Thermomechanical Waves Research Articles

Thermomechanical interaction in a living tissue due to variable thermal loading with memory

AbstractIn order to address various clinical applications within living tissue, the aim of this work is to analytically study the thermomechanical interaction for a living tissue which is subjected to variable thermal loadings. Human tissues undergoing regional hyperthermia treatment for cancer therapy is based on graded changes of the cells, and as a consequences, the constitutive equations have been formulated using the nonlocal elasticity theory. The heat transport equation for the present problem is formulated in the context of Moore‐Gibson‐Thompson theory of generalized thermoelasticity assimilating the memory‐dependent derivative within a slipping interval. Both the boundaries of the tissue is maintaining the condition of zero traction. The lower boundary of the tissue is subjected to prescribed thermal loading while, the upper boundary is kept at zero temperature. Utilizing the Laplace transform mechanism, the governing equations have been solved and the general solutions have been obtained in the transformed domain. In order to arrive at the solutions in the real space‐time domain, suitable inversion of the Laplace transform has been carried out numerically using the method of Zakian. Numerical findings suggest that thermomechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model. Significant effect due to different effective parameter such as nonlocal parameter and the time‐delay parameter is reported. Also, how a nonlinear kernel function can be more effective in bio‐heat transfer, is outlined in the study also.

3D wave dispersion analysis of graphene platelet-reinforced ultra-stiff double functionally graded nanocomposite sandwich plates with metamaterial honeycomb core layer

This research addresses the three-dimensional thermomechanical wave propagation behavior in sandwich composite nanoplates with a metamaterial honeycomb core layer and double functionally graded (FG) ultra-stiff surface layers. Due to its potential for high-temperature applications, pure nickel (Ni) is preferred for the honeycomb core layer, and an Al2O3/Ni ceramic-metal matrix is preferred for the surface layers. The functional distribution of graphene platelets (GPLs) in three different patterns, Type-U, Type-X, and Type-O, in the metal-ceramic matrix with a power law distribution provides double-FG properties to the surface layers. The mechanical and thermal material characteristics of the core and surface layers, as well as the reinforcing GPLs, are temperature-dependent. The pattern of temperature variation over the plate thickness is considered to be nonlinear. The sandwich nanoplate’s motion equations are obtained by combining the sinusoidal higher-order shear deformation theory (SHSDT) with nonlocal integral elasticity and strain gradient elasticity theories. The wave equations are established by using Hamilton’s principle. Parametric simulations and graphical representations are performed to analyze the effects of honeycomb size variables, wave number, the power law index, the GPL distribution pattern, the GPL weight ratio, and the temperature rise on three-dimensional wave propagation in an ultra-stiff sandwich plate. The results of the analysis reveal that the 3D wave propagation of the sandwich nanoplate can be significantly modified or tuned depending on the desired parameters and conditions. Thus, the proposed sandwich structure is expected to provide essential contributions to radar/sonar stealth applications in air, space, and submarine vehicles in high or low-temperature environments, protection of microelectromechanical devices from high noise and vibration, soft robotics applications, and wearable health and protective equipment applications.

Three-dimensional thermomechanical wave propagation analysis of sandwich nanoplate with graphene-reinforced foam core and magneto-electro-elastic face layers using nonlocal strain gradient elasticity theory

