Thermoviscoelastic Materials Research Articles

On the Double Moore–Gibson–Thompson System of Thermoviscoelasticity

ABSTRACTIn this paper, we address the system made by two coupled one‐dimensional Moore–Gibson–Thompson equations arising in the description of thermoviscoelastic materials. Here, while . When both the MGT equations lie in the subcritical regime, that is, we prove that the system generates an exponentially stable solution semigroup. This improves some recent results in the literature, where the exponential stability is attained only within either a stronger condition than subcriticality of both equations, or when and are sufficiently close. The key idea is to deduce the exponential stability from that of a related system, made by two coupled equations of the viscoelasticity type. The latter result has also an independent interest.

Analysis of a dynamic contact problem with long memory

We examine a mathematical framework detailing a dynamic frictional contact involving thermo-viscoelastic materials characterized by long memory and damage. The contact is modeled by the normal compliance condition with Coulomb's friction law, while surface wear is also factored in. The model was in the form of a coupled system which includes an evolution equation written in inclusion form for the frictional contact, parabolic variational inequality for the damage field, nonlinear differential equation for the temperature field and an equation for the wear particles and an evolution. A variational formulation for the model was derived and the existence of the unique weak solution established, under smallness assumptions on a part of the problem data. The proof used various results from the theory of evolution inequalities and repeated fixed-point arguments.

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.

Characterization of relaxation behaviour of CF/PEKK aerospace composites using the time-temperature-crystallinity superposition principle

In this study, the Time-Temperature-Crystallinity Superposition Principle (TTCSP) was applied to determine the viscoelastic behavior of Thermo-rheological Complex Materials (TCM), specifically Carbon fibre/Poly-Ether-Ketone-Ketone (CF/PEKK) composites. The study investigated the effects of various parameters on the viscoelastic behavior of the composites, such as the degree of crystallinity after different melting temperatures, relaxation, and crystallization times. The TTCSP was utilized on the relaxation data to generate great-grand master curves for the degree of crystallinity for different laminate lay-ups. Hot press forming was employed to manufacture samples under different processing conditions, including various melting and cold crystallization temperatures. Differential Scanning Calorimetry (DSC) was employed to calculate the degree of crystallinity of CF/PEKK composites, while the Dynamic Mechanical Analyzer (DMA) was used to obtain the relaxation data. The generated great-grand master curves proved effective in predicting the relaxation behavior of the composites consolidated using single and double hold cycles at different melting temperatures and crystallization times, respectively. The great-grand master curves presented in this study can serve as valuable tool to calibrate key viscoelastic and/or thermo-viscoelastic material models for aerospace-grade CF/PEKK composites. These models are crucial for simulations aimed at predicting residual stresses and process-induced deformations during the thermoforming process.

The influence of an internal variable heat source on the perfect contact of three thermoelastic layers characterized by hereditary features

In this work, we present a two-dimensional problem of thermoelastic and thermo-viscoelastic materials which consists of three thick layers with a finite thickness and infinite extent. These layers are placed in a perfect contact one on top of another. The outer surfaces of the layers are assumed to be thermally isolated and rigidly fixed. There is a disturbed variable heat source filling the middle layer. Continuity conditions between the layers ensure the continuity of the temperature, normal heat flux, displacement, and normal stresses across layers. Laplace and exponential Fourier transforms are used to solve the problem. Inverse transforms are computed numerically to obtain the solution in the physical domain. Graphical results are presented and discussed for all variable fields.

Frictional Contact Problem With Wear for Thermo-Viscoelastic Materials With Damage

We consider a mathematical model which describes a dynamic frictional contact problem for thermo-viscoelastic materials with long memory and damage. The contact is modeled by the normal compliance condition and wear between surfaces are taken into account. We establish a variational formulation for the model and prove the existence and uniqueness of the weak solution. The proof is based on arguments of hyperbolic nonlinear differential equations, parabolic variational inequalities and Banach fixed point.

