Articles de revista
http://hdl.handle.net/2117/3339
Wed, 25 May 2016 07:30:16 GMT2016-05-25T07:30:16ZOn chiral effects in strain gradient elasticity
http://hdl.handle.net/2117/84128
On chiral effects in strain gradient elasticity
Iesan, Dorin; Quintanilla de Latorre, Ramón
This paper is concerned with the problem of uniformly loaded bars in strain gradient elasticity. We study the deformation of an isotropic chiral bar subjected to body forces, to tractions on the lateral surface and to resultant forces and moments on the ends. Examples of chiral materials include some auxetic materials, bones, some honeycomb structures, as well as composites with inclusions. The three-dimensional problem is reduced to the study of some generalized plane strain problems. The method is used to study the deformation of a uniformly loaded circular cylinder. New chiral effects are presented. The flexure of a chiral cylinder, in contrast with the case of achiral materials, is accompanied by extension and bending. The salient feature of the solution is that a uniform pressure acting on the lateral surface of a chiral circular elastic cylinder produces a twist around its axis.
Thu, 10 Mar 2016 11:28:00 GMThttp://hdl.handle.net/2117/841282016-03-10T11:28:00ZIesan, DorinQuintanilla de Latorre, RamónThis paper is concerned with the problem of uniformly loaded bars in strain gradient elasticity. We study the deformation of an isotropic chiral bar subjected to body forces, to tractions on the lateral surface and to resultant forces and moments on the ends. Examples of chiral materials include some auxetic materials, bones, some honeycomb structures, as well as composites with inclusions. The three-dimensional problem is reduced to the study of some generalized plane strain problems. The method is used to study the deformation of a uniformly loaded circular cylinder. New chiral effects are presented. The flexure of a chiral cylinder, in contrast with the case of achiral materials, is accompanied by extension and bending. The salient feature of the solution is that a uniform pressure acting on the lateral surface of a chiral circular elastic cylinder produces a twist around its axis.Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation
http://hdl.handle.net/2117/84039
Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation
Iesan, Dorin; Quintanilla de Latorre, Ramón
In this paper, we use the Green–Naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of Cosserat thermoelastic bodies. The theory is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor. The constitutive equations for isotropic chiral thermoelastic materials are presented. In this case, in contrast with the classical Cosserat thermoelasticity, a thermal field produces a microrotation of the particles. The thermal field is influenced by the displacement and microrotation fields even in the equilibrium theory. Existence and uniqueness results are established. The theory is used to study the effects of a concentrated heat source in an unbounded homogeneous and isotropic chiral solid.
Wed, 09 Mar 2016 12:26:43 GMThttp://hdl.handle.net/2117/840392016-03-09T12:26:43ZIesan, DorinQuintanilla de Latorre, RamónIn this paper, we use the Green–Naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of Cosserat thermoelastic bodies. The theory is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor. The constitutive equations for isotropic chiral thermoelastic materials are presented. In this case, in contrast with the classical Cosserat thermoelasticity, a thermal field produces a microrotation of the particles. The thermal field is influenced by the displacement and microrotation fields even in the equilibrium theory. Existence and uniqueness results are established. The theory is used to study the effects of a concentrated heat source in an unbounded homogeneous and isotropic chiral solid.Exponential decay in nonsimple thermoelasticity of type III
http://hdl.handle.net/2117/83497
Exponential decay in nonsimple thermoelasticity of type III
Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
This paper deals with the model proposed for nonsimple materials
with heat conduction of type III.We analyze rst the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.
This is the peer reviewed version of the following article: Magaña, A., and Quintanilla, R. (2016) Exponential decay in nonsimple thermoelasticity of type III. Math. Meth. Appl. Sci., 39: 225–235. doi: 10.1002/mma.3472, which has been published in final form at http://dx.doi.org/10.1002/mma.3472. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
Fri, 26 Feb 2016 13:13:35 GMThttp://hdl.handle.net/2117/834972016-02-26T13:13:35ZMagaña Nieto, AntonioQuintanilla de Latorre, RamónThis paper deals with the model proposed for nonsimple materials
with heat conduction of type III.We analyze rst the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.Decay of solutions for a mixture of thermoelastic solids with different temperatures
http://hdl.handle.net/2117/83494
Decay of solutions for a mixture of thermoelastic solids with different temperatures
Muñoz Rivera, Jaime E.; Naso, Maria Grazia; Quintanilla de Latorre, Ramón
We study a system modeling thermomechanical deformations for mixtures of thermoelastic solids with two different temperatures, that is, when each component of the mixture has its own temperature. In particular, we investigate the asymptotic behavior of the related solutions. We prove the exponential stability of solutions for a generic class of materials. In case of the coupling matrix View the MathML source being singular, we find that in general the corresponding semigroup is not exponentially stable. In this case we obtain that the corresponding solution decays polynomially as t-1/2 in case of Neumann boundary condition. Additionally, we show that the rate of decay is optimal. For Dirichlet boundary condition, we prove that the rate of decay is t-1/6. Finally, we demonstrate the impossibility of time-localization of solutions in case that two coefficients (related with the thermal conductivity constants) agree.
