Exponential decay in one-dimensional Type II/III thermoelasticity with two porosities

In this paper we consider the theory of thermoelasticity with a double porosity structure in the context of the Green-Naghdi types II and III heat conduction models. For the type II, the problem is given by four hyperbolic equations and it is conservative (there is no energy dissipation). We introduce in the system a couple of dissipation mechanisms in order to obtain the exponential de- cay of the solutions. To be precise, we introduce a pair of the following damping mechanisms: viscoelasticity, viscoporosities and thermal dissipation. We prove that the system is exponentially stable in three different scenarios: viscoporosity in one structure jointly with thermal dissipation, viscoporosity in each structure, and viscoporosity in one structure jointly with viscoelasticity. However, if viscoelasticity and thermal dissipation are considered together, undamped solutions can be obtained.Peer ReviewedPostprint (author's final draft

State-space approach to 3D generalized thermoviscoelasticity under Green and Naghdi theory II

The present paper is aimed at studying the effects of viscosity on thermoelastic interactions in a three-dimensional homogeneous isotropic half-space solid medium whose surface is subjected to a thermal shock and is assumed to be stress free. The formulation is applied to the generalized thermoelasticity based on the GN model without energy dissipation (GN II model). The normal mode analysis together with state-space approach is used to obtain the exact analytical expressions for the field variables considered. Numerical computations are performed for a specific material and the results obtained are represented graphically. Comparisons are made within the theory in the presence and absence of viscosity effects

Anisotropy can imply exponential decay in micropolar elasticity

In this note, two problems arisen in micropolar elasticity are considered from the analytical point of view. Following the Kelvin–Voigt theory of micropolar viscoelasticity, two dissipative mechanisms are imposed: in the first problem, it is defined on the microscopic structure and, for the second problem, on the macroscopic structure. Then, an existence and uniqueness result, as well as an exponential energy decay, are proved for the first problem. Since similar arguments can be used for the second problem, only the main key points are commentedPeer ReviewedPostprint (published version

Exponential stability in three-dimensional type III thermo-porous-elasticity with microtemperatures

We study the time decay of the solutions for the type III thermoelastic theory with microtemperatures and voids. We prove that, under suitable conditions for the constitutive tensors, the solutions decay exponentially. This fact is in somehow striking because it differs from the behaviour of the solutions in the classical model of thermoelasticity with microtemperatures and voids, where the exponential decay is not expected in the general case.Peer ReviewedPostprint (author's final draft

Time decay for porosity problems

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGIn this paper, we numerically study porosity problems with three different dissipation mechanisms. The root behavior is analyzed for each case. Then, by using the finite element method and the Newmark-β scheme, fully discrete approximations are introduced and some numerical results are described to show the energy evolution depending on the viscosity coefficient.Agencia Estatal de Investigación | Ref. PGC2018‐096696‐B‐I00Agencia Estatal de Investigación | Ref. PID2019‐ 105118GB‐I0

Time decay for porosity problems

In this paper, we numerically study porosity problems with three different dissipa- tion mechanisms. The root behavior is analyzed for each case. Then, by using the finite element method and the Newmark- scheme, fully discrete approximations are introduced and some numerical results are described to show the energy evolution depending on the viscosity coefficient.Peer ReviewedPostprint (published version

Energy decay in thermoelastic bodies with radial symmetry

In this paper, we consider the energy decay of some problems involving domains with radial symmetry. Three different settings are studied: a strong porous dissipation and heat conduction, a weak porous dissipation and heat conduction and poro-thermoelasticity with microtemperatures. In all the three problems, the exponential energy decay is shown. Moreover, for each of them some finite element simulations are presented to numerically demonstrate this behaviorPeer ReviewedPostprint (published version

Decay of quasi-static porous-thermo-elastic waves

We study the behavior in time of the solutions to several systems of equations for porous-thermo-elastic problems when one of the variables is considered to be quasi-static or, in other words, whose second time derivative can be neglected. We analyze three different situations using the classical Fourier law and also the type II or type III Green–Naghdi heat conduction modelsPeer ReviewedPostprint (author's final draft