Thermomechanical response of nonlinear viscoelastic materials

In this article, the thermomechanical properties of the classical and nonclassical viscoelastic materials with particular emphasis on the entropy are studied in the framework of continuum thermodynamics. Specifically, considering the Clausius integral as “Part I” of the second law of thermodynamics in the classical formulation of continuum thermodynamics, the entropy function for various classes of nonclassical thermo-viscoelastic materials is shown to exist. This is achieved by employing the first law of thermodynamics and a scalar potential known as the Helmholtz free energy function. In addition, another function known as the internal rate of production of entropy defined for the classical and nonclassical thermo-viscoelastic materials is adopted to obtain a balance law for the entropy. Finally, upon linearizing the theory, a coupled system of differential equations is obtained for the nonclassical thermo-viscoelastic materials, which under some special circumstances, permits propagation of damped harmonic waves in the viscoelastic medium.

The effect of Seebeck–Peltier on the generalized magneto thermoviscoelastic medium under five theories

This study aims to research the influence of the magnetic field on the 2-D generalized thermo-viscoelastic material in five theories. The amended Ohm Law, which includes temperature gradient (effect of Seebeck) and charging density effects and the existing Fourier Law (effect of Peltier), is adopted. In the physical domain, the analytical expressions for the physical quantities are obtained using the normal mode analysis. These expressions are measured numerically for a specific substance and graphically illustrated. Moreover, the results predicted by (C-T, L-S, G-L, G-N II and DPL) theories also examined the existence and nonexistence of the viscosity and (Seebeck–Peltier) coefficients.

A new mixed finite element formulation for reorientation in liquid crystalline elastomers

Liquid crystalline elastomers (LCE) belong to the class of soft materials and are capable of large deformations induced by temperature changes and ultraviolet irradiation. These materials are under investigation as actuator materials in light-weight structures. In order to numerically simulate LCE materials by using a space–time finite element method, a continuum model is necessary which combines a thermo-viscoelastic material formulation with a dissipative reorientation process of mesogens. Mesogens are rigid and rod-shaped molecules linked with the polymer chains of the elastomer. The dissipative reorientation of the mesogens can be described by a combination of an independent field of orientation vectors with unit length and micropolar rotational degrees of freedom. The orientation vector field follow from a partial differential equation and possesses initial–boundary conditions. The unit length of the orientation vector field for any time is guaranteed by a local rotation with the micropolar rotational degrees of freedom. The dissipative reorientation process is introduced by a local time evolution equation with respect to the micropolar rotational degrees of freedom. This is analogous to thermo-viscoelasticity and can be variationally-based formulated. In this paper, we present this new variational-based reorientation finite element formulation in a dynamical framework. We arrive at an energy–momentum consistent mixed finite element formulation with a Galerkin-based space–time integration.

Multifield constitutive identification of non-conventional thermo-viscoelastic periodic Cauchy materials

The present work proposes a variational-asymptotic homogenization technique for non-conventional thermo-viscoelastic periodic microstructured materials. According to second sound theories, the heat flux vector linearly depends upon the history of temperature gradient and the heat conduction tensor represents the kernel of the relative hereditary integral, thus overcoming the paradox inferred from the usual Fourier’s law of thermal waves propagating at infinite speed. Down-scaling relations have been provided in the frequency domain, relating the transformed micro displacement and relative temperature fields to the corresponding macro variables and their gradients through frequency-dependent perturbation functions which convey the influence of the underlying microstructural heterogeneity. Average field equations of infinite order have been derived. Transformed field equations of the equivalent first-order medium have been obtained as Euler–Lagrange equations of a suitable functional whose first variation is properly truncated. They are characterized by frequency-dependent overall constitutive tensors, whose closed form has been provided. A benchmark test assesses the capabilities of the proposed homogenization method, where the solutions relative to a periodic, bi-phase, thermo-viscoelastic material and to the equivalent homogenized medium match under the hypothesis of periodic source terms.

The behavior and forming performance of vapor hydroforming process of thin aluminum sheets: Numerical and experimental analysis

This paper presents a study on the formability prediction, thickness variation, the influence of the gradient temperature, and prediction damage and failure behavior of aluminum sheets in a hydroforming vapor process through experimental and numerical investigations. A vapor hydroforming process that takes advantage of the coupling between thermal and mechanical loads applied to sheet metal is introduced. Uniaxial tensile tests and an optimization program developed in Matlab and based on the inverse method were conducted for identifying the coefficients of the Johnson-Cook law at room and at different temperatures. In parallel, a finite element model of the hydroforming vapor process was developed using ABAQUS/Explicit to reproduce the behavior of the aluminum sheet, where the behavior of the coupled thermo viscoelastic material and to the damage prediction of the plate being tested is analyzed using Johnson-Cook model. The results confirm the feasibility of the forming process. The variation of sheet thickness, the thinning mode of the tested sheet, and the effects of the hydroforming temperature are studied. A good agreement was achieved between experimental data and numerical results.

