Spatial Behavior in Linear Theory of Thermoviscoelasticity with Voids (original) (raw)
Related papers
On a Theory of Thermoviscoelastic Materials with Voids
Journal of Elasticity, 2011
In this paper we extend the theory of elastic materials with voids to the case when the time derivative of the strain tensor and the time derivative of the gradient of the volume fraction are included in the set of independent constitutive variables. First, the basic equations of the nonlinear theory of thermoviscoelastic materials with voids are established. Then, the linearized version of the theory is derived. We establish a uniqueness result and the continuous dependence of solution upon the initial data and supply terms. A solution of the field equations is also presented.
On uniqueness and analyticity in thermoviscoelastic solids with voids
Journal of Applied Analysis and Computation, 2011
In this paper we consider the most general system proposed to describe the thermoviscoelasticity with voids. We study two qualitative properties of the solutions of this theory. First, we obtain a uniqueness result when we do not assume any sign to the internal energy. Second we extend some previous results and prove the analyticity of the solutions. The impossibility of localization in time of the solutions is a consequence. Last result we present corresponds to the analyticity of solutions in case that the dissipation is not very strong, but with suitable coupling terms.
On the Nonlinear Theory of Thermoviscoelastic Materials with Voids
Journal of Elasticity, 2016
This article is devoted to a theory of thermoviscoelastic materials with voids where the time derivative of the strain tensor and the time derivative of the gradient of the volume fraction are included in the set of independent constitutive variables. The equations of the nonlinear theory are considered. A stability result for bodies which are non-conductor of heat is presented. The stability is interpreted as continuous dependence of the processes upon initial state and supply terms.
A theory of thermoelastic materials with voids
Acta Mechanica, 1986
A linear theory of thermoelastic materials with voids is considered. First, some general theorems (uniqueness, reciprocal and variational theorems) are established. Then, the acceleration waves and some problems of equilibrium are studied.
Plane harmonic waves in the theory of thermoviscoelastic materials with voids
Journal of Thermal Stresses, 2016
In this article we analyze the behavior of plane harmonic waves in the entire space lled by a linear thermoviscoelastic material with voids. We take into account the e ect of the thermal and viscous dissipation energies upon the corresponding waves and, consequently, we study the damped in time wave solutions. There are ve basic waves in an isotropic and homogeneous thermoviscoelastic porous space. Two of them are shear waves, while the remaining three are dilatational waves. The shear waves are uncoupled, damped in time with decay rate depending only on the viscosity coe cients. The three dilatational waves are coupled and consist of a predominantly dilatational damped wave of Kelvin-Voigt viscoelasticity, other is predominantly a wave carrying a change in the void volume fraction and the third takes the form of a standing thermal wave whose amplitude decays exponentially with time. The explicit form of the dispersion equation is obtained in terms of the wave speed and the thermoviscoelastic homogeneous pro le. Furthermore, we use numerical methods and computations to solve the secular equation for some special classes of thermoviscoelastic materials considered in literature.
Potential method in the theory of thermoelasticity for materials with triple voids
Archives of Mechanics, 2019
In the present paper the linear theory of thermoelasticity for isotropic and homogeneous solids with macro-, meso-and microporosity is considered. In this theory the independent variables are the displacement vector field, the changes of the volume fractions of pore networks and the variation of temperature. The fundamental solution of the system of steady vibrations equations is constructed explicitly by means of elementary functions. The basic internal and external boundary value problems (BVPs) are formulated and the uniqueness theorems of these problems are proved. The basic properties of the surface (single-layer and double-layer) and volume potentials are established and finally, the existence theorems for regular (classical) solutions of the internal and external BVPs of steady vibrations are proved by using the potential method (boundary integral equation method) and the theory of singular integral equations.
On the Existence and Uniqueness in Linear Thermoviscoelasticity
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1997
On the Existence and Uniqueness in Linear Thermoviscoelasticity Es wird ein Anfangs-Randwertproblem aus der Theorie der linearen Thermoviskoelastizitat betrachtet. Nach Formulierung des zugeordneten Variationsproblems werden Existenz und Eindeutigkeit seiner Losung in einem geeigneten funktionalanalytischen Rahmen studiert. An initial-boundary value problem of the theory of linear thermoviscoelasticity is considered. After formulating the corresponding variational problem, the existence and uniqueness of its solution are studied in an appropriate functional framework.
On the Nonlinear Theory of Nonsimple Thermoelastic Materials with Voids
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1993
On the Nonlinear Theory of Nonsimple Thermoelastic Materials with Voids E.Y wird eine nichtlineare Theorie des nichteinfachen, thermoelastischen Materials mit Poren aufgestellt. Die kontinuierliche Ahlzungigkeit con Anfangszustand und Erganzungstermen des glatten therrnodynamischen Prozesses wird untersuclzt. A nonlinear theory of nonsimple thermoelastic materials with voids is established. The continuous &pendenre upon initial state and supply terms of smooth thermodynamic processes is studied.
Zeitschrift für angewandte Mathematik und Physik, 2012
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