This article investigates the propagation of bending, longitudinal, and shear waves in a smart sandwich nanoplate with a graphene platelet (GPL)-reinforced foam core and magneto-electro-elastic (MEE) surface layers using sinusoidal higher-order shear deformation theory (SHSDT). The suggested nanoplate is comprised of a Ti–6Al–4V foam core placed between MEE surface layers. The MEE surface layers are composed of a volumetric combination of cobalt-ferrite (CoFe2O4) and barium-titanate (BaTiO3). The foam core and MEE face layers’ material characteristics are temperature dependent. In this study, three different core types are considered: metallic solid core (Type-I), GPL-reinforced solid core (Type-II) and GPL-reinforced foam core (Type-III), as well as three different foam distributions: symmetrical foam I (S-Foam I), symmetrical foam II (S-Foam II) and uniform foam (U-Foam). To derive the nanoplate's equations of motion and determine the system response, Hamilton's principle and Navier's method are employed. The effects of various parameters such as the wave number, nonlocal parameter, foam void coefficient and distribution pattern, GPL volume fraction, and thermal, electric, and magnetic charges, on the phase velocity and wave frequency are investigated via analytical calculations. The findings of the research indicate that the 3-D wave propagation characteristics of the sandwich nanoplate can be considerably modified or tuned with respect to external loads and material parameters. Thus, the proposed sandwich structure is expected to provide important contributions to radar stealth applications, protection of nanoelectromechanical devices from high frequency and temperature environments, advancement of smart nanoelectromechanical sensors characterized by lightweight and temperature sensitivity and wearable health equipment applications.

Coupled responses of thermomechanical waves in functionally graded viscoelastic nanobeams via thermoelastic heat conduction model including Atangana–Baleanu fractional derivative

Accurately characterizing the thermomechanical parameters of nanoscale systems is essential for understanding their performance and building innovative nanoscale technologies due to their distinct behaviours. Fractional thermal transport models are commonly utilized to correctly depict the heat transfer that occurs in these nanoscale systems. The current study presents a novel mathematical thermoelastic model that incorporates a new fractional differential constitutive equation for heat conduction. This heat equation is useful for understanding the effects of thermal memory. An application of a fractional-time Atangana–Baleanu (AB) derivative with a local and non-singular kernel was utilized in the process of developing the mathematical model that was suggested. To deal with effects that depend on size, nonlocal constitutive relations are introduced. Furthermore, in order to take into consideration, the viscoelastic behaviour of the material at the nanoscale, the fractional Kelvin–Voigt model is utilized. The proposed model is highly effective in properly depicting the unusual thermal conductivity phenomena often found in nanoscale devices. The study also considered the mechanical deformation, temperature variations, and viscoelastic characteristics of the functionally graded (FG) nanostructured beams. The consideration was made that the material characteristics exhibit heterogeneity and continuous variation across the thickness of the beam as the nanobeam transitions from a ceramic composition in the lower region to a metallic composition in the upper region. The complicated thermomechanical features of simply supported viscoelastic nanobeams that were exposed to harmonic heat flow were determined by the application of the model that was constructed. Heterogeneity, nonlocality, and fractional operators are some of the important variables that contribute to its success, and this article provides a full study and illustration of the significance of these characteristics. The results that were obtained have the potential to play a significant role in pushing forward the design and development of tools, materials, and nanostructures that have viscoelastic mechanical characteristics and graded functions.

Thermo-mechanical waves in a biological tissue under ramp and oscillatory heat in Atangana–Baleanu fractional theory

Thermo-mechanical waves in a biological tissue under ramp and oscillatory heat in Atangana–Baleanu fractional theory

A modified couple stress model to analyze the effect of size-dependent on thermal interactions in rotating nanobeams whose properties change with temperature

Understanding the behavior of rotating materials and structures on small scales is crucial for many scientific and engineering fields, and such studies play an important role in this regard. This paper aims to propose a novel paradigm for analyzing the vibrational characteristics of thermoelastic nanobeams with diverse physical attributes. The incorporation of size effects in the structural and thermal constitutive relationships involves the consideration of nonlocal elasticity theory (NET) and the modified couple stress (MCS) model, together with the utilization of the Euler–Bernoulli assumptions for thin beams. The work also involves the development of a new non-Fourier thermoelasticity model that incorporates the Moore–Gibson–Thompson (MGT) equation. Furthermore, it was taken into account that the thermal conductivity of the flexible materials is not consistent but rather changes with temperature. Periodic pulse heating was applied to rotating nanobeams, and the behavior of the nanobeams was investigated with respect to thermal, rotational, and length-scale effects. To demonstrate the impact of the distinctive characteristics of the MCS and MGT thermoelastic models on the physical fields, a range of numerical data are presented. The study also investigated the propagation characteristics of thermo-mechanical waves, taking into account aspects such as thermal relaxation time and the influence of temperature change on physical properties. Based on the observed results, including the size impact in the structural and thermal equations can lead to significant disparities when compared to conventional models. The inclusion of the length-scale component in the MCS theory, which increases the rigidity and hardiness of the nanobeam structure, may help to explain the observed effect.

