Displaying similar documents to “A quasistatic contact problem with unilateral constraint and slip-dependent friction”

Quasistatic frictional problems for elastic and viscoelastic materials

Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)

Applications of Mathematics

Similarity:

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...

Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion

Marius Cocu, Rémi Rocca (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We consider a two dimensional elastic body submitted to unilateral contact conditions, local friction and adhesion on a part of his boundary. After discretizing the variational formulation with respect to time we use a smoothing technique to approximate the friction term by an auxiliary problem. A shifting technique enables us to obtain the existence of incremental solutions with bounds independent of the regularization parameter. We finally obtain the existence of a quasistatic...

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

Weimin Han, Mircea Sofonea (1999)

Applicationes Mathematicae

Similarity:

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...

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

Abderrezak Kasri (2021)

Applications of Mathematics

Similarity:

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 study of a unilateral and adhesive contact problem with normal compliance

Arezki Touzaline (2014)

Applicationes Mathematicae

Similarity:

The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational...

A frictionless contact problem for elastic-viscoplastic materials with internal state variable

Lynda Selmani (2013)

Applicationes Mathematicae

Similarity:

We study a mathematical model for frictionless contact between an elastic-viscoplastic body and a foundation. We model the material with a general elastic-viscoplastic constitutive law with internal state variable and the contact with a normal compliance condition. We derive a variational formulation of the model. We establish existence and uniqueness of a weak solution, using general results on first order nonlinear evolution equations with monotone operators and fixed point arguments....

Frictionless contact problem with adhesion and finite penetration for elastic materials

Arezki Touzaline (2010)

Annales Polonici Mathematici

Similarity:

The paper deals with the problem of quasistatic frictionless contact between an elastic body and a foundation. The elasticity operator is assumed to vanish for zero strain, to be Lipschitz continuous and strictly monotone with respect to the strain as well as Lebesgue measurable on the domain occupied by the body. The contact is modelled by normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. In this problem we take into account adhesion...