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Search Results (4)

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Keywords = dipolar thermoelastic body

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12 pages, 262 KB  
Article
Some Results in Green–Lindsay Thermoelasticity of Bodies with Dipolar Structure
by Marin Marin, Eduard M. Craciun and Nicolae Pop
Mathematics 2020, 8(4), 497; https://doi.org/10.3390/math8040497 - 2 Apr 2020
Cited by 29 | Viewed by 3410
Abstract
The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, [...] Read more.
The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive. Full article
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
14 pages, 288 KB  
Article
A Study of Deformations in a Thermoelastic Dipolar Body with Voids
by Marin Marin, Ibrahim Abbas, Sorin Vlase and Eduard M. Craciun
Symmetry 2020, 12(2), 267; https://doi.org/10.3390/sym12020267 - 9 Feb 2020
Cited by 11 | Viewed by 2590
Abstract
In this paper, we consider the mixed initial boundary value problem in the context of a thermoelastic porous body having a dipolar structure. We intend to analyze the rate of decay of solutions to this problem to ensure that in a finite time, [...] Read more.
In this paper, we consider the mixed initial boundary value problem in the context of a thermoelastic porous body having a dipolar structure. We intend to analyze the rate of decay of solutions to this problem to ensure that in a finite time, they become null. In our main result, we find that the combined contribution of the dipolar constitution of the body together with voids dissipation and thermal behavior cannot cause vanishing of the deformations in a finite time. Full article
(This article belongs to the Special Issue Composite Structures with Symmetry)
16 pages, 326 KB  
Article
On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure
by M. Marin, S. Vlase, R. Ellahi and M.M. Bhatti
Symmetry 2019, 11(7), 863; https://doi.org/10.3390/sym11070863 - 2 Jul 2019
Cited by 124 | Viewed by 4551
Abstract
We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based [...] Read more.
We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
12 pages, 253 KB  
Article
Thermoelasticity of Initially Stressed Bodies with Voids: A Domain of Influence
by Marin Marin, Mohamed I. A. Othman, Sorin Vlase and Lavinia Codarcea-Munteanu
Symmetry 2019, 11(4), 573; https://doi.org/10.3390/sym11040573 - 19 Apr 2019
Cited by 14 | Viewed by 2825
Abstract
In our study, we will extend the domain of influence in order to cover the thermoelasticity of initially stressed bodies with voids. In what follows, we prove that, for a finite time t > 0 , the displacement field u i , the [...] Read more.
In our study, we will extend the domain of influence in order to cover the thermoelasticity of initially stressed bodies with voids. In what follows, we prove that, for a finite time t > 0 , the displacement field u i , the dipolar displacement field φ j k , the temperature θ and the change in volume fraction ϕ generate no disturbance outside a bounded domain B. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
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