Vittorio Zampoli

Fundamental Solutions in the Theory of Thermoelasticity for Solids with Double Porosity

In this article, the linear theory of thermoelasticity for solids with double porosity is considered. The fundamental solutions for the systems of steady vibrations (including quasi-static case) and equilibrium equations are constructed by means of elementary functions; the basic properties of such solutions are also established.

Fundamental Solution in the Theory of Micropolar Thermoelasticity without Energy Dissipation

ABSTRACT This paper concerns the linear theory of micropolar thermoelasticity without energy dissipation. We construct the fundamental solution of the system of differential equations in the case of steady oscillations in terms of elementary functions.

On the Uniqueness in Dynamical Thermoelasticity Backward in Time for Porous Media

The aim of this article is to study some uniqueness criteria for the solutions of boundary-final value problems associated with the linear theory of thermoelastic materials with voids. More precisely, the present study is devoted to the investigation of a backward in time problem associated with porous thermoelastic materials.

On the Heat-Flux Dependent Thermoelasticity for Micropolar Porous Media

In the present paper, in the context of the linear theory of heat-flux dependent thermoelasticity for micropolar porous media, we derive a uniqueness theorem with no positive definiteness assumption on the elastic constitutive coefficients. Moreover, we prove, under non homogeneous initial conditions, a reciprocal relation and a variational principle. These generalize previous results about inhomogeneous and anisotropic micropolar thermoelastic materials.

On the Theory of Micropolar Thermoelasticity without Energy Dissipation

The present paper deals with micropolar thermoelastic materials with a center of symmetry, investigated through the so-called thermoelasticity of type II or thermoelasticity without energy dissipation, which allows propagation of thermal waves at finite speed. In particular, for such a model, a uniqueness theorem, two variational principles (of Hamilton and Biot types, respectively) and a reciprocity result are derived.

A domain of influence result about the time differential three-phase-lag thermoelastic model

ABSTRACT This work represents a natural outlet of recent investigation about the well-posed question for the time differential three-phase-lag model of thermoelasticity. We deal with a cylindrical domain filled by an anisotropic and inhomogeneous thermoelastic material and assume that the initial-boundary data as well as the external supply terms that characterize the problem in concern are concentrated in a compact region of the considered volume. Within such a framework, we show the spatial behavior of the solutions in terms of existence of a domain of influence of the assigned data. We will remark that our results are obtained under restrictions involving the constitutive tensors and the delay times that are in complete agreement with the hypotheses that make the time differential three-phase-lag model thermodynamically consistent. The case of a semi-infinite cylindrical domain is also considered.

On the Theory of Direct and Inverse Problems in the Elastic Rectangle: Antiplane Case

In this article, we study the antiplane deformation of the boundary surface of a rectangular domain in the presence of a void and a shear force on the outer boundary surface. For a formulated inverse problem, we develop some analytical results and use them to solve the problem numerically for various elliptic geometrical configurations. The analytical method allows us to give an efficient representation for Greens function in the rectangular domain. Then we derive the same Greens function by an alternative method based on Fourier series expansions. Finally, for a number of configurations, we demonstrate the comparison between real and reconstructed defects.

Reconstruction of round voids in the elastic half-space: Antiplane problem

We study the reconstruction of geometry (position and size) of round voids located in the elastic half-space, in frames of antiplane two-dimensional problem. We assume that a known point force is applied to the boundary surface of the half-space, and we can measure the shape of the surface over a certain finite-length interval. Then, if the geometry of the defect is unknown, we construct an algorithm to restore its position and size. Some numerical examples demonstrate a good stability of the proposed algorithm.

Some continuous dependence results about high-order time differential thermoelastic models

ABSTRACT This article aims to contribute to the investigation of the well-posedness question for three different heat conduction thermoelastic models, obtained starting from the dual-phase-lag (DPL) constitutive equation in its most general time differential formulation and considering Taylor expansion orders higher than those most commonly studied in literature so far. It is necessary to emphasize right from now that the investigation of such thermomechanical models, although they originate in terms of constitutive equations from suitable Taylor series expansions, has to be properly interpreted not as an attempt to emulate the delayed behavior characteristic of the original (i.e. not expanded) DPL model, but rather with the awareness of deepening the well-posedness question for three different stand-alone and self-consistent models. In particular, three estimates are obtained (one for each of the considered models) able to show the continuous dependence of the solutions of the related initial boundary value problems with respect to the supply terms and to the initial given data. All the continuous dependence results are obtained without the need to impose particular restrictions involving the delay times, except for the requirement that they are strictly positive.