Articles de revista
http://hdl.handle.net/2117/3339
Fri, 25 Sep 2020 19:41:25 GMT2020-09-25T19:41:25ZSpatial estimates for Kelvin-Voigt finite elasticity with nonlinear viscosity: well behaved solutions in space.
http://hdl.handle.net/2117/328378
Spatial estimates for Kelvin-Voigt finite elasticity with nonlinear viscosity: well behaved solutions in space.
Quintanilla de Latorre, Ramón; Saccomandi, Giuseppe
We provide some spatial estimates for the nonlinear partial di erential equation governing anti-plane motions in a nonlinear viscoelastic theory of Kelvin-Voigt type when the viscosity is a function of the strain rate. The spatial estimates we prove are an alternative of Phragmen-Lindel of type. These estimates are possible when a precise balance between the elastic and viscoelastic nonlinearities holds
Fri, 04 Sep 2020 07:24:45 GMThttp://hdl.handle.net/2117/3283782020-09-04T07:24:45ZQuintanilla de Latorre, RamónSaccomandi, GiuseppeWe provide some spatial estimates for the nonlinear partial di erential equation governing anti-plane motions in a nonlinear viscoelastic theory of Kelvin-Voigt type when the viscosity is a function of the strain rate. The spatial estimates we prove are an alternative of Phragmen-Lindel of type. These estimates are possible when a precise balance between the elastic and viscoelastic nonlinearities holdsExponential decay of solutions in type II porous-thermo-elasticity with quasi-static microvoids
http://hdl.handle.net/2117/328352
Exponential decay of solutions in type II porous-thermo-elasticity with quasi-static microvoids
Magaña Nieto, Antonio; Miranville, Alain; Quintanilla de Latorre, Ramón
In this note we study the problem proposed by the one-dimensional thermo-porous-elasticity of type II with quasi-static microvoids or, in mathematical terms, when the second time derivative of the volume fraction is so small that it can be negligible. It is known that the isothermal deformations decay in a slow way. Here we prove that the introduction of a conservative mechanism, as it is the type II heat conduction, makes the deformations damp generically in an exponential way, which is a striking fact.
Thu, 03 Sep 2020 11:21:42 GMThttp://hdl.handle.net/2117/3283522020-09-03T11:21:42ZMagaña Nieto, AntonioMiranville, AlainQuintanilla de Latorre, RamónIn this note we study the problem proposed by the one-dimensional thermo-porous-elasticity of type II with quasi-static microvoids or, in mathematical terms, when the second time derivative of the volume fraction is so small that it can be negligible. It is known that the isothermal deformations decay in a slow way. Here we prove that the introduction of a conservative mechanism, as it is the type II heat conduction, makes the deformations damp generically in an exponential way, which is a striking fact.Numerical analysis of a type III thermo-porous-elastic problem with microtemperatures
http://hdl.handle.net/2117/328344
Numerical analysis of a type III thermo-porous-elastic problem with microtemperatures
Bazarra, Noelia; Fernández, Jose R.; Quintanilla de Latorre, Ramón
In this work, we consider, from the numerical point of view, a poro-thermoelastic problem. The thermal law is the so-called of type III and the microtemperatures are also included into the model. The variational formulation of the problem is written as a linear system of coupled first-order variational equations. Then, fully discrete approximations are introduced by using the classical finite-element method and the implicit Euler scheme. A discrete stability
property and an a priori error estimates result are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some one- and two-dimensional numerical simulations are presented to show the accuracy of the approximation and the behavior of the solution.
Thu, 03 Sep 2020 10:49:24 GMThttp://hdl.handle.net/2117/3283442020-09-03T10:49:24ZBazarra, NoeliaFernández, Jose R.Quintanilla de Latorre, RamónIn this work, we consider, from the numerical point of view, a poro-thermoelastic problem. The thermal law is the so-called of type III and the microtemperatures are also included into the model. The variational formulation of the problem is written as a linear system of coupled first-order variational equations. Then, fully discrete approximations are introduced by using the classical finite-element method and the implicit Euler scheme. A discrete stability
property and an a priori error estimates result are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some one- and two-dimensional numerical simulations are presented to show the accuracy of the approximation and the behavior of the solution.A poro-thermoelastic problem with dissipative heat conduction
http://hdl.handle.net/2117/328295
A poro-thermoelastic problem with dissipative heat conduction
Bazarra, Noelia; Fernández, Jose R.; Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
In this work, we study from the mathematical and numerical points of view a poro-thermoelastic problem. A long-term memory is assumed on the heat equation. Under some assumptions on the constitutive tensors, the resulting linear system is composed of hyperbolic partial differential equations with a dissipative mechanism in the temperature equation. An existence and uniqueness result is proved using the theory of contractive semigroups.
Then, a fully discrete approximation is introduced applying the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is obtained. A priori error estimates are also shown, from which the linear convergence of the approximation is derived under suitable additional regularity conditions. Finally, one- and two-numerical simulations are presented to demonstrate the accuracy of the algorithm and the behavior of the solution.
