Thermoviscoelastic Response Research Articles

A PROBLEM IN FRACTIONAL ORDER THERMO-VISCOELASTICITY THEORY FOR A POLYMER MICRO-ROD WITH AND WITHOUT ENERGY DISSIPATION

A new study has been developed that considers the size-dependent interaction between viscoelastic deformation and thermal fields, incorporating the fractional heat conduction law with and without energy dissipation. The model is used for a particular one-dimensional problem involving a polymer micro-rod of arbitrary length experiencing three different types of thermal loading without the presence of any heat source. The study uses Laplace transforms and numerical inversion to examine how fractional order, nonlocal elasticity, and nonlocal thermal conduction impact thermal dispersion and thermo-viscoelastic response. Comparative numbers demonstrate the effects of various parameters. Findings demonstrate that nonlocal thermal and viscoelastic characteristics have a significant impact on all recorded field values, offering possible suggestions for the creation and assessment of thermal-mechanical attributes in nanoscale devices.

Micro/nano-scale transient thermo-viscoelastic responses for 1D temperature-dependent polymer-based rod heated by the ultra-short pulse laser based on nonlocal single-phase-lag heat conduction and Eringen’s differential elasticity

Micro/nano-scale transient thermo-mechanical responses are significantly important with rapid development and applications of ultra-short pulse in micro-machining of viscoelastic structure. This work aims to establish non-Fourier thermo-viscoelastic model based on nonlocal single-phase-lag heat conduction and Eringen’s differential elasticity. The developed model is applied to study thermo-viscoelastic responses for 1D temperature-dependent polymer-based rods subjected to non-Gaussian laser pulse excitation by Kirchhoff and Laplace transformation techniques. The results reveal that the parameters of the deformation, pulse laser, and nonlocal single-phase-lag heat conduction remarkably affect the wave propagations and thermo-viscoelastic response at micro/nano-scale nanoscale.

Thermoviscoelastic response of skin tissue via fractional Pennes bioheat and fractional viscoelasticity

In this paper, the thermoviscoelastic response of skin tissue, as a typical class of viscoelastic biological tissue, subject to thermal shock is studied based on the fractional Kelvin-Voigt model and fractional Pennes bioheat conduction. A time-fractional biothermoviscoelastic governing equation is derived and initial-boundary value conditions are given for monolayer skin tissue of finite thickness. The temperature change and thermal stress of viscoelastic skin tissue are obtained by the Laplace transform and its inversion using matlab software. The influences of viscosity coefficient, relaxation times, fractional-order viscosity/heat parameter, and blood perfusion rate of skin tissue on the temperature distribution and the elastic displacement are analyzed. The numerical results show that fractional-order viscosity does not affect temperature, whereas fractional-order heat flow does. Moreover, fractional-order heat flow affects the sensitivity of blood perfusion rate to the thermodynamic response.

Electromagnetic thermo-viscoelastic response of piezoelectric rods considering memory dependent effects

Based on the theory of nonlocal elasticity and nonlocal heat conduction, a new dual-phase-lag heat conduction model with memory dependent effect is proposed in this article to explore the thermodynamic behavior of functionally graded rotating piezoelectric rods under the action of moving heat sources. Assuming that the material properties of functionally graded piezoelectric rods vary exponentially along the length direction, the end of the rod is rigid and fixed without voltage. Use Laplace transform to transform the problem into the spatial domain and perform analytical solutions, then use inverse Laplace transform to obtain the time-domain solution. Numerical solutions were performed for dimensionless displacement, temperature, electric potential, and stress, and the variation patterns of the physical quantities involved were described in graphical form. The calculation provides the effects of functional gradient non-uniformity index, thermal nonlocal parameters, kernel function, and viscoelastic parameters on the physical quantities involved.

