Stan Chiriţă

Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua

Abstract The present paper describes a method for studying the spatial behaviour of the thermodynamic processes. The method is based on a set of properties for an appropriate time-weighted surface power function associated with the process in question. It allows to obtain a more precisely idea of domain of influence in linear elastodynamics and viscoelastodynamics and, furthermore, to get spatial decay estimates with time-independent decay rate inside of the domain of influence. It also allows to obtain a good description for the spatial behaviour of the thermoelastic processes by means of spatial estimates characterized by independent as well as time-dependent decay and growth rates.

ON THE BEHAVIOR OF STEADY TIME-HARMONIC OSCILLATIONS IN THERMOELASTIC MATERIALS WITH VOIDS

We study the spatial behavior in a cylinder made of an isotropic and homogeneous thermoelastic material with voids when it is subjected to plane boundary data varying harmonically in time on its lateral surface and on one of the bases. For oscillations with an angular frequency lower than a critical frequency, we show that some appropriate measures associated with the amplitude of the vibration decays exponentially with the distance to the bases.

Structural stability in porous elasticity

We consider the linearized system of equations for an elastic body with voids as derived by Cowin & Nunziato. We demonstrate that the solution depends continuously on changes in the coefficients, which couple the equations of elastic deformation and of voids. It is also shown that the solution to the coupled system converges, in an appropriate measure, to the solutions of the uncoupled systems as the coupling coefficients tend to zero.

On the wave propagation in the time differential dual-phase-lag thermoelastic model

We study the propagation of plane time harmonic waves in the infinite space filled by a time differential dual-phase-lag thermoelastic material. There are six possible basic waves travelling with distinct speeds, out of which, two are shear waves, and the remaining four are dilatational waves. The shear waves are found to be uncoupled, undamped in time and travels independently with the speed that is unaffected by the thermal effects. All the other possible four dilatational waves are found to be coupled, damped in time and dispersive due to the presence of thermal properties of the material. In fact, there is a damped in time longitudinal quasi-elastic wave whose amplitude decreases exponentially to zero when the time is going to infinity. There is also a quasi-thermal mode, like the classical purely thermal disturbance, which is a standing wave decaying exponentially to zero when the time goes to infinity. Furthermore, there are two possible longitudinal quasi-thermal waves that are damped in time with different decreasing rates or there is one plane harmonic in time longitudinal thermal wave, depending on the values of the time delays. The surface wave problem is studied for a half space filled by a dual-phase-lag thermoelastic material. The surface of the half space is free of traction and it is free to exchange heat with the ambient medium. The dispersion relation is written in an explicit way and the secular equation is established. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.

A Mixture Theory for Microstretch Thermoviscoelastic Solids

A nonlinear theory is developed for a heat-conducting viscoelastic composite which is modelled as a mixture consisting of a microstretch Kelvin–Voigt material and a microstretch elastic solid. The strain measures, the basic laws and the constitutive equations are established and presented in Lagrangian description. The initial boundary value problem associated to such model is also formulated. Then the linearized theory is considered and the constitutive equations are given for both anisotropic and isotropic bodies. Finally, a uniqueness result is established within the framework of the linear theory.

On Some Growth-Decay Results in Thermoelasticity of Porous Media

In this paper we study the spatial behaviour for a large class of isotropic and homogeneous porous thermoelastic materials for which the constitutive coefficients are supposed to satisfy some relaxed positive definiteness conditions. By using some appropriate measures, we are able to establish results describing the spatial behaviour of transient and steady-state solutions in these enlarged classes of thermoelastic porous materials.

SOME FURTHER GROWTH AND DECAY RESULTS IN LINEAR THERMOELASTODYNAMICS

Two time-weighted measures are introduced for studying the spatial behavior of the thermoelastic processes in an isotropic thermoelastic body in order to relax the hypotheses of positive definiteness on the thermoelastic coefficients. For the first measure we establish some spatial estimates describing the spatial behavior of solutions for the class of thermoelastic materials for which the Lamé moduli u and w range so that w >0 and \lambda >-{4 \over 3} \mu . The second measure allows us to establish spatial estimates describing the spatial behavior of the thermoelastic processes in an isotropic and homogeneous thermoelastic material for which the Lamé moduli range so that w >0 and m 2 w < u <0.

Uniqueness and continuous dependence of solutions to the incompressible micropolar flows forward and backward in time

This paper studies the continuous dependence of the solutions for the boundary-initial and boundary-final value problems associated with the incompressible micropolar flows. For the incompressible micropolar flows forward in time, the continuous dependence of solutions with respect to the changes in the body force and body couple and in the initial data is established by means of a method based on a Gronwall-type inequality, while an adapted version of the logarithmic convexity method is used to study the continuous dependence of solutions for the incompressible micropolar flows backward in time. As a direct consequence, some uniqueness results are obtained.

ON THE SPATIAL BEHAVIOR IN THE DYNAMIC THEORY OF MIXTURES OF THERMOELASTIC SOLIDS

ABSTRACT This paper is concerned with a dynamic linear theory for binary mixtures of thermoelastic bodies. We study the spatial behavior for some classes of isotropic and homogeneous thermoelastic mixture materials for which the constitutive coefficients are supposed to satisfy various mild positive definiteness conditions. By introducing some appropriate measures, we are able to establish results describing the spatial behavior of the transient solutions in bounded as well as unbounded bodies.

Plane harmonic waves in the theory of thermoviscoelastic materials with voids

ABSTRACT In this article we analyze the behavior of plane harmonic waves in the entire space filled by a linear thermoviscoelastic material with voids. We take into account the effect of the thermal and viscous dissipation energies upon the corresponding waves and, consequently, we study the damped in time wave solutions. There are five 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 coefficients. 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 profile. Furthermore, we use numerical methods and computations to solve the secular equation for some special classes of thermoviscoelastic materials considered in literature.