GRAA - Grup de Recerca en Anàlisi Aplicada
http://hdl.handle.net/2117/3338
Thu, 25 Feb 2021 17:39:45 GMT2021-02-25T17:39:45ZOn the quasi-static approximation in the initial boundary value problem of linearised elastodynamics
http://hdl.handle.net/2117/336991
On the quasi-static approximation in the initial boundary value problem of linearised elastodynamics
Knops, Robin J.; Quintanilla de Latorre, Ramón
Continuous data dependence estimates are employed to rigorously derive conditions that validate the quasi-static approximation for the initial homogeneous boundary value problem in the theory of small elastic deformations superposed upon large elastic deformations. This theory imposes no sign-definite assumptions on the linearised elastic moduli and in consequence the requisite estimates are established using methods principally motivated by known Lagrange identity arguments
Fri, 05 Feb 2021 11:05:54 GMThttp://hdl.handle.net/2117/3369912021-02-05T11:05:54ZKnops, Robin J.Quintanilla de Latorre, RamónContinuous data dependence estimates are employed to rigorously derive conditions that validate the quasi-static approximation for the initial homogeneous boundary value problem in the theory of small elastic deformations superposed upon large elastic deformations. This theory imposes no sign-definite assumptions on the linearised elastic moduli and in consequence the requisite estimates are established using methods principally motivated by known Lagrange identity argumentsMoore-Gibson-Thompson theory for thermoelastic dielectrics
http://hdl.handle.net/2117/335985
Moore-Gibson-Thompson theory for thermoelastic dielectrics
Fernández, José Ramón; Quintanilla de Latorre, Ramón
We consider the system of equations determining the linear thermoelastic deformations of dielectrics within the recently called Moore-Gibson-Thompson (MGT) theory. First, we obtain the system of equations for such a case. Second, we consider the case of a rigid solid and show the existence and the exponential decay of solutions. Third, we consider the thermoelastic case and obtain the existence and the stability of the solutions. Exponential decay of solutions in the one-dimensional case is also recalled
Tue, 26 Jan 2021 10:08:57 GMThttp://hdl.handle.net/2117/3359852021-01-26T10:08:57ZFernández, José RamónQuintanilla de Latorre, RamónWe consider the system of equations determining the linear thermoelastic deformations of dielectrics within the recently called Moore-Gibson-Thompson (MGT) theory. First, we obtain the system of equations for such a case. Second, we consider the case of a rigid solid and show the existence and the exponential decay of solutions. Third, we consider the thermoelastic case and obtain the existence and the stability of the solutions. Exponential decay of solutions in the one-dimensional case is also recalledA type III thermoelastic problem with mixtures
http://hdl.handle.net/2117/335976
A type III thermoelastic problem with mixtures
Bazarra, Noelia; Fernández, Jose R.; Quintanilla de Latorre, Ramón
In this work we study a thermoelastic problem involving binary mixtures. Type III thermal theory is considered for the modeling of the heat conduction. Existence, uniqueness and continuous dependence of solutions are proved by using the semigroup theory. Then, the numerical analysis of the resulting variational problem is considered, by using the finite element method for the spatial approximation and the implicit Euler scheme to discretize the time derivatives. An a priori error analysis is performed and the linear convergence is derived under adequate additional regularity conditions. Finally, some numerical examples involving one- and two-dimensional examples are shown to demonstrate the convergence of the approximations and the behavior of the solution
Tue, 26 Jan 2021 09:06:10 GMThttp://hdl.handle.net/2117/3359762021-01-26T09:06:10ZBazarra, NoeliaFernández, Jose R.Quintanilla de Latorre, RamónIn this work we study a thermoelastic problem involving binary mixtures. Type III thermal theory is considered for the modeling of the heat conduction. Existence, uniqueness and continuous dependence of solutions are proved by using the semigroup theory. Then, the numerical analysis of the resulting variational problem is considered, by using the finite element method for the spatial approximation and the implicit Euler scheme to discretize the time derivatives. An a priori error analysis is performed and the linear convergence is derived under adequate additional regularity conditions. Finally, some numerical examples involving one- and two-dimensional examples are shown to demonstrate the convergence of the approximations and the behavior of the solutionSpatial 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.