Fri, 26 Feb 2016 12:23:01 GMThttp://hdl.handle.net/2117/834942016-02-26T12:23:01ZMuñoz Rivera, Jaime E.Naso, Maria GraziaQuintanilla de Latorre, RamónWe study a system modeling thermomechanical deformations for mixtures of thermoelastic solids with two different temperatures, that is, when each component of the mixture has its own temperature. In particular, we investigate the asymptotic behavior of the related solutions. We prove the exponential stability of solutions for a generic class of materials. In case of the coupling matrix View the MathML source being singular, we find that in general the corresponding semigroup is not exponentially stable. In this case we obtain that the corresponding solution decays polynomially as t-1/2 in case of Neumann boundary condition. Additionally, we show that the rate of decay is optimal. For Dirichlet boundary condition, we prove that the rate of decay is t-1/6. Finally, we demonstrate the impossibility of time-localization of solutions in case that two coefficients (related with the thermal conductivity constants) agree.Spatial behaviour in thermoelastostatic cylinders of indefinitely increasing cross-section
http://hdl.handle.net/2117/78647
Spatial behaviour in thermoelastostatic cylinders of indefinitely increasing cross-section
Knops, Robin J.; Quintanilla de Latorre, Ramón
Alternative growth and decay estimates, reminiscent of the classical Phragmén-Lindelöf principle, are derived for a linearised thermoelastic body whose plane crosssections increase unboundedly with respect to a given direction. The proof uses a modified Poincaré inequality to construct a differential inequality for a weighted linear combination
of the cross-sectional mechanical and thermal energy fluxes. Decay estimates are deduced also for the cross-sectional mean square measures of the displacement and temperature. An explicit upper bound in terms of base data is established for the amplitude occurring in the decay estimates.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10659-015-9523-8
Mon, 02 Nov 2015 14:30:12 GMThttp://hdl.handle.net/2117/786472015-11-02T14:30:12ZKnops, Robin J.Quintanilla de Latorre, RamónAlternative growth and decay estimates, reminiscent of the classical Phragmén-Lindelöf principle, are derived for a linearised thermoelastic body whose plane crosssections increase unboundedly with respect to a given direction. The proof uses a modified Poincaré inequality to construct a differential inequality for a weighted linear combination
of the cross-sectional mechanical and thermal energy fluxes. Decay estimates are deduced also for the cross-sectional mean square measures of the displacement and temperature. An explicit upper bound in terms of base data is established for the amplitude occurring in the decay estimates.Spatial behavior for solutions in heat conduction with two delays
http://hdl.handle.net/2117/77992
Spatial behavior for solutions in heat conduction with two delays
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
In this note, we investigate the spatial behavior of the solutions of the equation proposed to describe a theory for the heat conduction with two delay terms. We obtain an alternative of the Phragmén-Lindelöf type, which means that the solutions either decay or blow-up at infinity, both options in an exponential way. We also describe how to obtain an upper bound for the amplitude term. This is the first contribution on spatial behavior for partial differential equations involving two delay terms. We use energy arguments. The main point of the contribution is the use of an exponentially weighted energy function.
Tue, 20 Oct 2015 15:32:43 GMThttp://hdl.handle.net/2117/779922015-10-20T15:32:43ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónIn this note, we investigate the spatial behavior of the solutions of the equation proposed to describe a theory for the heat conduction with two delay terms. We obtain an alternative of the Phragmén-Lindelöf type, which means that the solutions either decay or blow-up at infinity, both options in an exponential way. We also describe how to obtain an upper bound for the amplitude term. This is the first contribution on spatial behavior for partial differential equations involving two delay terms. We use energy arguments. The main point of the contribution is the use of an exponentially weighted energy function.On the time decay of solutions in micropolar viscoelasticity
http://hdl.handle.net/2117/76207
On the time decay of solutions in micropolar viscoelasticity
Leseduarte Milán, María Carme; Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
This paper deals with isotropic micropolar viscoelastic materials.
It can be said that that kind of materials have two internal structures: the
macrostructure, where the elasticity effects are noticed, and the microstructure,
where the polarity of the material points allows them to rotate. We introduce,
step by step, dissipation mechanisms in both structures, obtain the corresponding
system of equations and determine the behavior of its solutions with respect the
time.
The final publication is available at Springer via http://dx.doi.org/10.1007/s11012-015-0117-0
Mon, 20 Jul 2015 07:18:57 GMThttp://hdl.handle.net/2117/762072015-07-20T07:18:57ZLeseduarte Milán, María CarmeMagaña Nieto, AntonioQuintanilla de Latorre, RamónThis paper deals with isotropic micropolar viscoelastic materials.
