Linear Theory Of Thermoviscoelasticity Research Articles

On the coupled linear theory of thermoviscoelasticity of porous materials

On the coupled linear theory of thermoviscoelasticity of porous materials

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.

Fundamental solution and uniqueness theorems in the linear theory of thermoviscoelasticity for solids with double porosity

ABSTRACTIn this article, the linear theory of thermoviscoelasticity for Kelvin–Voigt materials with double porosity is considered. The fundamental solution of the system of equations of steady vibrations is constructed by elementary functions and its basic properties are established. The Green’s first identity in the considered theory is obtained. A wide class of the internal and external boundary value problems (BVPs) of steady vibrations is formulated. Finally, on the basis of the Green’s identity, the uniqueness theorems for regular (classical) solutions of these BVPs are proved.

About analyticity for the coupled system of linear thermoviscoelastic equations

In this paper we consider the classical linear theory of thermoviscoelasticity for inhomogeneous and anisotropic materials in three dimensional space. We show that under suitable conditions, the semigroup associated with the system of the viscoelastic equation of motion coupled with the parabolic equation of energy is analytic.

Spatial Behavior in Linear Theory of Thermoviscoelasticity with Voids

In the present article we study the spatial behavior of the solutions to the initial boundary value problem associated with the linear theory of thermoviscoelastic materials with voids. We prove a set of properties for an appropriate time-weighted surface power function, which allows us to obtain an idea of the domain of influence in linear thermoviscoelasticity with voids. Some spatial estimates of the Saint–Venant type, for bounded bodies, and Phragmén–Lindelöf type, for unbounded bodies, are obtained. Such estimates are characterized by time-dependent as well as time-independent decay and growth rates.

Potential method in the steady vibrations problems of the theory of thermoviscoelasticity for Kelvin‐Voigt materials with voids

AbstractIn this paper the linear theory of thermoviscoelasticity for Kelvin‐Voigt materials with voids is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are formulated. The uniqueness and existence theorems for classical solutions of the above mentioned BVPs are proved by using the potential method (boundary integral equation method) and the theory of singular integral equations. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Potential Method in the Theory of Thermoviscoelasticity for Materials with Voids

In the present article, the linear theory of thermoviscoelasticity for Kelvin–Voigt materials with voids is considered. The Sommerfeld-Kupradze type radiation conditions are established. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) of steady vibrations are proved. The Green's formulas and integral representations of Somigliana type of regular vector and classical solution are obtained. The basic properties of thermoelastopotentials and singular integral operators are given. Finally, the existence theorems for classical solutions of the above mentioned BVPs are proved by using the potential method (boundary integral method) and the theory of singular integral equations.

On the Solutions of Equations of the Linear Thermoviscoelasticity Theory for Kelvin–Voigt Materials with Voids

In this article, the linear theory of thermoviscoelasticity for Kelvin–Voigt materials with voids is considered. The fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions and its basic properties are established. The representation of a Galerkin-type solution is obtained. The formula of representation of the general solution for the system of homogeneous equations of steady vibrations in terms of six metaharmonic functions is established. The completeness of these representations of solutions is proved.

Thermo-Viscoelastic Analysis of Warp for Laminated Body Consisting of Epoxy Resin and Steel with Thermal Deterioration by Thermal Load

The mechanical and thermal properties of epoxy resin used for electronic parts are changed by thermal load in manufacturing processes and prolonged use, and these properties make defective of electronic devices. In this report, warp behavior of a two-layer-laminated body consisting of epoxy resin and steel caused by thermal load were examined from both sides of experiment and theory. As a result, it was clarified that viscoelastic properties of epoxy resin, such as storage modulus, loss modulus, loss tangent and glass transition temperature were changed by thermal load, and that warp behavior could be predicted by thermo-viscoelastic analysis based on linear thermo-viscoelastic theory by using these viscoelastic properties.

Thermoviscoelasticity: continuum-molecular connections

A connection between the linear thermoviscoelastic theory in continuum mechanics and the corresponding molecular theory is established. Specifically, it is shown that both theories lead to the same equation of change for temperature. Also they both predict a memory effect in the heat capacity.

Residual stress and deformation during rapid cooling process in an epoxy plate

AbstractResidual stress in the epoxy plate during a rapid cooling process was measured by the layer removal method and calculated by the linear thermoviscoelastic theory considering specific volume relaxation. The relaxations of the tensile modulus and specific volume were measured by an Instron thermomechanical analyzer. When the starting temperature of the cooling process was near the glass transition temperature of the cured epoxy, the residual stress in the epoxy plate was smaller than when the starting temperature was higher than the glass transition temperature. However, the transient stress in the cured epoxy plate was higher when the starting temperature was near the glass transition temperature than when the starting temperature was higher than the glass transition temperature. The quenched epoxy plate was compressed in the direction parallel to the surface and expanded in the thickness direction.

Prediction of residual stress in LSI plastic packages by thermoviscoelastic analysis for a 3-layer laminated beam.

Fundamental equations based on the linear-thermoviscoelastic theory were established to obtain the temperature and residual stress by cooling in a 3-layer laminated beam. The transient thermal stress and deformation in the laminated beam made of composite materials constructed LSI plastic packages were calculated using these fundamental equations. It was found that the residual stress is strongly related to glass transition temperature and Young's modulus of epoxy resins, and the material design method necessary in order to decrease the residual stress was clarified.

