Marin

A mathematical model for three-phase-lag dipolar thermoelastic bodies

In this study we approach a mixed initial-boundary value problem to modeling a three-phase-lag dipolar thermoelastic body. The constitutive laws in this context are given. We establish a uniqueness result and prove a reciprocal theorem. The variational principle obtained in this context is a generalization of the known Gurtin’s principle for classical elasticity.

The theory of generalized thermoelasticity with fractional order strain for dipolar materials with double porosity

This article continues the work on dipolar thermoelastic materials, which are a special case of multipolar continuum mechanics. This theory allows a double-porous structure: a macro-porosity related to pores in the material and a microporosity, which shows fissures in the porous skeleton. This paper constructs a mathematical model for dipolar materials, which have a double-porosity structure by considering a fractional order Duhamel–Neumann stress–strain relation. The heat conduction is described by Cattaneo’s equations. The results are the constitutive equations of the linear theory of thermoelasticity with fractional order strain. The equations are valid for anisotropic materials and are called the Duhamel–Neumann equations with fractional order. Finally, the isotropic case is considered under the conditions of plane strain in order to perform some numerical simulations for samples of porous copper.

Effect of internal state variables in thermoelasticity of microstretch bodies

Abstract First, we formulate the mixed initial boundary value problem in the theory of thermoelastic microstretch bodies having certain internal state variables. Then by using some approachable computing techniques and the known Gronwalls inequality we will prove that the presence of internal state variables do not influence the uniqueness of solution of the mixed problem.

Coupled transverse and torsional vibrations in a mechanical system with two identical beams

The paper aims to study a plane system with bars, with certain symmetries. Such problems can be encountered frequently in industry and civil engineering. Considerations related to the economy of the design process, constructive simplicity, cost and logistics make the use of identical parts a frequent procedure. The paper aims to determine the properties of the eigenvalues and eigenmodes for transverse and torsional vibrations of a mechanical system where two of the three component bars are identical. The determination of these properties allows the calculus effort and the computation time and thus increases the accuracy of the results in such matters.The paper aims to study a plane system with bars, with certain symmetries. Such problems can be encountered frequently in industry and civil engineering. Considerations related to the economy of the design process, constructive simplicity, cost and logistics make the use of identical parts a frequent procedure. The paper aims to determine the properties of the eigenvalues and eigenmodes for transverse and torsional vibrations of a mechanical system where two of the three component bars are identical. The determination of these properties allows the calculus effort and the computation time and thus increases the accuracy of the results in such matters.

Axisymmetric Distributions of Thick Circular Plate in a Modified Couple Stress Theory

In this paper, the two-dimensional axisymmetric distributions of thick circular plate in modified couple stress theory with heat and mass diffusive sources is investigated. The problem is considered in the context of the theories of thermodiffusion elastic solid with one and two relaxation time developed by Sherief et al. [Int. J. Eng. Sci. 42, 591 (2004)] and Kumar and Kansal [Int. J. Solid Struct. 45, 5890 (2008)] by using Laplace and Hankel transforms technique. The displacements, stress components, temperature change and chemical potential are obtained in transformed domain. Particular cases of interest are also deduced.

Effect of intrinsic rotations, microstructural expansion and contractions in initial boundary value problem of thermoelastic bodies

This study is dedicated to some basic theorems in the thermoelastodynamics of microstretch bodies. Our intention is to show that the presence of the microstretch does not affect the main characteristics of the mixed initial boundary value problem for thermoelastic bodies. The result regarding the uniqueness theorem is derived with no definiteness assumptions on the elastic coefficients and in the absence of the restriction that the conductivity tensor is positive definite. In the last part of the paper we establish a basic relation which leads to the reciprocal theorem and to another uniqueness result.MSC:35M30, 35Q74, 74A15, 74A60, 74M25.

Diffusion in Microstretch Thermoelasticity with Microtemperatures and Microconcentrations

This chapter is dealing with the linear theory of microstretch thermoelasticity for materials whose particles have microelements that are equipped with microtemperatures and microconcentrations. The focus is on isotropic and homogeneous bodies, for which we derive the field equations and the constitutive equations. Then we introduce some dimensionless quantities and establish the continuous dependence of solutions upon initial data and body loads by means of the Gronwall inequality. This extension of mechanics of generalized continua that includes both thermal and diffusion effects aims at providing a rigorous mathematical model with various possible applications in materials science, engineering and even biology.

Micropolar Thermoelasticity with Voids Using Fractional Order Strain

The chapter is dealing with the study of the thermoelasticity of the micropolar materials with voids that uses the fractional order strain, in order to determine some equations of this linear thermoelasticity theory, as well as of a reciprocity relation for the mentioned bodies. Finding the form of the constitutive equations and using them for analyzing the reciprocity, toghether with obtaining the equation of thermal conductivity under the terms of our theory is the main purpose, realizing a parallel between classical theory and this specific case, leading to a better understanding of the behaviour of these materials.

The Theory of Potential

The Newtonian potential, or the potential of volume, associated to the Laplace equation (Delta u=0) is, by definition, the following improper integral: n n