Elasto-Thermodiffusive Microtemperature Model Induced by a Mechanical Ramp-Type of Nanoscale Photoexcited Semiconductor

ABSTRACT In this study, a novel theoretical approach to describe thermo-optical elastic materials is proposed. This formulation offers insights into the relationship between plasma waves and thermomechanical waves when the microtemperature properties of semiconductor materials such as silicon are taken into account. The proposed model involves incorporating the concept of microtemperature effect according to photothermal (PT) excitation processes in nonlocal photo-thermoelasticity. The investigation of the electron-hole interaction concerning the elasto-thermodiffusion (ETD) theory in the context of thermoelastic (TD) and electronic (ED) deformation is the main focus of the work. The advanced model is utilized to analyze how the mechanical loading of ramp-like structures impacts the unrestricted nonlocality semiconductor material on a free outer plane. The Laplace transform approach in one-dimensional (1D) provides an analytical solution for main non-dimensional thermo-photo-elastic fields (the hole charge carrier field, the displacement (acoustic) wave, thermal wave, and plasma wave (carrier density). The primary fields in the Laplace domain are obtained analytically, and boundary conditions are established using a mechanical ramp type. Using a numerical inverse Laplace transform, full time domain solutions for the fundamental fields are obtained numerically according to the Riemann-sum approximation approach. The graphical representations illustrate and discuss the outcomes of the main physical fields.

The impact of fractional derivative on thermomechanical interactions in two-dimensional skin tissues throughout hyperthermia treatment

This work aims to study the influence of fractional derivatives and thermal relaxation time on two-dimensional biological tissues using an eigenvalue-based approach. Understanding the heat transfer mechanism and its thermomechanical interactions with the skin tissue of patients is crucial for the successful implementation of thermal treatment procedure. The study employs Laplace and Fourier transforms, and the resulting formulations are applied to human tissues undergoing regional hyperthermia treatment for tumor therapy. The numerical inversion process for Laplace and Fourier transformations utilizes the Stehfest numerical inverse method. The results demonstrate that thermal relaxation time and fractional order parameter significantly influence all analyzed distributions. The numerical findings suggest that thermo-mechanical waves propagate through the skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.

Generalized thermomechanical interaction in two-dimensional skin tissue using eigenvalues approach

The aim of this work is to analytically study the thermo-mechanical response of two-dimensional skin tissues when subjected to instantaneous heating. A complete understanding of the heat transfer process and the associated thermal and mechanical effects on the patient's skin tissues is critical to ensuring the effective applications of thermal therapy techniques and procedures. The surface boundary of the half-space undergoes a heat flux characterized by an exponentially decaying pulse, while maintaining a condition of zero traction. The utilization of Laplace and Fourier transformations is employed, and the resulting formulations are then applied to human tissues undergoing regional hyperthermia treatment for cancer therapy. To perform the inversion process for Laplace and Fourier transforms, a numerical programming method based on Stehfest numerical inverse method is employed. The findings demonstrate that blood perfusion rate and thermal relaxation time significantly influence all the analyzed distributions. Numerical findings suggest that thermo-mechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.

The influence of the mechanical damage on a viscothermoelastic nanobeam due to ramp-type heating under Green-Naghdi theory type-II

The main object of this work is to analyze viscothermoelastic homogeneous and isotropic nanobeams under the effect of mechanical damage. A Green-Naghdi type-II model of thermoelasticity has been constructed under simply supported conditions. Moreover, the Laplace transforms have been applied for the governing differential equations. Tzou iteration method with approximation has been applied to calculate the Laplace inverse transforms. The numerical results are presented and validated for use in a viscothermoelastic rectangular nanobeam of silicon nitride when it has been thermally loaded by ramp-type heating and simple support. The numerical results have been demonstrated in different figures to stand on the effects of the mechanical damage variable, mechanical relaxation times parameters, and ramp-time heat parameter on all the studied functions. We conclude that the effect of the mechanical damage variable, ramp-time heating parameter, and mechanical relaxation times parameters are highly influential on all the studied functions and thermomechanical waves.

