Frictional contact problems with normal compliance

Klarbring, Anders; Mikelić, Andro; Shillor, Meir

doi:10.1016/0020-7225(88)90032-8

Cited by 198 publications

(87 citation statements)

References 14 publications

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“…Equation (19) represents the viscoelastic constitutive law of the material, already introduced in (1). Equation (20) is the equation of equilibrium; we use it here since we assume that process is quasistatic.…”

Section: The Modelmentioning

confidence: 99%

“…In the study of the mechanical problem (19)- (25) we assume that the viscosity operator, the elasticity operator and the relaxation tensor satisfy the following conditions.…”

Section: The Modelmentioning

confidence: 99%

“…It was introduced in [29], describes the contact with a perfectly rigid foundation and is expressed in terms of unilateral constraints for the displacement field. The normal compliance contact condition was introduced in [25] and used in a large number of papers, see [13,19,20,23,28] and the references therein. It represents a regularization of the Signorini contact condition and it describes the contact with an elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a contact problem with normal damped response and unilateral constraint

Barboteu

Danan

Sofonea

2015

Z. Angew. Math. Mech.

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We consider a mathematical model which describes the equilibrium of a viscoelastic body in frictional contact with an obstacle. The contact is modeled with normal damped response and unilateral constraint for the velocity field, associated to a version of Coulomb's law of dry friction. We present a weak formulation of the problem, then we state and prove an existence and uniqueness result of the solution. The proof is based on arguments of history-dependent quasivariational inequalities. We also study the dependence of the solution with respect to the data and prove a convergence result. Further, we introduce a fully discrete scheme to solve the problem numerically. Under certain solution regularity assumptions, we derive an optimal order error estimate of the discretization. Finally, we provide numerical simulations which illustrate the behavior of the solution with respect to the frictional contact conditions and validate the theoretical convergence results.

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Section: The Modelmentioning

confidence: 99%

“…In the study of the mechanical problem (19)- (25) we assume that the viscosity operator, the elasticity operator and the relaxation tensor satisfy the following conditions.…”

Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of a contact problem with normal damped response and unilateral constraint

Barboteu

Danan

Sofonea

2015

Z. Angew. Math. Mech.

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“…We notice that the fully discrete Problem VP hk can be seen as a coupled system of variational equations. Using classical results of nonlinear variational equations (see [16] …”

Section: Fully Discrete Approximations: Error Estimatesmentioning

confidence: 99%

Variational Analysis and the Convergence of the Finite Element Approximation of an Electro-Elastic Contact Problem with Adhesion

Drabla

Zellagui

2011

Arab J Sci Eng

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A model for the adhesive, quasi-static and frictionless contact between an electro-elastic body and a rigid foundation is studied in this paper. The contact is modelled with Signorini's conditions with adhesion. We provide variational formulation for the problem and prove the existence of a unique weak solution to the model. The proofs are based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point. Then, a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. Error estimates are derived on the approximative solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions.

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“…We note that the history-dependent operators have been considered for quasistatic and evolutionary contact problems by several authors, for example, by Sofonea et al in [8,21,[26][27][28] and [29], Migórski et al in [5,15,19] and [20], Ogorzały in [23], Yao et al in [31], and Zhu in [33]. The normal compliance contact condition was introduced in [13,14,22] and it was used in many papers, see, e.g., [3,9,25] and [29]. In [28], Sofonea and Patrulescu considered a contact condition which describes a foundation that is rigid if the penetration reaches a critical bound.…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Contact Problem with History-Dependent Operators

Ogorzaly

2016

J Elast

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In this paper we present results on existence, uniqueness and convergence of solutions to the Cauchy problem for abstract first order evolutionary inclusion which contains two operators depending on the history of the solution. These results are applicable to a dynamic contact problem for viscoelastic materials with a normal compliance contact condition with memory and a friction law in which the friction bound depends on the magnitude of the tangential displacement. The proofs are based on recent results for hemivariational inequalities and a fixed point argument.

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Frictional contact problems with normal compliance

Cited by 198 publications

References 14 publications

Analysis of a contact problem with normal damped response and unilateral constraint

Analysis of a contact problem with normal damped response and unilateral constraint

Variational Analysis and the Convergence of the Finite Element Approximation of an Electro-Elastic Contact Problem with Adhesion

A Dynamic Contact Problem with History-Dependent Operators

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