It can be said that that kind of materials have two internal structures: the
macrostructure, where the elasticity effects are noticed, and the microstructure,
where the polarity of the material points allows them to rotate. We introduce,
step by step, dissipation mechanisms in both structures, obtain the corresponding
system of equations and determine the behavior of its solutions with respect the
time.A generalization of the Allen–Cahn equation
http://hdl.handle.net/2117/27478
A generalization of the Allen–Cahn equation
Miranville, Alain; Quintanilla de Latorre, Ramón
Our aim in this paper is to study generalizations of the Allen–Cahn equation based on a modification of the Ginzburg–Landau free energy proposed in S. Torabi et al. (2009, A new phase-field model for strongly anisotropic systems. Proc. R. Soc. A, 465, 1337–1359). In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor. Furthermore, we study the convergence to the Allen–Cahn equation, when the Willmore regularization goes to zero. We finally study the spatial behaviour of solutions in a semi-infinite cylinder, assuming that such solutions exist.
This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record: Miranville, A.; Quintanilla, R. A generalization of the Allen–Cahn equation. "IMA Journal of Applied Mathematics", 01 Abril 2015, vol. 80, núm. 2, p. 410-430 is available online at:http://imamat.oxfordjournals.org/content/80/2/410.
Tue, 21 Apr 2015 13:31:16 GMThttp://hdl.handle.net/2117/274782015-04-21T13:31:16ZMiranville, AlainQuintanilla de Latorre, RamónOur aim in this paper is to study generalizations of the Allen–Cahn equation based on a modification of the Ginzburg–Landau free energy proposed in S. Torabi et al. (2009, A new phase-field model for strongly anisotropic systems. Proc. R. Soc. A, 465, 1337–1359). In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor. Furthermore, we study the convergence to the Allen–Cahn equation, when the Willmore regularization goes to zero. We finally study the spatial behaviour of solutions in a semi-infinite cylinder, assuming that such solutions exist.Lower bounds of end effects for a nonhomogeneous isotropic linear elastic solid in anti-plane shear
http://hdl.handle.net/2117/26875
Lower bounds of end effects for a nonhomogeneous isotropic linear elastic solid in anti-plane shear
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
In this paper we give lower bounds for the spatial decay of the solutions for anti-plane shear deformations in the case of
isotropic inhomogeneous elastic materials. We first consider the case when the shear modulus only depends on the lateral
direction. By means of the logarithmic convexity arguments we obtain the required estimates. Some pictures illustrate
our results. We also study the general inhomogeneity. We give some lower bounds whenever shear modulus
satisfies several requirements.
Thu, 19 Mar 2015 18:59:40 GMThttp://hdl.handle.net/2117/268752015-03-19T18:59:40ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónIn this paper we give lower bounds for the spatial decay of the solutions for anti-plane shear deformations in the case of
isotropic inhomogeneous elastic materials. We first consider the case when the shear modulus only depends on the lateral
direction. By means of the logarithmic convexity arguments we obtain the required estimates. Some pictures illustrate
our results. We also study the general inhomogeneity. We give some lower bounds whenever shear modulus
satisfies several requirements.Spatial stability in linear thermoelasticity
http://hdl.handle.net/2117/26874
Spatial stability in linear thermoelasticity
Knops, Robin J.; Quintanilla de Latorre, Ramón
Uniqueness and spatial stability are investigated for smooth solutions to boundary value
problems in non-classical linearised and linear thermoelasticity subject to certain conditions
on material coefficients. Uniqueness is derived for standard boundary conditions
on bounded regions using a generalisation of Kirchhoff’s method. Spatial stability is discussed
for the semi-infinite prismatic cylinder in the absence of specified axial asymptotic
behaviour. Alternative growth and decay estimates are established principally for the
cross-sectional energy flux that is shown to satisfy a first order differential inequality.
Uniqueness in the class of solutions with bounded energy follows as a corollary.
Separate discussion is required for the linearised and linear theories. Although the general
approach is similar for both theories, the argument must be considerably modified for
the treatment of the linear theory.
Thu, 19 Mar 2015 18:33:43 GMThttp://hdl.handle.net/2117/268742015-03-19T18:33:43ZKnops, Robin J.Quintanilla de Latorre, RamónUniqueness and spatial stability are investigated for smooth solutions to boundary value
problems in non-classical linearised and linear thermoelasticity subject to certain conditions
on material coefficients. Uniqueness is derived for standard boundary conditions
on bounded regions using a generalisation of Kirchhoff’s method. Spatial stability is discussed
for the semi-infinite prismatic cylinder in the absence of specified axial asymptotic
behaviour. Alternative growth and decay estimates are established principally for the
cross-sectional energy flux that is shown to satisfy a first order differential inequality.
Uniqueness in the class of solutions with bounded energy follows as a corollary.
Separate discussion is required for the linearised and linear theories. Although the general
approach is similar for both theories, the argument must be considerably modified for
the treatment of the linear theory.