Displaying similar documents to “On the frictionless unilateral contact of two viscoelastic bodies.”

Quasistatic frictional problems for elastic and viscoelastic materials

Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)

Applications of Mathematics

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We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution...

Analysis and numerical approximation of an elastic frictional contact problem with normal compliance

Weimin Han, Mircea Sofonea (1999)

Applicationes Mathematicae

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We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show...

Numerical analysis of a frictionless viscoelastic piezoelectric contact problem

Mikael Barboteu, Jose Ramon Fernández, Youssef Ouafik (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete...

A frictional contact problem with wear and damage for electro-viscoelastic materials

Mohamed Selmani, Lynda Selmani (2010)

Applications of Mathematics

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We consider a quasistatic contact problem for an electro-viscoelastic body. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We present a weak formulation for the model and establish existence and uniqueness results. The proofs are based on classical results for elliptic...

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

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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...

Quasistatic problems in contact mechanics

Meir Shillor (2001)

International Journal of Applied Mathematics and Computer Science

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We describe some of our recent results concerning the modeling and analysis of quasistatic contact problems between a deformable body and a foundation. We concentrate mainly on frictional contact, and in some of the problems thermal effects and the wear of the contacting surfaces are also taken into account. We describe the physical processes involved, the mathematical models, their variational formulation and then present statements of our results. We conclude with a description of...

A viscoelastic contact problem with normal damped response and friction

B. Awbi, El H. Essoufi, M. Sofonea (2000)

Annales Polonici Mathematici

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We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions.