A quasistatic contact problem with directional friction and damped response

Rochdi, M.; Shillor, Meir; Sofonea, Mircea

doi:10.1080/00036819808840639

Cited by 42 publications

(38 citation statements)

References 7 publications

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“…In this problem the contact condition describes the normal damped response of a thin lubricant layer and has recently been considered in [14], [15]. The contact pressure depends on the velocity, but only under compression, and the contact conditions…”

Section: Vol 2 (2005) a Class Of Frictional Contact Problems 123mentioning

confidence: 99%

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Analysis of a Class of Frictional Contact Problems for the Bingham Fluid

Selmani

Merouani

Selmani

2005

MedJM

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We consider a mathematical model which describes the stationary flow of a Bingham fluid with friction. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive a weak formulation of the model which consists in a variational inequality for the velocity field. We establish the existence and uniqueness of the weak solution as well as its continuous dependence with respect to the contact condition. Finally, we describe a number of concrete friction conditions which may be set in this general framework and for which our results apply. Mathematics Subject Classification (2000). Primary 74M10; Secondary 74M15, 76M30.

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Section: Vol 2 (2005) a Class Of Frictional Contact Problems 123mentioning

confidence: 99%

“…Here 0 < q ≤ 1, h, k ≥ 0 and the normal contact stress depends on a power of the normal speed (this condition may describe the motion of a body, say a wheel, on a fine granular material, say the sand on the beach, see e. g. [15], [16]). …”

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confidence: 99%

Analysis of a Class of Frictional Contact Problems for the Bingham Fluid

Selmani

Merouani

Selmani

2005

MedJM

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“…In this problem the contact condition describes the normal damped response of a thin lubricant layer, and has recently been considered in [24], [25]. The contact pressure depends on the velocity, but only under compression, and the contact conditions are Here g ∈ L ∞ (Γ 3 ) and k ∈ L ∞ (Γ 3 ) are given positive functions, p 0 ∈ L ∞ (Γ 3 ) and r + = max{r, 0}.…”

Section: Examples Of Subdifferential Conditions With Frictionmentioning

confidence: 99%

“…The existence of a weak solution to the quasistatic Signorini's contact problem with friction for elastic materials has been established in [8]. The variational analysis of some quasistatic frictional contact problems can be found for instance in [24], [25], [27], within nonlinear viscoelasticity. There, the problems were formulated as evolution variational inequalities for which existence and uniqueness results were obtained.…”

Section: Introductionmentioning

confidence: 99%

Quasistatic Frictional Problems for Elastic and Viscoelastic Materials

Chau

Motreanu

Sofonea

2002

Applications of Mathematics

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“…Recent existence and uniqueness results for quasistatic contact problems can be found in [2,7,18,21,22,24], However, this paper is the first to investigate the general bilateral quasistatic contact problem in three dimensions in which the thermal effects of friction are taken into account.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness for a quasistatic frictional bilateral contact problem in thermoviscoelasticity

Rochdi¹,

Shillor²

2000

Quart. Appl. Math.

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Abstract.We prove the existence and uniqueness of the weak solution for a quasistatic thermoviscoelastic problem which describes bilateral frictional contact between a deformable body and a moving rigid foundation. The model consists of the heat equation for the temperature, the elliptic viscoelasticity system for the displacements, the SJK-Coulomb law of friction and frictional heat generation condition. The proof is accomplished in two steps. First, the existence of solutions for a regularized problem is established and a priori estimates obtained. Then the limit function, which is the weak solution of the original problem, is shown to be the unique fixed point of the solution operator when the friction coefficient is small.

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A quasistatic contact problem with directional friction and damped response

Cited by 42 publications

References 7 publications

Analysis of a Class of Frictional Contact Problems for the Bingham Fluid

Analysis of a Class of Frictional Contact Problems for the Bingham Fluid

Quasistatic Frictional Problems for Elastic and Viscoelastic Materials

Existence and uniqueness for a quasistatic frictional bilateral contact problem in thermoviscoelasticity

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