Theory Of Thermoviscoelasticity Research Articles

A second gradient theory of thermoviscoelasticity

This paper is concerned with a rate-type theory of thermoviscoelasticity in which the second gradient of the displacement and the second temperature gradient are added to the classical set of independent constitutive variables. Viscoelasticity and related phenomena are of great importance in the study of biological materials. An adequate modeling of rubber-like materials and of biological soft tissues requires the use of the theory of viscoelasticity. Introduction of the concept of thermal displacement and the theory of multipolar continua allows us to show that Green-Naghdi thermomechanics can be used to derive a second gradient theory. The basic equations of the theory are established and the boundary conditions associated to nonsimple materials are investigated. The stress tensor and hyperstress tensor are shown to depend on the first and second temperature gradients. For rigid heat conductors we find that the temperature satisfies a fourth order equation. The boundary-initial-value problems are formulated. A uniqueness result in the dynamic theory of thermoviscoelastic materials is presented. We establish an existence result and prove the analyticity of the solutions. As a consequence, the exponential decay of the solutions and their impossibility of localization are obtained.

On the coupled linear theory of thermoviscoelasticity of porous materials

On the coupled linear theory of thermoviscoelasticity of porous materials

Effect of shell-induced stresses on the magnetic properties of Fe-based glass-coated microwires: Accounting of initial technical parameters

The study focuses on examining the impact of shell-induced stresses on the magnetic characteristics of Fe-based microwires encased in glass, with particular attention given to the critical fabrication parameters employed in the microwire production process utilizing the Taylor-Ulitovsky method. We systematically investigate how internal stresses affect magnetization reversal behaviors in both glass-coated and uncoated Fe77.5Si7.5B15 microwires through experimental analysis and compare these effects with those resulting from stress-annealing procedures. The simulation of stress distribution caused by the solidification process is based on thermo viscoelasticity theory considering a non-constant glass transition temperature. The analysis also includes the knowledge of the initial parameters of the microwires during the manufacturing.

The vibration of a nanobeam under generalized thermoviscoelasticity theory based on thermomass motion subjected to ramp-type heat

The vibration of a nanobeam under generalized thermoviscoelasticity theory based on thermomass motion subjected to ramp-type heat

Numerical Simulation of Sintering of DLP Printed Alumina Ceramics

Digital Light Processing (DLP) technology exhibits the capability of producing components with complex structures for a variety of technical applications. Postprocessing of additively printed ceramic components has been shown to be an important step in determining the final product resolution and mechanical qualities, particularly with regard to distortions and resultant density. The goal of this research is to study the sintering process parameters to create a nearly fully dense, defect-free, ceramic component. A high-solid-loading alumina slurry with suitable rheological and photopolymerisable characteristics for DLP was created. TGA/DSC analysis was used to estimate thermal debinding parameters. The sintering process of the debound parts was studied by employing a numerical model based on thermo-viscoelasticity theory to describe the sintering process. The validated Finite Element Modelling (FEM) code was capable of predicting shrinkage and relative density changes during the sintering cycle, as well as providing meaningful information on the final shape. Archimedes’ principle and scanning electron microscope (SEM) were used to characterise the sintered parts and validate the numerical model. Samples with high relative density (>98.5%) were produced and numerical data showed close matches for predicted shrinkages and relative densities, with less than 2% mismatch between experimental results and simulations. The current model may allow to effectively predict the properties of alumina ceramics produced via DLP and tailor them for specific applications.

Thermoviscoelastic dynamics of composite thin-walled booms on spacecrafts subjected to solar radiation

Viscoelastic behavior of polymer-matrix composites depends very strongly on temperature. This paper presents a thermoviscoelastic dynamics modelling for fiber-reinforced polymeric composite structures with time-varying and nonuniform temperature field. It is used to investigate the thermally induced vibrations of spacecraft booms, for which a new anisotropic thin-walled beam model based on the generalized beam theory is also proposed. Furthermore, efficient evaluation of the thermoviscoelastic constitutive equations in hereditary integral form is performed by means of the derived recursion formula. A harmonic balance procedure in the circumferential direction of tubular booms is devised for both thermal and structural analyses. By comparing the results of viscoelastic and elastic models, the influence of thermoviscoelastic effects on dynamical responses of composite booms under thermal shock is illustrated. The results show that viscoelasticity may play a significant role in vibration suppression of on-orbit flexible structures, especially at high temperature. The work not only provides a novel model for thermal-structural dynamic analysis, but also develops thermoviscoelasticity theory oriented toward engineering and numerical applications.

