Page 1

Displaying 1 – 7 of 7

Showing per page

A frictional contact problem with adhesion for viscoelastic materials with long memory

Abderrezak Kasri (2021)

Applications of Mathematics

We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb's law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization...

A quasistatic contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline (2010)

Applicationes Mathematicae

We consider a mathematical model which describes the contact between a deformable body and a foundation. The contact is frictional and is modelled by a version of normal compliance condition and the associated Coulomb's law of dry friction in which adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behaviour is modelled by a nonlinear viscoelastic constitutive law. We derive a variational formulation...

A viscoelastic model with non-local damping application to the human lungs

Céline Grandmont, Bertrand Maury, Nicolas Meunier (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we elaborate a model to describe some aspects of the human lung considered as a continuous, deformable, medium. To that purpose, we study the asymptotic behavior of a spring-mass system with dissipation. The key feature of our approach is the nature of this dissipation phenomena, which is related here to the flow of a viscous fluid through a dyadic tree of pipes (the branches), each exit of which being connected to an air pocket (alvelola) delimited by two successive masses. The...

An a posteriori error analysis for dynamic viscoelastic problems

J. R. Fernández, D. Santamarina (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An a priori error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an a posteriori...

An a posteriori error analysis for dynamic viscoelastic problems

J. R. Fernández, D. Santamarina (2011)

ESAIM: Mathematical Modelling and Numerical Analysis


In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An a priori error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an a posteriori error...

Analysis of a viscoelastic antiplane contact problem with slip-dependent friction

Thierry-Vincent Hoarau-Mantel, Andaluzia Matei (2002)

International Journal of Applied Mathematics and Computer Science

We study a mathematical problem modelling the antiplane shear deformation of a viscoelastic body in frictional contact with a rigid foundation. The contact is bilateral and is modelled with a slip-dependent friction law. We present the classical formulation for the antiplane problem and write the corresponding variational formulation. Then we establish the existence of a unique weak solution to the model, by using the Banach fixed-point theorem and classical results for elliptic variational inequalities....

Analysis of crack singularities in an aging elastic material

Martin Costabel, Monique Dauge, SergeïA. Nazarov, Jan Sokolowski (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a quasistatic system involving a Volterra kernel modelling an hereditarily-elastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of cracks. In this paper, we investigate the case of a straight crack in a two-dimensional domain with a possibly anisotropic material law. We study the asymptotics of the time dependent solution near the crack tips. We prove that, depending on the regularity of the material law and the Volterra kernel,...

Currently displaying 1 – 7 of 7

Page 1