Nonlinear Models of Thermo-Viscoelastic Materials.

The paper develops a general scheme for viscoelastic materials, where the constitutive properties are described by means of measures of strain, stress, heat flux, and their time derivatives. The constitutive functions are required to be consistent with the second law of thermodynamics. Indeed, a new view is associated with the second law: the non-negative expression of the entropy production is set equal to a further constitutive function. The introduction of the entropy production as a constitutive function allows for a much wider range of models. Within this range, a scheme to obtain nonlinear models of thermo-viscoelastic materials subject to large deformations is established. Notably, the Kelvin–Voigt, Maxwell, Burgers, and Oldroyd-B viscoelastic models, along with the Maxwell–Cattaneo heat conduction, are obtained as special cases. The scheme allows also for modelling the visco-plastic materials, such as the Prandtl–Reuss work-hardening function and the Bingham–Norton fluid.

A novel model of multi-temperatures theory in generalized thermo-viscoelasticity

In this paper, a new relation of multi-temperatures was presented. This new connection to the problem of the general thermo-viscoelastic material in the context of Lord-Shulman (L-S) theory was applied. The analytical expressions for physical quantities are obtained using normal mode analysis in the physical domain. These expressions are numerically calculated and graphically illustrated for a given material. The findings were predicted and tested in the presence and absence of viscosity by various models of the theory of one-temperature (1-Temperature), classical two-temperature (2-Temperature) and hyperbolic two-temperature (Hyper-Temperature).

Plane dilatational and shear waves in a uniformly rotating thermo-viscoelastic material with voids

Effects of uniform rotation on propagating plane waves in a thermo-viscoelastic material with voids are explored. Five distinct modes are found to propagate in the considered rotating medium. Only in some specific directions relative to the axis of rotation, these modes may behave like pure dilatational or pure shear waves. Considering copper as a rotating thermo-viscoelastic material with voids, phase speeds and corresponding attenuations of all the existing pure modes are computed numerically and depicted graphically. Several well-known results are reduced as particular cases from the present formulation. Some facts regarding the directions of the pure modes are pointed out.

Physics-Informed Data-Driven Models for Predicting Time- and Temperature-Dependent Viscoelastic Material Behaviors of Optical Glasses

In glass transition regime, glass exhibits a viscoelastic property. This is a time-dependent property inherited from a nonequilibrium and non-crystalline state of materials. The property, furthermore, varies significantly with temperature. Understanding the complex time- and temperature-dependent viscoelastic material behaviors of glass is highly essential in numerous glass processing such as hot forming of glass. In conventional studies, characterization of the viscoelastic responses is prerequisite, requiring intensive experiments conducted over the entire temperature range of the glass transition. Instead, this work introduces an alternative data-driven approach using machine learning, indicating that the time- and temperature-dependent viscoelasticity in the temperature range from glass transition to softening temperatures can be predicted. Different supervised machine learning algorithms were implemented to understand the complexity of the intrinsically non-linear relationships of the existing viscoelastic data, while the most robust and reliable machine learning model was eventually determined by comparing the prediction performance of the selected learning algorithms. Furthermore, the models were developed by employing physics-informed descriptors using the Mauro-Yue-Ellison-Gupta-Allan (MYEGA) viscosity model. We demonstrate that the physics-informed descriptors are beneficial to enhance the extrapolation capability of the predictive model for two extreme temperature ranges of glass viscosity e.g., at the softening temperature and in the vicinity of glass transition temperature, while the dimensionality of the model is reduced. The promising result of this study allows glass manufacturers to bypass the costly experimental characterization required for understanding the thermo-viscoelastic material behaviors in glass processing.