Wed, 02 Sep 2020 11:32:04 GMThttp://hdl.handle.net/2117/3282952020-09-02T11:32:04ZBazarra, NoeliaFernández, Jose R.Magaña Nieto, AntonioQuintanilla de Latorre, RamónIn this work, we study from the mathematical and numerical points of view a poro-thermoelastic problem. A long-term memory is assumed on the heat equation. Under some assumptions on the constitutive tensors, the resulting linear system is composed of hyperbolic partial differential equations with a dissipative mechanism in the temperature equation. An existence and uniqueness result is proved using the theory of contractive semigroups.
Then, a fully discrete approximation is introduced applying the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is obtained. A priori error estimates are also shown, from which the linear convergence of the approximation is derived under suitable additional regularity conditions. Finally, one- and two-numerical simulations are presented to demonstrate the accuracy of the algorithm and the behavior of the solution.Two-temperatures thermo-porous-elasticity with microtemperatures
http://hdl.handle.net/2117/327968
Two-temperatures thermo-porous-elasticity with microtemperatures
Fernández, Jose R.; Quintanilla de Latorre, Ramón
In this note, we study a linear system of partial differential equations modelling a one-dimensional two-temperatures thermo-porous-elastic problem with microtemperatures. A new system of conditions is proposed to guarantee the existence, uniqueness and exponential decay of solutions. Our arguments are based on the theory of semigroups of linear operators.
Wed, 29 Jul 2020 10:40:05 GMThttp://hdl.handle.net/2117/3279682020-07-29T10:40:05ZFernández, Jose R.Quintanilla de Latorre, RamónIn this note, we study a linear system of partial differential equations modelling a one-dimensional two-temperatures thermo-porous-elastic problem with microtemperatures. A new system of conditions is proposed to guarantee the existence, uniqueness and exponential decay of solutions. Our arguments are based on the theory of semigroups of linear operators.An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures
http://hdl.handle.net/2117/327958
An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures
Baldonado, Jacobo; Bazarra, Noelia; Fernández, Jose R.; Quintanilla de Latorre, Ramón
In this paper, we deal with the numerical analysis of the Lord–Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacement field and the volume fraction, the temperature and the microtemperatures. An existence and uniqueness result is stated. Then, a fully discrete approximation is introduced using the finite element method and the implicit Euler scheme. A discrete stability property is shown, and an a priori error analysis is provided, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation, the comparison with the classical Fourier theory and the behavior of the solution in two-dimensional examples.
Wed, 29 Jul 2020 10:07:43 GMThttp://hdl.handle.net/2117/3279582020-07-29T10:07:43ZBaldonado, JacoboBazarra, NoeliaFernández, Jose R.Quintanilla de Latorre, RamónIn this paper, we deal with the numerical analysis of the Lord–Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacement field and the volume fraction, the temperature and the microtemperatures. An existence and uniqueness result is stated. Then, a fully discrete approximation is introduced using the finite element method and the implicit Euler scheme. A discrete stability property is shown, and an a priori error analysis is provided, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation, the comparison with the classical Fourier theory and the behavior of the solution in two-dimensional examples.Moore-Gibson-Thompson thermoelasticity with two temperatures
http://hdl.handle.net/2117/327481
Moore-Gibson-Thompson thermoelasticity with two temperatures
Quintanilla de Latorre, Ramón
In this note we propose the Moore-Gibson-Thompson heat conduction equation with two temperatures and prove the well posedness and the exponential decay of the solutions under suitable conditions on the constitutive parameters. Later we consider the extension to the Moore-Gibson-Thompson thermoelasticity with two temperatures and prove that we cannot expect for the exponential stability even in the one-dimensional case. This last result contrasts with the one obtained for the Moore-Gibson-Thompson thermoelasticity where the exponential decay was obtained. However we prove the polynomial decay of the solutions. The paper concludes by giving the main ideas to extend the theory for inhomogeneous and anisotropic materials.
Thu, 23 Jul 2020 11:21:36 GMThttp://hdl.handle.net/2117/3274812020-07-23T11:21:36ZQuintanilla de Latorre, RamónIn this note we propose the Moore-Gibson-Thompson heat conduction equation with two temperatures and prove the well posedness and the exponential decay of the solutions under suitable conditions on the constitutive parameters. Later we consider the extension to the Moore-Gibson-Thompson thermoelasticity with two temperatures and prove that we cannot expect for the exponential stability even in the one-dimensional case. This last result contrasts with the one obtained for the Moore-Gibson-Thompson thermoelasticity where the exponential decay was obtained. However we prove the polynomial decay of the solutions. The paper concludes by giving the main ideas to extend the theory for inhomogeneous and anisotropic materials.Analysis of a Moore-Gibson-Thompson thermoelastic problem
http://hdl.handle.net/2117/327455
Analysis of a Moore-Gibson-Thompson thermoelastic problem
Bazarra, Noelia; Fernández, Jose R.; Quintanilla de Latorre, Ramón
In this work, we numerically consider a thermoelastic problem where the thermal law is modeled using the so-called Moore-Gibson-Thompson equation. This thermomechanical problem is written as a coupled system composed of a hyperbolic partial differential equation for a transformation of the displacement field and a parabolic partial differential equation for a transformation of the temperature. Its variational formulation is written in terms of the derivatives of the above transformed functions, leading to a coupled linear system made of two first-order variational equations. Then, a fully discrete algorithm is introduced and a discrete stability property is proved. A priori error estimates are also provided, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical results are shown, including the numerical convergence of the approximations, comparisons with the Lord-Shulman and type III Green–Naghdi theories, and two-dimensional examples which demonstrate the behavior of the solution.
