1,720,979 research outputs found
On heat-flux dependent thermopiezoelectricity of nonsimple materials
No full textA theory of thermopiezoelectricity for nonsimple materials is developed by incorporating heat flux as an independent constitutive variable. The linearized version of this theory reveals the presence of second-sound effects. A reciprocity relation which involves two processes at different times and a theorem on the uniqueness of solutions are deduced for anisotropic materials. Finally, a variational principle is established
Pollution overturning instability in an incompressible fluid with a Maxwell-Cattaneo-Mariano model for the pollutant field
No full textWe develop a model for a pollutant dissolved in or dispersed in an incompressible Navier–Stokes fluid when the diffusion theory for the pollutant obeys a second order in time system of equations rather than the first order in time system obtained from Fourier's law. A detailed analysis is performed for a layer of fluid where a pollutant is such that the top of the layer will be heavier in concentration. A detailed expression for the critical pollutant Rayleigh number is found indicating precise conditions under which a convective overturning motion will arise. The investigation is performed by a linear instability analysis, but additionally we provide a completely nonlinear energy stability analysis. Diffusion of flux is also added to a Cattaneo-like equation and this leads to surprising results
Exponential stability in Mindlin's Form II gradient thermoelasticity with microtemperatures of type III: Mindlin's II gradient thermoelastic
No full textIn this paper, we derive a nonlinear strain gradient theory of thermoelastic materials with microtemperatures taking into account micro-inertia effects as well. The elastic behaviour is assumed to be consistent with Mindlin's Form II gradient elasticity theory, while the thermal behaviour is based on the entropy balance of type III postulated by Green and Naghdi for both temperature and microtemperatures. The work is motivated by increasing use of materials having microstructure at both mechanical and thermal levels. The equations of the linear theory are also obtained. Then, we use the semigroup theory to prove the well-posedness of the obtained problem. Because of the coupling between high-order derivatives and microtemperatures, the obtained equations do not have exponential decay. A frictional damping for the elastic component, whose form depends on the micro-inertia, is shown to lead to exponential stability for the type III model
Uniform Decay for Thermoelastic Diffusion Problem of Type III with Delays
No full textIn this article, we consider a thermoelastic diffusion problem of type III in one space dimension with boundary constant delays. First we prove that the one-dimensional problem is well-posed by the semigroup theory. By introducing a suitable energy and an appropriate Lyapunov functional, we show under smallness conditions that the damping delay effect through heat and mass diffusion conduction is strong enough to uniformly stabilize the system. Moreover, our results can be extended to the case where our system is subjected to other damping functions as the time-varying delay or the distributed delay
Analytical aspects in strain gradient theory for chiral Cosserat thermoelastic materials within three Green-Naghdi models
No full textThis work is motivated by the recent interest in using strain gradient theory to model the chiral behavior of elastic materials. In this paper, we derive a linear strain gradient theory for Cosserat thermoelastic materials according to the three models (types I, II and III) of Green-Naghdi theory. Models II and III permit propagation of thermal waves at finite speeds, while model I coincides with the classical Fourier’s law. The thermal field is influenced by the displacement and the microrotation fields and by some additional parameters that describe the chiral behavior. We prove the well-posedness for the three models and the asymptotic behavior for models I and III by the semigroup theory of linear operators
Stabilization in extensible thermoelastic Timoshenko microbeam based on modified couple stress theory
No full textIn this article we derive the equations that constitute the nonlinear model of extensible thermoelastic Timoshenko microbeam. The constructed mathematical model is based on the modified couple stress theory which implies prediction of size dependent effects in microbeam resonators, by applying the Hamilton principle to full von Karman equations. This takes account of the effects of extensibility where the dissipations are entirely contributed by temperature. Based on semigroups theory, we establish existence and uniqueness of weak and strong solutions to the derived problem. By an approach based on the Gearhart-Herbst-Pruss-Huang theorem, we prove that the associated linear semigroup (without extensibility) is not analytic in general. In the absence of additional mechanical dissipations, the system is often not highly stable. Then by adding a damping frictional function to the first equation of the derived model and using the multiplier method, we show that the solutions decay exponentially under a condition on the physical coefficients
Buoyancy driven convection with a Cattaneo flux model
No full textWe review models for convective motion which have a flux law of Cattaneo type. This includes thermal convection where the heat flux law is a Cattaneo one. We additionally analyse models where the convective motion is due to a density gradient caused by a concentration of solute. The usual Fick's law in this case is replaced by a Cattaneo one involving the flux of solute and the concentration gradient. Other effects such as rotation, the presence of a magnetic field, Guyer-Krumhansl terms, or Kelvin-Voigt theories are briefly introduced
Some properties of solutions in linear theory for semi-strongly elliptic porous elastic materials
No full textThis paper is concerned with the linear theory of elastodynamics for homogeneous, isotropic, porous elastic materials with memory effects for the intrinsic equilibrated body forces. We are able to relax the conditions on constitutive coefficients and to determine the wider class of materials for which the internal energy is positive semi-definite, when boundary conditions are homogeneous. We found the class of semi-strongly elliptic porous elastic materials. For this class of materials, the above conditions may be relaxed without loss of some well-posedness properties of the solutions. In particular, we obtain uniqueness of the solutions and we study the spatial behavior problem
Analyticity of solutions to thermoviscoelastic diffusion mixtures problem in higher dimension
No full textIn this paper, we consider the linear theory of binary mixtures for thermoviscoelastic diffusion materials derived by Aouadi et al. (J Therm Stress 41:1414–1431, 2018). We establish the necessary and sufficient conditions to get a dissipation inequality for isotropic centrosymmetric materials. With the help of the semigroup theory of linear operators, we prove the well posedness of the higher-dimensional problem. Then, we show that the associated C-semigroup is analytic. Exponential stability and impossibility of localization of the solutions in time are immediate consequences
Strain gradient thermopiezoelectric materials
No full textResults from the linear theory of thermopiezoelectricity are discussed in this article. A brief introduction to dielectric materials and the phenomenon of direct and inverse piezoelectricity is given. Then, a general theory of thermopiezoelectricity for strain gradient materials is given, where the second gradient of the displacement field and electric potential enter into the set of independent constitutive variables. The second law of thermodynamics is formulated following an entropy production inequality proposed by Green and Laws. The thermodynamics restrictions are obtained, then the linear constitutive equations and the mixed initial-boundary value problem are established. On the basis of this theory, a uniqueness result and a variational principle are obtained
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