A quasistatic contact problem with slip-dependent coefficient of friction

Amassad, Amina; Shillor, Meir; Sofonea, Mircea

doi:10.1002/(sici)1099-1476(199902)22:3<267::aid-mma40>3.0.co;2-a

Cited by 20 publications

(3 citation statements)

References 15 publications

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“…Moreover several extensions of this work could lead to new interesting problems. In particular the study of the relation between these nonuniqueness results and the uniqueness of the solutions in quasistatic frictional contact problems for viscoelastic materials (see, e.g., [2,15]) as well as the generalization to the three-dimensional case.…”

Section: Resultsmentioning

confidence: 99%

“…The boundary Γ of Ω is assumed to be Lipschitz and is divided as follows: Γ =Γ D ∪Γ N ∪Γ C , where Γ D , Γ N and Γ C are three open disjoint parts with meas(Γ D ) > 0. The given displacements U are prescribed on the portion Γ D , the part Γ N is subjected to a density of surface forces denoted F ∈ (L 2 (Γ N )) 2 and Ω is being acted upon by the body forces f ∈ (L 2 (Ω)) 2 . On the part Γ C the body can come into contact with a rigid foundation.…”

Section: Introduction and Problem Set-upmentioning

confidence: 99%

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On solution multiplicity in friction problems with normal compliance

Hild

Sakki

2004

Journal of Mathematical Analysis and Applications

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This work is concerned with the normal compliance model and friction in linear elastostatics. We consider the two-dimensional sliding problem and we seek those interface parameters leading to infinitely many solutions of the continuous and the finite element discretized problem. The determination of the interface parameters uses a specific eigenvalue problem. In the discrete case the framework is illustrated with an elementary example and some finite element computations.  2004 Elsevier Inc. All rights reserved.

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Section: Resultsmentioning

confidence: 99%

Section: Introduction and Problem Set-upmentioning

confidence: 99%

On solution multiplicity in friction problems with normal compliance

Hild

Sakki

2004

Journal of Mathematical Analysis and Applications

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“…For recent mathematical results and further references about slip rate and temperature dependence of the reader is referred to [1,10,[12][13][14]23,25] and references therein.…”

Section: Classical Formulationmentioning

confidence: 99%

Existence for a thermoviscoelastic beam model of brakes

Kuttler

Shillor

Fernández

2004

Nonlinear Analysis: Real World Applications

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Frictional Wear of a Thermoelastic Beam

Kuttler

Shillor

2000

Journal of Mathematical Analysis and Applications

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We present two versions of a mathematical model for the evolution of wear in a thermoelastic beam resulting from frictional contact with a rigid moving surface. One version is quasistatic and the other dynamic. We show that the quasistatic problem allows for the decoupling of the mechanical and thermal aspects of the process. The problem reduces to that of the heat equation with nonlinear and history-dependent boundary conditions. Then the displacements, shear stresses, and wear can be obtained by quadrature. We establish the existence of a local weak solution for the problem and a partial uniqueness result and obtain conditions for the solution's further regularity. The dynamic problem consists of the heat equation coupled with the equation of motion and the Archard wear equation. We prove the existence and uniqueness of the local weak solution of this problem too.

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A quasistatic contact problem with slip-dependent coefficient of friction

Cited by 20 publications

References 15 publications

On solution multiplicity in friction problems with normal compliance

On solution multiplicity in friction problems with normal compliance

Existence for a thermoviscoelastic beam model of brakes

Frictional Wear of a Thermoelastic Beam

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