Michele Ciarletta

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.

A THEORY OF MICROPOLAR THERMOELASTICITY WITHOUT ENERGY DISSIPATION

In this article we use the results of Green and Naghdi Proc. Roy. Soc. London A, vol. 432, pp. 171-194, 1991 and vol. 357, pp. 253-270, 1977 and J. Elasticity, vol. 31, pp. 189-209, 1993] to establish a theory of micropolar thermoelasticity that permits propagation of thermal waves at a finite speed. A solution of Galerkin type for homogeneous and isotropic bodies is also established. This solution is used to study the effect of a concentrated heat source. The continuous dependence of the solution with respect to body loads and initial data is finally studied.

On stress analysis for cracks in elastic materials with voids

Abstract The paper deals with classical problem for cracks dislocated in a certain very specific porous elastic material, described by a Cowin–Nunziato model. We propose a method based upon a reducing of stress concentration problem for cracks to some integral equations. By applying Fourier integral transforms the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. In the axially symmetric case, for the penny-shaped crack, the problem is reduced to a regular Fredholm integral equation of the second kind. In the both cases we study stress-concentration factor, and investigate its behavior versus porosity of the material. More in particular the stress concentration factor in the medium with voids is always higher, under the same conditions, than in the classical elastic medium made of material of the skeleton. Further, as can be seen, the influence of the porosity becomes more significant for larger cracks; that is also quite natural from a physical point of view.

Poroacoustic acceleration waves

A model for acoustic waves in a porous medium is investigated. Due to the use of lighter materials in modern buildings and noise concerns in the environment, such models for poroacoustic waves are of much interest to the building industry. The model has been investigated in some detail by P. M. Jordan. Here we present a rational continuum thermodynamic derivation of the Jordan model. We then present results for the amplitude of an acceleration wave making no approximations whatsoever.

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 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 THE UNIQUENESS AND CONTINUOUS DEPENDENCE OF SOLUTIONS IN DYNAMICAL THERMOELASTICITY BACKWARD IN TIME

This article studies the uniqueness and continuous dependence problems for the thermoelastic processes backward in time. Using some Lagrange-Brun identities combined with Gronwalls lemma, it is shown that the boundary final value problem associated with the linear thermoelasticity has at most one solution provided that some mild requirements are assumed concerning the thermoelastic coefficients. Some estimates are outlined that exhibit continuous dependence with respect to the final data, on the whole time interval without any kind of constraint on the solutions.

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.

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 bending of microstretch elastic plates

Abstract This paper is concerned with the linear theory of microstretch elastic solids introduced by Eringen (A.C. Eringen, in: Prof. Dr. Mustafa Inan Anisina, Ari Kitabevi Matbaasi, Istanbul, 1971, pp. 1–18; A.C. Eringen, Int. J. Eng. Sci. 28 (1990) 1290–1301). First, a theory of bending of homogeneous and isotropic plates is studied. Then, a uniqueness theorem, with no definiteness assumptions on the elastic coefficients, is presented.