Refined Green–Lindsay Model for the Response of Skin Tissue under a Ramp-Type Heating

Based on Green–Lindsay generalized thermoelasticity theory, this paper presents a new refined higher-order time-derivative thermoelasticity model. Thinner one-dimensional skin tissue is considered when its inner surface is free of traction and does not show any temperature increase. The skin tissue’s bounding surface has been heated by ramp-type heating. The classical thermoelastic theories are obtained from the present general formula. The governing equations of the present model are obtained. To move the system into a space state, the Laplace transform is used. The inverse of the Laplace transform is also used with Tzuo’s method to solve the problem. As a result, the field quantities are obtained numerically, and the results of the current model are graphically represented with a comparison to two different theories of thermoelasticity. The effects of various parameters on thermomechanical waves through the skin tissue are analyzed. The theory notes a vibrational behavior in heat transfer and a different effect on the parameters discussed in this article.

Photo-Thermoelasticity Heat Transfer Modeling with Fractional Differential Actuators for Stimulated Nano-Semiconductor Media

The term “optical thermoelasticity” is used to describe how the optical properties of a material change when it is heated or deformed mechanically. The issues of effective elastic and heat transfer symmetry are given particular focus. This study gives a new nonlocal theoretical formulation for a thermo-optical elastic material that can be used to describe how thermomechanical waves and plasma waves relate to the symmetry of semiconductor materials such as silicon or germanium. The suggested model includes the idea of nonlocal elasticity and a modified Moore–Gibson–Thompson (MGT) heat conduction equation with nonsingular fractional derivative operators. The heat transfer equation has been converted and generalized into a nonsingular fractional form based on the concepts of Atangana and Baleanu (AB) using the Mittag–Leffler kernel. The developed model is used to examine the effect of thermal loading by ramp-type heating on a free plane of unbounded semiconductor material symmetries. Using the Laplace transform approach, we may analytically obtain linear solutions for the investigated thermo-photo-elastic fields, such as temperature. The Discussion section includes a set of graphs that were generated using Mathematica to evaluate the impact of the essential parameters.

Response of excited microelongated non-local semiconductor layer thermomechanical waves to photothermal transport processes

Response of excited microelongated non-local semiconductor layer thermomechanical waves to photothermal transport processes

Thermo-mechanical waves of excited microelongated semiconductor layer during photothermal transport processes

The governing equations for microelongated semiconductors are provided using a unique mathematical-physical approach. When the microelongated elastic semiconductor medium is energized, the model is investigated following the photo-generated transport processes. When microelongation is taken into consideration, the primary governing equations show the interplay between elastic, thermal, and plasma waves. The generalized photo-thermoelasticity hypothesis is taken into account in this context. The harmonic wave method has been used to translate the dimensionless formulas for temperature, carrier density, displacement, stresses, and microelongation distributions. The general solutions of the principal distributions are derived during the electronic and thermoelastic deformation processes in two dimensions (2D). The application of some thermal-mechanical stresses as well as plasma conditions occurs when the semiconductor medium is homogeneous, linear, and isotropic. A numerical simulation using the semiconductor material silicon (Si) is done to demonstrate the findings. Graphical representations of the variations in the wave propagations of the principal physical fields have been made.

Hyperbolic two-temperature generalized thermoelastic infinite medium with cylindrical cavity subjected to the non-Gaussian laser beam

The present work is devoted to a study of the induced temperature and stress fields in an elastic infinite medium with a cylindrical cavity under the purview of hyperbolic two-temperature thermoelasticity. The medium is an isotropic homogeneous thermoelastic material. The bounding plane surface of the cavity is loaded thermally by a non-Gaussian laser beam with a pulse duration of two ps. An exact solution to the problem is obtained in the Laplace transform space and the inversions of the Laplace transform have been carried out numerically. The derived expressions are computed numerically for copper and the results are presented in graphical form. The two-temperature parameter has significant effects on all the studied functions and plays a vital role in the speed propagation of the thermomechanical waves.

