Antonio Scalia

ON THE SPATIAL AND TEMPORAL BEHAVIOR IN LINEAR THERMOELASTICITY OF MATERIALS WITH VOIDS

The present article studies the spatial and temporal behavior of the solutions to the initial boundary value problems associated with the linear theory of thermoelastic materials with voids. The spatial behavior is described by spatial estimates of Saint-Venant type (for bounded bodies) and Phragmén-Lindelöf type (for unbounded bodies) with time-dependent and time-independent rates. Some appropriate time-weighted integral measures are used. The temporal behavior is studied using the Cesaro means of various parts of the total energy. The relations describing the asymptotic behavior of the Cesaro means are established.

ON THE REPRESENTATION OF SOLUTIONS OF THE THEORY OF THERMOELASTICITY WITH MICROTEMPERATURES

In the present paper the linear theory of thermoelasticity with microtemperatures is considered. First, the representation of Galerkin type solution of equations of motion is obtained. Then, the representation theorem of Galerkin type of the system of equations of steady oscillations (vibrations) is presented. Finally, the general solution of the system of homogeneous equations of steady oscillations in terms of nine metaharmonic functions is established.

On the asymptotic spatial behavior in linear thermoelasticity of materials with voids

The comparison principle involving solutions of the one-dimensional heat equation is used to investigate the spatial decay of solutions to initial-boundary value problems for the linear theory of thermoelasticity with voids. A spatial decay estimate is established for an appropriate volumetric measure of the solution in an unbounded body. This proves that at large distances from the support of the external given data the decay of the mechanical and thermal effects is controlled only by the thermal characteristic coefficients of the material.

Basic Theorems in the Equilibrium Theory of Thermoelasticity with Microtemperatures

In this paper we consider the linear equilibrium theory of thermoelasticity with microtemperatures and some basic results of the classical theories of elasticity and thermoelasticity are generalized. The Greens formulae in the considered theory are obtained. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) are proved. The representation of Galerkin type solution is obtained and the completeness of this solution is established. The formulae of integral representations of regular vector and regular (classical) solutions are obtained. The basic properties of thermoelastopotentials and singular integral operators are presented. Finally, the existence theorems for the internal and external basic BVPs are proved by means of the potential method and the theory of singular integral equations.

Fundamental Solution in the Theory of Micropolar Thermoelasticity for Materials with Voids

This paper concerns with the linear theory of micropolar thermoelasticity for materials with voids. We construct the fundamental solution of the system of differential equations in the case of steady oscillations in terms of elementary functions. Some basic properties of this solution are established.

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.

On uniqueness and reciprocity in linear thermoelasticity of materials with voids

A linear thermoelastic theory of materials with voids is considered. First, we establish a uniqueness theorem with no definiteness assumption on the elasticities and in the absence of restriction that the conductivity tensor is positive definite. Then, we establish a basic relation which leads in a simple manner to the reciprocal theorem and to another uniqueness result. Some applications of the reciprocity relation are presented.

On some theorems in the linear theory of viscoelastic materials with voids

A linear theory of viscoelasticity of materials with voids is considered. Some theorems concerning uniqueness and continuous dependence are established.

Potential Method in the Linear Theory of Thermoelasticity with Microtemperatures

In the present paper the linear theory of thermoelasticity with microtemperatures is considered. The basic boundary value problems of steady vibrations are investigated using the potential method. Sommerfeld–Kupradze type radiation conditions and the basic properties of thermoelastopotentials are established. The uniqueness and existence theorems of classical solutions of the external (with respect to an unbounded domain) boundary value problems are proved.

Mathematical problems in the coupled linear theory of bone poroelasticity

This paper concerns with the quasi-static coupled linear theory of bone poroelasticity for materials with double porosity and some basic results of the classical theories of elasticity and thermoelasticity are generalized. The system of equations of this theory is based on the equilibrium equations, conservation of fluid mass, the effective stress concept and Darcys law for material with double porosity. The Greens formulas in the considered theory are obtained, the formulas of Somigliana type integral representations of regular vector and regular (classical) solutions are presented. The uniqueness theorems for classical solutions of the internal and external boundary value problems (BVPs) are proved. The single-layer, double-layer and volume potentials are constructed and their basic properties are established. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral method) and the theory of singular integral equations.