Qualitative results for a mixture of Green-Lindsay thermoelastic solids

We study qualitative properties of the solutions of the system of partial differential equations modeling thermomechanical deformations for mixtures of thermoelastic solids when the theory of Green and Lindsay for the heat conduction is considered. Three dissipation mechanisms are proposed in the system: thermal dissipation, viscosity e ects on one constituent of the mixture and damping in the relative velocity of the two displacements of both constituents. First, we prove the existence and uniqueness of the solutions. Later we prove the exponential stability of the solutions over the time. We use the semigroup arguments to establish our resultsPeer ReviewedPostprint (author's final draft

Decay of solutions for strain gradient mixtures

We study antiplane shear deformations for isotropic and homogeneous strain gradient mixtures of the Kelvin-Voigt type in a cylinder. Our aim is to analyze the behaviour of the solutions with respect to the time variable when a dissipative structural mechanism is considered. We study three different cases, each at a time. For each case we prove existence and uniqueness of solutions. We obtain the exponential decay of the solutions in the hyperviscosity and viscosity cases. Exponential decay is also expected when the dissipation is generated by the relative velocity (in the generic case, although a particular combination of the constitutive parameters leads to slow decay). These results are proved with the help of the theory of semigroupsPeer ReviewedPostprint (published version

A problem with viscoelastic mixtures: numerical analysis and computational experiments

In this paper, we study, from the numerical point of view, a dynamic problem involving a mixture of two viscoelastic solids. The mechanical problem is written as a system of two coupled partial differential equations. Its variational formulation is derived and an existence and uniqueness result, and an energy decay property, are recalled. Then, fully discrete approximations are introduced by using the classical finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are shown, from which we deduce the linear convergence of the algorithm. Finally, some numerical simulations, including examples in one and two dimensions, are presented to show the accuracy of the approximation and the behaviour of the solution.Peer ReviewedPostprint (author's final draft

On the viscoelastic mixtures of solids

The final publication is available at link.springer.com via https://doi.org/10.1007/s00245-017-9439-8In this paper we analyze an homogeneous and isotropic mixture of viscoelastic solids. We propose conditions to guarantee the coercivity of the internal energy and also of the dissipation, first in dimension two and later in dimension three. We obtain an uniqueness result for the solutions when the dissipation is positive and without any hypothesis over the internal energy. When the internal energy and the dissipation are both positive, we prove the existence of solutions as well as their analyticity. Exponential stability and impossibility of localization of the solutions are immediate consequences.Peer ReviewedPostprint (author's final draft

Articles indexats publicats per investigadors del Campus de Terrassa: 2013

Aquest informe recull els 228 treballs publicats per 177 investigadors/es del Campus de Terrassa en revistes indexades al Journal Citation Report durant el 2013Preprin

Decay of solutions for a mixture of thermoelastic one dimensional solids

We study a PDE system modeling thermomechanical deformations for a mixture of thermoelastic solids. In particular we investigate the asymptotic behavior of the solutions. First, we identify conditions on the constitutive coefficients to guarantee that the imaginary axis is contained in the resolvent. Subsequently, we find the necessary and sufficient conditions to guarantee the exponential decay of solutions. When the decay is not of exponential type, we prove that the solutions decay polynomially and we find the optimal polynomial decay rate.Peer Reviewe

Decay of solutions for a mixture of thermoelastic one dimensional solids

We study a PDE system modeling thermomechanical deformations for a mixture of thermoelastic solids. In particular we investigate the asymptotic behavior of the solutions. First, we identify conditions on the constitutive coefficients to guarantee that the imaginary axis is contained in the resolvent. Subsequently, we find the necessary and sufficient conditions to guarantee the exponential decay of solutions. When the decay is not of exponential type, we prove that the solutions decay polynomially and we find the optimal polynomial decay rate.Peer Reviewe