and the linked transverse (SV) wave. Wave properties (phase velocity and attenuation coefficient) are calculated numerically and shown visually. A few special examples are also investigated and compared with the established findings. The framework for additional research into basic issues in thermoelastic continua under various physical field variables is provided by this work. Numerous applications in material science, geomechanics, soil dynamics, and the electronic sector can be made of the current findings. [ABSTRACT FROM AUTHOR]

Abstract This research problem is an investigation of reflection amplitude in a nonlocal porous-thermo-micropolar diffusion half-space under memory dependent derivative (MDD) thermo-elasticity subjected to impedance boundary reflecting surface. The governing equations for nonlocal porous-thermo-micropolar diffusion medium in MDD theory are formulated. This research challenge is solved analytically for a two-dimensional model in order to demonstrate the presence of four coupled longitudinal waves and two paired transverse waves denoted as coupled longitudinal displacement wave ( cLDW − I ), coupled longitudinal thermal wave ( cLDW − I I ), coupled longitudinal mass diffusion wave ( cLDW − III ), coupled longitudinal void volume fraction wave ( cLDW − I V ), and coupled transverse displacement wave ( cTDW ) and coupled transverse micro-rotational wave ( cTMW ). When there is nonlocality, diffusion, and porous characteristics in the medium, it is discovered to have an impact on these coupled longitudinal waves, making them dispersive and attenuating. The transverse wave is non-attenuating but dispersive, it is unaffected by diffusion and porous characteristics. To find the expression for the reflection coefficients of reflected waves, the plane wave reflection from a thermally insulated surface subjected to an impedance boundary is explored. For a specific material, the reflection coefficients of the reflected waves are calculated, and graphic representations of the fluctuations of the reflection coefficients versus the incidence angle, nonlocality, diffusion and porous constants are provided. For further investigation, energy ratio can be studied in future. [ABSTRACT FROM AUTHOR]