Modified bond-based peridynamic approach for modeling the thermoviscoelastic response of bimaterials with viscoelastic–elastic interface

Modified bond-based peridynamic approach for modeling the thermoviscoelastic response of bimaterials with viscoelastic–elastic interface

Three-Dimensional Thermoelasticity Analysis of Viscoelastic FGM Plate Embedded in Piezoelectric Layers under Thermal Load

Due to the high importance of viscoelastic materials in modern industrial applications, besides the intensive popularity of piezoelectric smart structures, analyzing their thermoelastic response in extreme temperature conditions inevitably becomes very important. Accordingly, this research explores the thermoviscoelastic response of sandwich plates made of a functionally-graded Boltzmann viscoelastic core and two surrounding piezoelectric face-layers subjected to electrothermal load in the platform of three-dimensional elasticity theory. The relaxation modulus of the FG viscoelastic layer across the thickness follows the power law model. the plate’s governing equations are expressed in the Laplace domain to handle mathematical complications corresponding to the sandwich plate with a viscoelastic core. Then, the state-space method, combined with Fourier expansion, is utilized to extract the plate response precisely. Finally, the obtained solution is converted to the time domain using the inverse Laplace technique. Verification of the present formulation is compared with those reported in the published papers. Finally, the influences of plate dimension, temperature gradient, and relaxation time constant on the bending response of the above-mentioned sandwich plate are examined. As an interesting finding, it is revealed that increasing the length-to-thickness ratio leads to a decrease in deflections and an increase in stresses.

Mean-field descriptions for the viscoelastic response of thermorheologically complex reinforced solids

Mean-field descriptions for the thermo-viscoelastic response of reinforced solids undergoing small deformations but large temperature changes are presented. The descriptions follow from an approximate homogenization scheme that identifies macroscopic internal variables with low-order statistics of the microscopic internal variable fields as a result of a variational model reduction. Unlike descriptions based on the correspondence principle, these descriptions can account for thermorheologically complex constitutive laws with multiple internal times and/or temperature-dependent stiffnesses, and can provide information not only on the macroscopic response but also on the statistics of the microscopic mechanical fields; it is further demonstrated that the descriptions can even accommodate a special class of hereditary laws often employed for polymeric materials. Simple expressions for material systems with elastically rigid but thermally dilatant reinforcements are provided. By way of example, reduced descriptions are presented for a special class of material systems for which the thermomechanical response can be computed exactly by means of the correspondence principle. In the case of isotropic particle-reinforced solids under hydrostatic loadings, the reduced descriptions can reproduce the exact response identically; in the case of transversely isotropic fiber-reinforced solids subject to monotonic coolings, the reduced and exact descriptions provide indistinguishable macroscopic strains and stresses for the entire range of temperature drops and cooling rates considered.

Nonlocal dual-phase-lag thermoviscoelastic response of a polymer microbeam incorporating modified couple stress and fractional viscoelastic theories

Ultra-slow relaxation process of polymers has the memory-dependent feature, integer-order thermoviscoelastic models may fail to describe the dynamic behaviors of viscoelastic structures accurately. Additionally, it is noticed that the small-scale effect of elastic deformation and heat conduction in a non-isothermal temperature environment is becoming significant due to the development of micro-devices. To better capture the memory-dependent effect and the small-scale effect of viscoelastic micro-structures in heat transfer environment, as a first attempt, present work focuses on developing a refined fractional Kelvin-Voigt thermoviscoelastic model by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). Then, the model is applied to investigating the transient response of a polymer microbeam subjected to a harmonic thermal loading. The governing equations involving the modified parameters are formulated and then solved by Laplace transform method. Some parametric results are demonstrated to display the impacts of the nonlocal thermal parameter, the material length-scale parameter and the fractional-order parameter on the considered physical quantities. The results show that the small-scale effect and the memory-dependent effects strongly depend on the polymer micro-structure characteristics in thermal environment.

Modeling nonequilibrium thermoviscoelastic material behaviors of glass in nonisothermal glass molding

AbstractNonisothermal glass molding (NGM) is developed aiming to satisfy the fabrication of complex and precision optical elements at high production volumes. The technology, however, was encountered by the high form deviation of manufactured glass optics. During the nonisothermal compression molding, glass undergoes a rapid temperature change making it a transition from equilibrium to nonequilibrium nature of matter. Owing to this characteristic, viscoelastic material behaviors of glass depend on not only temperature but also thermal history. Understanding the nature of nonequilibrium thermoviscoelasticity, the central importance to control the final shape and optical characteristics of the manufactured glass optics is the focus of this research. First, this study presents preliminary experimental investigations indicating the difference in viscoelastic deformation responses under the equilibrated and nonequilibrated glass specimens. In the following, modeling the temperature‐dependent viscoelasticity over a wide temperature range in glass transition region is described, where temperature is directly coupled in each parameter of a rheological constitutive model. This concept allows us to bypass the thermorheologically simple assumption used to tolerate the description of thermoviscoelastic responses in most of the earlier works. Finally, we propose a modeling method that incorporates temperature and thermal history into the rheological model parameters, each of which is described by employing the Mauro–Allan–Potuzak viscosity equation. Viscoelastic experiments were carried out to validate the model. The results show that the time‐dependent responses varying with temperature are well predicted in both equilibrium and nonequilibrium regimes of glass‐forming systems. The benefit of this research is that a unique material model is entirely applicable for numerical studies of various hot forming processes such as annealing when glass undergoes pure thermal loads, as well as precision glass molding and NGM when glass is deformed by fully coupled thermal–mechanical loads under either its equilibrium or nonequilibrium state of materials, respectively.