Thermal stresses due to cooling of a viscoelastic oceanic lithosphere

Theories based upon thermal contraction of cooling oceanic lithosphere provide a successful basis for correlating seafloor bathymetry and heat flow. The horizontal components of the contraction of the lithosphere as it cools potentially give rise to large thermal stresses. Current methods to calculate these stresses assume that on the time scales of cooling, the lithosphere initially behaves as an inviscid fluid and instantly freezes into an elastic solid at some critical temperature. These instant‐freezing methods inaccurately predict transient thermal stresses in rapidly cooling silicate glass plates because of the temperature dependent rheology of the material. The temperature dependent rheology of the lithosphere may affect the transient thermal stress distribution in a similar way, and for this reason we use a thermoviscoelastic model to estimate thermal stresses in young oceanic lithosphere. This theory is formulated here for linear creep processes that have an Arrhenius rate dependence on temperature. Our results show that the stress differences between instant freezing and linear thermoviscoelastic theory are most pronounced at early times (0–20 m.y.) when the instant freezing stresses may be twice as large. The solutions for the two methods asymptotically approach the same solution with time. A comparison with intraplate seismicity shows that both methods underestimate the depth of compressional stresses inferred from the seismicity in a systematic way.

SOME THEOREMS IN THE THEORY OF THERMOVISCOELASTICITY

The paper is concerned with the linear theory of thermoviscoelasticity established by M. E. Gurtin. Some theorems concerning the reciprocity relation, the variational characterization of the solution, and uniqueness are presented. A continuous dependence result is also established

Identifying governing relations of the linear theory of thermoviscoelasticity

Identifying governing relations of the linear theory of thermoviscoelasticity

Thermoviscoelastic analysis of residual stress by cooling in a thermosetting resin/metal laminated beam.

Fundamental equations based on the linear-thermoviscoelastic theory were established to obtain the residual stress and deformation by cooling in a multi-layer laminated beam. The transient thermal stress distribution and deformation in an epoxy resin/Al alloy laminated beam during the cooling process were calculated using these fundamental equation, then these beams were actually subjected to the cooling process. The experimentally obtained values revealed a high level of correlation with values theoretically calculated by the thermoviscoelastic analysis. The results demonstrate the nesessity of thermoviscoelastic analysis for obtaining the residual stress and deformation by cooling of multi-layer laminated beams made of thermosetting resin.

Temperature dependence of viscoelastic properties of polymers under dynamic conditions on the basis of the linear theory of thermoviscoelasticity

Another method of taking the temperature dependence of the deformation properties of a material into account is based on the use of relationships between the coefficients of the determining equations and the temperature as a parameter [5, 6]. In this case, the temperaturedependence of the inelastic constants is usually studied by conducting long-term creep or relaxation tests [6]. Short-term tests wherein specimens are loaded with a constant strain rate [7] are occasionally employed to ascertain the temperature dependence of the modulus of instantaneous elasticity -- in this case, the initial segments of the e-e diagram or dynamic tests, conducted at various temperatures to determine the resonant vibration frequencies, are analyzed [8]. In view o f the vigorous effect of elevated temperature on the deformability of polymers, however, the inelastic properties may manifest themselves significantly even during short-term loading and in dynamic tests [4, 9, I0]. Analysis of similar experience should therefore be made, generally speaking, on the basis of equations of thermoviscoelasticity, while the temperature dependence of the effective elastic modulus, which is derived experimentally from short-term tests, reflects the effect of inelasticity to a significantly greater degree than the temperature dependence of the modulus of instantaneous elasticity. In our study, we attempted to describe quantitatively the temperature dependence of the dynamic shear modulus and the loss factor of a rigid cellular polymer from the results of quasistatic ~ tensile-creep tests conducted at room and elevated temperatures on the assumption that the modulus of instantaneous elasticity is a constant independent of temperature. We compared comlmted results with experimental data obtained at different temperatures during torsion tests under conditions of natural damping vibrations. Initial data on the viscoelastic properties of ED-6 epoxy resin were obtained from ten

Some fundamental problems of the theory of thermoviscoelasticity

Methods of solving quasistatic problems of the linear theory of thermoviscoelasticity are discussed. Special attention is given to the method of approximations. Modern methods of solving contact problems with a variable boundary and problems with a time-dependent boundary are briefly reviewed. Methods of solving problems with a nonuniform temperature field are outlined. The basic relations of the nonlinear theory of thermoviscoelasticity are given. Its various modifications and simplifications associated with the introduction of fairly general assumptions are examined. Methods of solving problems in certain nonlinear theories are noted. Nonisothermal (coupled) problems of thermoviscoelasticity and questions relating to the general theory with physical and geometric nonlinearity are discussed.

Method of approximations for solving problems of the linear theory of thermoviscoelasticity

A general approximate method of solving problems of the linear theory of thermoviscoelasticity is proposed. Use is made of the Laplace transformation and certain properties of the dependence of solutions to problems of the theory of elasticity on Poisson's ratio that make possible a simple approximation. As a result, the inverse transforms become elementary and the general solution of the problem is expressed by creep and relaxation functions.

Linear viscoelastic materials with environmental dependent properties

This study expands on the linear theory of thermo-viscoelasticity to include a larger group of materials and environmental effects. The development rests on the observation that for many materials the creep curve which results from a test at one steady value of an environmental parameter can be mapped onto the creep curve at another value of the environmental parameter by: (1) displacing the curve along the logarithmic time axis, (2) scaling the initial elastic response, and (3) scaling the long term or residual response. A thickwall, environmental-dependent, incompressible, viseoelastic cylinder is analyzed for a material that can be modeled by the proposed mapping. It is found that this mapping can have a profound effect on the resulting stress distributions. Further, using the above mapping a constitutive relationship is developed for transient environmental fields.