State-space approach to nonlocal thermo-viscoelastic piezoelectric materials with fractional dual-phase lag heat transfer

Purpose The purpose of this study is to develop a comprehensive size-dependent piezoelectric thermo-viscoelastic coupling model that accounts for two fundamentally distinct size-dependent models that govern fractional dual-phase lag heat transfer and viscoelastic deformation, respectively. Design/methodology/approach The fractional calculus has recently been shown to capture precisely the experimental effects of viscoelastic materials. The governing equations are combined into a unified system, from which certain theorems results on linear coupled and generalized theories of thermo-viscoelasticity may be easily established. Laplace transforms and state–space approach will be used to determine the generic solution when any set of boundary conditions exists. The derived formulation is used to two concrete different problems for a piezoelectric rod. The numerical technique for inverting the transfer functions is used to generate observable numerical results. Findings Some analogies of impacts of nonlocal thermal conduction, nonlocal elasticity and DPL parameters as well as fractional order on thermal spreads and thermo-viscoelastic response are illustrated in the figures. Originality/value The results in all figures indicate that the nonlocal thermal and viscoelastic parameters have a considerable influence on all field values. This discovery might help with the design and analysis of thermal-mechanical aspects of nanoscale devices.

Structural dynamic responses of layer-by-layer viscoelastic sandwich nanocomposites subjected to time-varying symmetric thermal shock loadings based on nonlocal thermo-viscoelasticity theory

Structural dynamic responses of layer-by-layer viscoelastic sandwich nanocomposites subjected to time-varying symmetric thermal shock loadings based on nonlocal thermo-viscoelasticity theory

A modified fractional order thermo-viscoelastic theory with fractional order strain and its application in a thermo-viscoelastic problem containing a spherical cavity

A modified fractional order thermo-viscoelastic theory with fractional order strain and its application in a thermo-viscoelastic problem containing a spherical cavity

Thermo-mechanical memory responses in a thick tumorous skin tissue during hyperthermia treatment

In this work, we will present a model that is useful in treating skin tumors of severe thickness by local hyperthermia. The generalized thermo-viscoelasticity theory with memory-dependent derivative (MDD) is used to investigate the transfer of bioheat and heat-induced response in a thick plate of skin tissue with rheological properties. Laplace and Fourier transformations as well as the state space approach are used. The resulting formulation is applied to the surface of a thick tumorous skin tissue with finite thickness subjected to regional hyperthermia therapy for cancer treatment. The inversion process for Fourier and Laplace transforms is carried out using a numerical method based on Fourier series expansions. Comparisons are made with the results anticipated through the coupled and generalized theories.

Analytical study of two-dimensional thermo-mechanical responses of viscoelastic skin tissue with temperature-dependent thermal conductivity and rheological properties

The generalized thermo-viscoelastic theory without energy dissipation is used in this work to investigate the transfer of bioheat and the mechanical heat-induced response in a human skin plane tissue with variable thermal and rheological properties. Integral transformations are used for Laplace and Fourier. In the scheme of two-dimensional equations, the exponential matrix procedure, which forms the basis of the state-space approach of modern control theory, is applied. The resulting formulation is applied to a thermal shock half-space problem. The inversion process for Fourier and Laplace transforms is carried out using a numerical method based on Fourier series expansions. Comparisons between computational measurements and Penne’s experimental verification indicate that the Green–Naghdi (II) bioheat mathematical model is an effective method for estimating the transition of bioheat to viscoelastic skin tissue. The influences of variable thermal conductivity and volume materials properties on all fields are examined.

Fractional order thermo-viscoelastic theory of biological tissue with dual phase lag heat conduction model

Viscoelasticity is an inherent property of the biological tissue and is often used as a diagnosis parameter in characterizing cancer. Recently, it has been found that fractional calculus agrees well with experimental results when describing the viscoelastic materials. In this study, the fractional linear thermo-viscoelastic theory is developed with considering the fractional relaxation effect of dual phase lag heat conduction model and viscoelastic constitutive relation simultaneously. The transient coupling thermal and mechanical behavior of biological tissue are investigated. The governing equations are solved by Laplace transformation. The effects of fractional parameter on the distributions of temperature, displacement and stress are obtained and illustrated graphically.