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.

Size-dependent generalized thermo-viscoelastic response analysis of multi-layered viscoelastic laminated nanocomposite account for imperfect interfacial conditions

Multi-layered viscoelastic laminated nanocomposites have been widely used as a kind of representative active/passive vibration isolator and high-efficient damper in the practical applications of nanoengineering, due to their high energy dissipation, wide damping band and lower cost, and such composite structures often serve in a non-isothermal environment. In this work, an analytical study is conducted to investigate the size-dependent generalized thermoviscoelastic responses of multi-layered viscoelastic laminated nanocomposites. Governing equations of each homogeneous viscoelastic layer, accounting for imperfect interfacial conditions, are formulated in the context of the size-dependent generalized thermo-viscoelasticity model. Solutions accounting for non-idealized interfacial and proper boundary conditions are first presented to characterize the thermomechanical coupling of multi-layered viscoelastic laminated nanocomposites. Transient results of temperature, displacement and stresses in time domain can be achieved via Laplace inversion. Then the transient solutions obtained are applied to a one-dimensional bi-layered medium. It is found that properly selecting the nonlocal parameter and viscoelastic material constants ratios can maximally improve the heat isolation and avoid the larger harmful thermal stresses, especially at surface coating of the nanocomposites. The strategy adopted in this work is expected to be beneficial to thermal management and vibration control in nanoengineering.

Magnetothermoelastic vibrations on a viscoelastic microbeam subjected to a laser heat source

The linear theory of viscoelasticity remains an important field of research like most solids and polymer materials when exposed to a vicious dynamic loading effect. This article introduces a new model for describing the behavior of thermoviscoelastic microbeams considering the effects of temperature change and the longitudinal magnetic field. The governing equations in this model are derived based on the Euler–Bernoulli beam theory, Kelvin–Voigt model of viscosity, the generalized thermoelasticity, and the classical Maxwell equations. The two ends of the microbeam are clamped and subjected to the influence of a laser pulse with a temporal intensity profile. The analytical solutions to the physical fields are evaluated using the Laplace transform and its inversion transforms are performed numerically. The thermo-viscoelastic responses of the microbeam are calculated numerically and investigated graphically. The effect of different parameters such as viscosity, laser intensity, and the magnitude of the magnetic field are studied in detail.

Thermo-Viscoelastic Response of 3D Braided Composites Based on a Novel FsMsFE Method.

A homogenization-based five-step multi-scale finite element (FsMsFE) simulation framework is developed to describe the time-temperature-dependent viscoelastic behavior of 3D braided four-directional composites. The current analysis was performed via three-scale finite element models, the fiber/matrix (microscopic) representative unit cell (RUC) model, the yarn/matrix (mesoscopic) representative unit cell model, and the macroscopic solid model with homogeneous property. Coupling the time-temperature equivalence principle, multi-phase finite element approach, Laplace transformation and Prony series fitting technology, the character of the stress relaxation behaviors at three scales subject to variation in temperature is investigated, and the equivalent time-dependent thermal expansion coefficients (TTEC), the equivalent time-dependent thermal relaxation modulus (TTRM) under micro-scale and meso-scale were predicted. Furthermore, the impacts of temperature, structural parameters and relaxation time on the time-dependent thermo-viscoelastic properties of 3D braided four-directional composites were studied.