Experimental characterization and modeling of the material behavior of an epoxy system

This work presents the experimental characterization and modeling of the material behavior of a filled epoxy system between ambient ( $${20}\,^{\circ }\hbox {C}$$ ) and elevated ( $${180}\,^{\circ }\hbox {C}$$ ) temperatures for future use in structural evaluations of epoxy-based potting materials in electric traction drives. An initial classification of the material behavior is carried out based on monotonic tensile tests of various strain rates. The material is then characterized experimentally in a testing program which includes a dynamic mechanical analysis, step relaxation tests with intermediate unloading, a thermomechanical analysis, a curing shrinkage analysis, and tensile and compression tests. The characterized behavior is modeled using a linear thermo-viscoelastic material model with time-temperature superposition governed by the Arrhenius shift function. A successful validation of the resulting model is presented. The material model can accurately predict the epoxy system’s rate- and temperature-dependent constitutive behavior, as well as effective chemical shrinkage, which is of particular importance for the structural evaluations of potting materials in electric traction drives.

On thermo-electro-viscoelastic relaxation functions in a Green–Naghdi type theory

We find restrictions on the relaxation functions of thermo-electro-viscoelastic materials. This is achieved within an extension of the Green–Naghdi theory for thermoelasticity, which uses the energy equation to exploit constitutive equations. These restrictions extend the results previously found for thermo-viscoelastic materials and for the classical infinitesimal theory of viscoelasticity.

Elastodynamic Response of a Three-Phase-Lag Model of Orthorhombic Thermoviscoelastic Material with Reference Temperature Dependent Properties

A three-phase-lag model of a homogeneous thermally conducting orthorhombic thermoviscoelastic material under the effect of the dependence of reference temperature on all elastic and thermal parameters is investigated. The Laplace and Fourier transform and eigenvalue approach techniques are used to solve the resulting nondimensional coupled equations. As an application of the problem, harmonically varying and sinusoidal pulse functions are considered. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made for thermoviscoelastic temperature dependent, thermoviscoelastic and thermoelastic materials, respectively, for different values of time, for temperature gradient boundary.

Mean-field homogenization of thermoelastic material properties of a long fiber-reinforced thermoset and experimental investigation

Fiber-reinforced polymers contribute significantly to weight-reducing components for various industrial applications. A discontinuous glass fiber-reinforced thermoset resin is considered which is produced by the sheet molding compound (SMC) process. Related to the production process, the samples considered in this work exhibit an anisotropic fiber orientation distribution which highly affects the thermomechanical properties. The thermoviscoelastic material behavior of three selected samples is characterized by means of dynamic mechanical analysis. These tests show the temperature-dependent elastic modulus and the glass transition of the composite. Measurements of the thermal expansion of the SMC composite provide data on the coefficient of thermal expansion (CTE). These experimental investigations provide data for the thermoelastic material modeling. Aiming at the prediction of the effective thermal and mechanical properties, a Hashin–Shtrikman-based homogenization method is presented. Based on an eigenstrain formulation, the effective Young’s modulus and CTE are computed in two steps. Moreover, the mean-field method is given in dependence of a variable reference stiffness allowing to tailor the approach to the material system. The influence of this variable reference stiffness on the effective quantities as well as the predicted behavior is analyzed with respect to the experiments. The presented numerical results are in good agreement with the experimental data.

Numerical modeling method for UV imprint process simulation using thermoviscoelastic constitutive equations

A novel numerical modeling method for UV imprint process simulation using thermoviscoelastic constitutive equations is proposed. The purpose of the process simulation is to predict transfer errors caused by UV shrinkage when a soft mold such as polydimethylsiloxane (PDMS) is used. The proposed method introduces an imaginary physical quantity, “virtual temperature,” as a measure of UV reaction progress and then replaces the UV curing/shrinkage phenomenon with the thermoviscoelastic cooling solidification/contraction phenomenon. A series of rheometry experiments are conducted for a general UV resin to identify the material properties of the UV resin as a thermoviscoelastic material. For the purpose of verification, the proposed method with the identified material properties is applied to the simulation of the rheometry experiments. Moreover, for the sake of validation, it is also applied to an actual UV imprinting process for a micromirror array molding with a PDMS mold. These analysis results prove the effectiveness of the present method in predicting transfer errors caused by UV shrinkage.