АБЕЗПЕЧЕННЯ ДОВГОВІЧНОСТІ АСФАЛЬТОБЕТОННОГО ПОКРИТТЯ НА ЖОРСТКІЙ ОСНОВІ АВТОМОБІЛЬНИХ ДОРОГАХ

The article is devoted to the development of practical methods to ensure the durability of asphalt pavement on a rigid basis of roads. The goal of the work. Practical methods of ensuring the durability of asphalt pavement on a rigid basis of roads are proposed. The object of research is asphalt-concrete pavement on a hard base of highways. Research method: analytical-experimental using the provisions of the theory of elasticity and thermo-viscoelasticity and experimental methods of research of track formation in asphalt concrete pavement on a rigid basis; mathematical statistics; statistical analysis of scientific publications, technical and normative literature. The article presents the features of the design of grain warehouses of asphalt mixtures, namely: The proposed features of the design of grain warehouses of asphalt concrete, taking into account the rate of resistance to track formation; Requirements for designing the grain composition of asphalt concrete of high resistance to track formation with optimization in terms of estimated service life are proposed. The conducted researches allowed to develop a method of estimating the homogeneity from the time of transportation of the asphalt concrete mixture in the car body to the object according to the resistance of asphalt concrete to the formation of the track. Requirements for checking the flow rate in the crushed-mastic asphalt-concrete mixture due to the terms of its storage and transportation have been developed, which avoids segregation of the coating. The criterion of strength of asphalt concrete pavement on a rigid basis of the highway is improved due to the consideration of different time of action of tensile load at bending that will allow to design more precisely a covering of the increased durability. The technique of the minimum admissible temperature of consolidation of asphalt concrete mix at the device of a covering on a rigid basis of highways that will allow to provide durability of a covering is offered for practical application. KEY WORDS: ASPHALT CONCRETE, TRACK RESISTANCE, GRAIN COMPOSITION DESIGN, TEMPERATURE, TRANSPORTATION, SEALING

Fractional thermo-viscoelasticity theory with and without energy dissipation

In the present paper, a new fractional model of fractional order thermo-viscoelasticity theory with and without energy dissipation is constructed. Some basic theorems can easily obtain in both theories. A three-dimensional model of fractional thermo-viscoelasticity is established. The model is applied to a specific problem of a half space subjected to harmonic heating and traction free surface. The reverses of Fourier transforms and Laplace processes are obtained numerically. Numerical results are given and illustrated graphically for temperature, displacement, and stress distributions. A comparison of coupled and generalized thermo-viscoelasticity theories are made.

Generalized thermo-viscoelasticity with memory-dependent derivative: uniqueness and reciprocity

This article theoretically demonstrates the reciprocity and uniqueness theorems for generalized theory of thermo-viscoelasticity involving memory-dependent derivative (MDD). To prove the theorems, a thermo-viscoelastic initial-boundary value problem under the domain of three-phase-lag (TPL) model is taken into consideration for an isotropic, homogeneous medium. The theorems are proved with the help of the Laplace transform of the thermophysical quantities. Finally, a few special cases in the generalized theory of thermo-elasticity and thermo-viscoelasticity with MDD and without MDD are derived from the present model.

The effects of thermal and mechanical material properties on tumorous tissue during hyperthermia treatment.

Although there have been numerous reports in several articles about the viscoelastic properties of biological tissues, no effort has been made to investigate the combined thermal and mechanical behavior of the viscoelastic tissue. At present, the model of thermo-viscoelasticity theory with variable thermal conductivity and rheological properties of the volume is considered to investigate bio-thermo-mechanics behavior in living tissue within the context of the Lord-Shulman theory. The model is applied to a limited thickness, cancerous layer problem. The problem was solved analytically in the transformed domain using Laplace transform as a tool. The exact solution is obtained in the context of transformation Laplace. Numerical results are given and illustrated graphically for the distributions of temperature, displacement, and stress. Some correlations are produced with the results obtained for the absence of the thermal relaxation parameter. The effects of variable thermal and volume materials properties, blood perfusion rate on the behavior of various fields are examined.