Thu, 23 Jul 2020 09:35:35 GMThttp://hdl.handle.net/2117/3274552020-07-23T09:35:35ZBazarra, NoeliaFernández, Jose R.Quintanilla de Latorre, RamónIn this work, we numerically consider a thermoelastic problem where the thermal law is modeled using the so-called Moore-Gibson-Thompson equation. This thermomechanical problem is written as a coupled system composed of a hyperbolic partial differential equation for a transformation of the displacement field and a parabolic partial differential equation for a transformation of the temperature. Its variational formulation is written in terms of the derivatives of the above transformed functions, leading to a coupled linear system made of two first-order variational equations. Then, a fully discrete algorithm is introduced and a discrete stability property is proved. A priori error estimates are also provided, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical results are shown, including the numerical convergence of the approximations, comparisons with the Lord-Shulman and type III Green–Naghdi theories, and two-dimensional examples which demonstrate the behavior of the solution.On the analyticity of the MGT-viscoelastic plate with heat conduction
http://hdl.handle.net/2117/192903
On the analyticity of the MGT-viscoelastic plate with heat conduction
Conti, Monica; Pata, Vittorino; Pellicer, Marta; Quintanilla de Latorre, Ramón
We consider a viscoelastic plate equation of Moore-Gibson-Thompson type coupled with two different kinds of thermal laws, namely, the usual Fourier one and the heat conduction law of type III. In both cases, the resulting system is shown to generate a contraction semigroup of solutions on a suitable Hilbert space. Then we prove that these semigroups are analytic, despite the fact that the semigroup generated by the mechanical equation alone does not share the same property. This means that the coupling with the heat equation produces a regularizing effect on the dynamics, implying in particular the impossibility of the localization of solutions. As a byproduct of our main result, the exponential stability of the semigroups is established.
Mon, 13 Jul 2020 12:13:55 GMThttp://hdl.handle.net/2117/1929032020-07-13T12:13:55ZConti, MonicaPata, VittorinoPellicer, MartaQuintanilla de Latorre, RamónWe consider a viscoelastic plate equation of Moore-Gibson-Thompson type coupled with two different kinds of thermal laws, namely, the usual Fourier one and the heat conduction law of type III. In both cases, the resulting system is shown to generate a contraction semigroup of solutions on a suitable Hilbert space. Then we prove that these semigroups are analytic, despite the fact that the semigroup generated by the mechanical equation alone does not share the same property. This means that the coupling with the heat equation produces a regularizing effect on the dynamics, implying in particular the impossibility of the localization of solutions. As a byproduct of our main result, the exponential stability of the semigroups is established.Analysis of a thermoelastic problem of type III
http://hdl.handle.net/2117/190455
Analysis of a thermoelastic problem of type III
Bazarra, Noelia; Fernández, Jose R.; Quintanilla de Latorre, Ramón
This paper investigates several aspects of the linear type III thermoelastic theory. First, we consider the most general system of equations for this theory in the case that the conductivity rate is not definite and we prove an existence theorem by means of the semigroups theory. In fact, we show that the solutions of the problem generate a quasi-contractive semigroup. Then, assuming that the internal energy is positive definite, the numerical analysis of this problem is performed, by using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property and a priori error estimates are shown, from which the linear convergence of the algorithm is deduced. Finally, some one- and two-dimensional numerical simulations are presented, for the homogeneous and isotropic case, to demonstrate the accuracy of the approximation and the behaviour of the solution.
Wed, 10 Jun 2020 12:01:20 GMThttp://hdl.handle.net/2117/1904552020-06-10T12:01:20ZBazarra, NoeliaFernández, Jose R.Quintanilla de Latorre, RamónThis paper investigates several aspects of the linear type III thermoelastic theory. First, we consider the most general system of equations for this theory in the case that the conductivity rate is not definite and we prove an existence theorem by means of the semigroups theory. In fact, we show that the solutions of the problem generate a quasi-contractive semigroup. Then, assuming that the internal energy is positive definite, the numerical analysis of this problem is performed, by using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property and a priori error estimates are shown, from which the linear convergence of the algorithm is deduced. Finally, some one- and two-dimensional numerical simulations are presented, for the homogeneous and isotropic case, to demonstrate the accuracy of the approximation and the behaviour of the solution.