Thermoviscoelastic fracture analysis of a cracked orthotropic fiber reinforced composite strip by the dual-phase-lag theory

Fiber-reinforced polymer composites have gained tremendous popularities in various engineering applications due to their superior mechanical performances. This work is devoted to investigating the transient thermomechanical responses of an orthotropic fiber-reinforced strip containing a crack aligned along the fiber direction. The non-Fourier, dual-phase-lag theory is employed to account for the finite time required to complete the process of transporting heat and building local thermal equilibrium in composites, while the Generalized Maxwell viscoelastic model is utilized to characterize the constitutive law of the polymeric matrix and the fibers are treated to be elastic. By using Laplace transform and Fourier transform, the mixed, boundary-value problems are finally reduced to the Cauchy-type singular integral equations, which are solved by the Lobatto-Chebyshev technique numerically. The temperatures and thermal stress intensity factors in the time domain are evaluated through the numerical inversion of Laplace transform. Numerical results are displayed graphically based on graphite fiber reinforced epoxy composite, and detailed comparisons are made to investigate the effects of thermal lags, viscoelastic properties, and fiber volume fractions on the thermoviscoelastic responses.

A unified formulation for thermoviscoelasticity of hollow sphere based on the second sound theories

By proposing the unifier factors, a unified formulation for the generalized coupled thermo-visco-elasticity response of hollow spheres based on the Lord–Shulman, Green–Lindsay, and Green–Naghdi models is developed. Kelvin–Voigt model is used in the current research to consider the viscoelastic response of the sphere. This formulation is used to capture the thermoviscoelastic response of finite isotropic hollow sphere under thermal shock. After transforming the one-dimensional radial equations into the non-dimensional form, finite element method (FEM) based on the Galerkin weak formulation is implemented. The governing equations are discretized through the radial domain utilizing FEM. The determined system of ordinary differential equations is traced using the average acceleration method as a type of Newmark time marching scheme. After validation, novel numerical results are demonstrated to analyze the influences of viscoelastic damping on the response of hollow sphere under rapid surface heating based on various types of generalized theories.

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.

Nonlocal dual-phase-lag heat conduction and the associated nonlocal thermal-viscoelastic analysis

In this paper, the extension of the nonlocal dual-phase-lag (DPL) theory is formulated to account for the heat conduction at nanoscale. Both the temporally and spatially nonlocal effects are considered in heat conduction, which are verified experimentally by the size-dependent thermal conductivity of silicon nanofilms and the transient temperature variation during the femtosecond laser heating of gold films. A generalized uncoupled nonlocal thermoviscoelasticity is hence proposed, which is applied to a one-dimensional analysis of a finite plate under sudden thermal shock. Non-dimensional numerical analyses are performed to illustrate the effects of both nonlocal heat conduction and nonlocal elasticity on thermal propagations and thermoviscoelastic responses.

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.

An analytical study of transient thermo-viscoelastic responses of viscoelastic laminated sandwich composite structure for vibration control

Viscoelastic laminated sandwich composite structure has been used as a new class of high-efficient structural damping in the passive vibration control systems. This work aims to investigate transient thermo-viscoelastic responses of viscoelastic laminated sandwich composite structure. The effects of fractional order parameters and material constants ratio on the structural transient thermo-viscoelastic responses are evaluated and discussed. For each homogeneous isotropic layer, the governing equations are formulated and solved by Laplace transformation techniques. The results are expected to provide new insights on the vibration control and thermal management of viscoelastic laminated sandwich composite structure under extreme non-isothermal conditions.

Thermo-viscoelastic Modeling of Nonequilibrium Material Behavior of Glass in Nonisothermal Glass Molding

Nonisothermal Glass Molding (NGM) has become a viable replicative manufacturing technology for the cost-efficient production of complex precision optical components made of glass. During the pressing stage in NGM, glass materials undergo a huge temperature change in the glass transition range. In this range, glass exhibits thermo-viscoelastic responses, and the temperature drop through the glass transition leads glass structure to depart from an equilibrium to a nonequilibrium state. Thermo-viscoelastic properties of the nonequilibrium glass material greatly depend on temperature and thermal history. This paper presents a phenomenological constitutive model developed for modeling the thermo-viscoelastic responses of nonequilibrium glass. We propose a direct incorporation of the temperature -and thermal history effects into each parameter of the phenomenological model. This novelty allows the model to describe the nonequilibrium phenomena and to study temperature-dependent viscoelasticity of glass without assuming thermo-rheologically simple characteristics. Furthermore, the phenomenological model enables the coupling of structural -and stress relaxation phenomena. The model validation conducted for creep experiments demonstrates an enhancement in numerical predictions of the nonequilibrium material behaviors of glass over wide ranges of temperature and thermal history.