Fractional thermo-viscoelastic response of biological tissue with variable thermal material properties

In this study, the fractional model of thermo-viscoelasticity theory with variable thermal conductivity and rheological properties of the volume is considered to investigate bio-thermo-mechanics behavior in living tissue. The model is applied to a problem of cancerous layer with arbitrary thickness and its outer surface traction free. The bounding plane of the cancerous tissue is subjected to two different types of thermal loading; a non-Gaussian laser beam and harmonic heating. The problem is solved analytically by Kirchhoff and Laplace transformation. The exact solution in Laplace’s transform domain is obtained. Numerical results for the temperature, displacement, and stress distributions are given and illustrated graphically. The effects of time-fractional parameter and materials properties on the behavior of various fields are examined.

Nonlinear thermomechanical vibration mitigation analysis in rotating fractional-order viscoelastic bidirectional FG annular disks under nonuniform shocks

The current article is concerned with the investigation of the formation of the time-dependent three-dimensional distributions and redistributions of the stress and displacement fields of the rotating annular and circular plates/disks under the nonuniform distributions of the dynamic thermomechanical loads or shocks. Redistribution of the stress and displacement fields happens due to the Gerasimov-Caputo-type relaxation kernel of the fractional viscoelastic model of the material in addition to the dynamic nature of the loading. All the mechanical and thermal material properties of the plate or disk may be tailored in both radial and transverse directions. The 3D thermoviscoelasticity theory is employed to develop the governing equations of motion (3D vibration) and heat transfer. Different thermal and mechanical boundary conditions are implemented. The resulting nonlinear time-dependent fractional-order thermoviscoelastic integro-differential equations are solved by proposing and implementing a special procedure that uses numerical evaluation of the singular-kernel Caputo-integral and second-order forward, backward, and central discretization of the spatial and time domains. Eventually, the influences of the bidirectional distribution of the material properties, 2D temperature distribution, fractional order and parameters of the viscoelasticity model, and thermomechanical boundary conditions are investigated on the distributions of the displacement and stress components rigorously and accompanied by 3D demonstrations.

Transient thermomechanical responses of multilayered viscoelastic composite structure with non-idealized interfacial conditions in the context of generalized thermoviscoelasticity theory with time-fractional order strain

Nowadays, a multilayered viscoelastic composite structure stands as one of the most representative active/passive vibration isolator and high-efficient damper to avoid unwanted vibrations in civil and ocean engineering, which is commonly applied in harsh non-uniform temperature environment (e.g., high heat-flux, drastic changes of temperature, etc.). In such a case, thermoviscoelastic response analysis is of great importance for the safety design of viscoelastic composites, and so a thorough and comprehensive study on this issue is imperatively needed. This work aims to conduct an analytical study of transient thermomechanical responses of multilayered viscoelastic composite structure under time-dependent heating loads. In the context of generalized thermoviscoelasticity theory with time-fractional order strain, a composite laminated viscoelastic plate is chosen as the analytical model while governing equations of each homogeneous layer accounting for non-idealized interfacial conditions are systematically formulated. Then, a semi-analytical approach via Laplace transform is adopted to deal with the problem. The effects of fractional order parameters and material constants’ ratio on the structural dynamic responses are fully discussed to provide new insights and basic guidelines for vibration control and thermal management of viscoelastic composites, especially for the surface coating at the interface between any two adjacent viscoelastic layers.

3D nonlinear variable strain-rate-dependent-order fractional thermoviscoelastic dynamic stress investigation and vibration of thick transversely graded rotating annular plates/discs

In the present article, the idea of using the variable-order fractional-derivative thermoviscoelastic constitutive laws in dynamic stress and vibration analysis of the engineering structures, the required implementation backgrounds, and the relevant numerical solution procedures are investigated for the first time. In this regard, dynamic 3D stress and displacement fields and radial/transverse vibrations of transversely graded viscoelastic spinning thick plates/discs exposed to sudden thermoelastic loads are investigated. Instead of using the approximate plate theories, the exact thermoviscoelasticity theory is employed in the development of the governing equations. Since the variable fractional order is dependent on the localized deformation rates, the resulting thermoviscoelastic integro-differential equations are nonlinear. These equations are solved by utilizing a combination of the second-order backward/central/forward finite difference discretization of the spatial and time domains, numerical evaluation and updating of the Caputo-type fractional derivatives, updating the growing number of terms of the governing equations, and Picard's iterations. Various edge conditions are considered. Finally, comprehensive sensitivity analyses and various 3D plots are presented and discussed regarding the effects of the variable fractional order of the constitutive law, time variations of the nonuniformly distributed transverse loads, and edge conditions on the distributions and damping of the resulting displacement and stress components.