Response of thermo-mechanical waves of an excited microelongated semiconductor layer according to photothermal transport processes

A novel mathematical-physical governing equations of microelongated semiconductor are presented. According to the photo-generated transport processes the model is studied when the microelongated elastic semiconductor medium is excited. The main governing equations display the interaction between elastic-thermal-plasma waves when the microelongation is taken into account. In this context, the generalized photo-thermoelasticity theory is considered. The dimensionless expressions for temperature, carrier density, displacement, stresses and microelongation distributions have been converted using the harmonic wave technique. During the electronic and thermoelastic deformation processes in two-dimensional (2D) the general solutions of the main distributions are obtained. Some thermal-mechanical loads and plasma conditions are applied when the semiconductor medium is isotropic, homogeneous, and linear. In order to display the obtained results, a numerical simulation for silicon (Si) as semiconductor material is carried out. The variations of the wave propagations of main physical fields have been depicted graphically.

Moore-Gibson-Thompson theory of a non-local excited semiconductor medium with stability studies

The present study introduces a theoretical framework according to the Moore-Gibson-Thompson (MGT) Model in the context of generalized thermoelasticity theory. The excited semiconductor material is utilized to formulate the governing equations in one dimensional (1D) with a non-local parameter. According to the photo- thermoelasticity theory, the overlapping between the electronic (optical) deformation and elastic deformation is taken into account. During the photo-excitation processes, the non-local equation of motion and the heat equation is introduced according to the model of Moore-Gibson-Thompson (MGT). The novel model describes the interaction between plasma and thermomechanical waves in a non-dimensional form. Laplace transform for time variable is applied to convert the governing equations into system of ordinary differential equations. The vector-matrix differential equation with the eigenvalues approach method is employed to obtain the solutions of the physical quantities analytically. Laplace transform invers numerically is utilized when some boundary conditions are applied at the semiconductor free surface to obtain the complete general of the main physical quantities. The numerical computations for the input parameters of Silicon as semiconductor material are used to illustrate the obtained results graphically and discussed.

Power law modeling of functionally graded Adomian’s decomposition method for thermoelastic materials in heat transfer and thermal stress analysis

This work deals with applying the iteration method for the numerical solutions of a one-dimensional thermoelastic material. The governing equations have been constructed in the context of generalized thermoelasticity with one relaxation time model of Lord and Shulman (L-S). Some properties have been considered functional graded based on power law, and the lattice design parameter has been assumed. Adomian's decomposition method (ADM) and iteration techniques have been applied to solve the governing differential equations with an algorithm method. The numerical results have been represented in figures. The numerical results affirm that Adomian's decomposition method is a successful iteration method for solving and modeling thermoelastic problems. The lattice design parameter, empirical parameter, and ratio of the material properties significantly impact the temperature increment, strain, stress, displacement distributions, where they play vital roles in transferring the thermo-mechanical waves through the thermoelastic materials.

Thermomechanical Waves in the Elastic Lithosphere–Viscous Asthenosphere System

Thermomechanical Waves in the Elastic Lithosphere–Viscous Asthenosphere System

Diagonalization Method to Hyperbolic Two-Temperature Generalized Thermoelastic Solid Sphere under Mechanical Damage Effect

This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage. The fundamental equations were derived using the hyperbolic two-temperature generalized thermoelasticity theory with mechanical damage taken into account. The outer surface of the sphere has been assumed to have been shocked thermally without cubical dilatation. The numerical results for the dynamical and conductive temperatures increment, strain, displacement, and average of the principal stresses components have been represented graphically with different values of the hyperbolic two-temperature parameter and mechanical damage parameters. The two-temperature model parameter and the mechanical damage parameter have significant effects. The propagations of the thermomechanical waves take place at finite speeds in the context of the hyperbolic two-temperature theory as well as in the usual context of the Lord–Shulman theory with one-temperature.