On the contact problem with slip displacement dependent friction in elastostatics

Ionescu, Ioan R.; Paumier, Jean-Claude

doi:10.1016/0020-7225(95)00109-3

Cited by 58 publications

(39 citation statements)

References 16 publications

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“…The strict inequality in (13) holds in the stick zone and the equality holds in the slip zone. This physical model of slip-dependent friction was introduced by Rabinowicz (1951) for the geophysical context of earthquake modeling, and was also studied by Ionescu and Paumier (1996), Ionescu and Nguyen (2002), Ionescu et al (2003), Shillor et al (2004), as well as Migórski and Ochal (2005). Due to the basic properties of the Clarke subdifferential (cf.…”

Section: Mechanical Problem and Variational Formulationmentioning

confidence: 99%

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

Barboteu¹,

Bartosz²,

Kalita³

2013

International Journal of Applied Mathematics and Computer Science

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We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.Keywords: linearly elastic material, bilateral contact, nonmonotone friction law, hemivariational inequality, finite element method, error estimate, nonconvex proximal bundle method, quasi-augmented Lagrangian method, Newton method.

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Section: Mechanical Problem and Variational Formulationmentioning

confidence: 99%

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

Barboteu¹,

Bartosz²,

Kalita³

2013

International Journal of Applied Mathematics and Computer Science

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“…Another novel feature of this paper is the analysis of the dynamics. In contrast to other contributions in the field, cf., e.g., [1,12,17,27] and [31], we treat a dynamic contact problem for which the mathematical techniques are less developed than for quasistatic evolutionary models. We underline that there are no results on existence, uniqueness and convergence of solutions to the dynamic hemivariational inequality in Problem 17, which models the contact problem under consideration.…”

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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“…The same frictional instabilities can occur when the coefficient of friction fi is a smooth and decreasing function of the slip rate (see [13] and [20].) This model of friction was studied by Ionescu and Paumier [5], [6] for the one-dimensional shearing problem of an infinite elastic slab. They pointed out that the solution of the problem is not uniquely determined.…”

Section: Introductionmentioning

confidence: 99%

“…It comes from catastrophe theory (see, for instance, [15]) and is implicitly present in the analysis of many physical problems. It is used in the study of static or quasi-static problems (see, for instance, [7] for a slip-dependent, model of friction), and it is justified by a dynamic stability analysis. That is, the static (or quasi-static) position chosen by the perfect delay convention is always stable.…”

Section: Introductionmentioning

confidence: 99%

“…Whatever is the selection rule to choose the solution, shocks will occur. A possible choice for this criterion is the so-called perfect delay convention: the system only jumps when it has no other choice (see [6] and [1]). In this way, different paths of solutions are obtained in acceleration and deceleration processes and a hysteresis phenomenon occurs.…”

Section: Introductionmentioning

confidence: 99%

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Viscosity solutions for dynamic problems with slip-rate dependent friction

Ionescu¹

2002

Quart. Appl. Math.

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Abstract.The dynamic evolution of an elastic medium undergoing frictional slip is considered. The Coulomb law modeling the contact uses a friction coefficient that is a non-monotone function of the slip-rate. This problem is ill-posed, the solution is nonunique and shocks may be created on the contact interface. In the particular case of the one-dimensional shearing of an elastic slab, the (perfect) delay convention can be used to select a unique solution. Different solutions in acceleration and deceleration processes are obtained. To transform the ill-posed problem into a well-posed one and to justify the choice of the perfect delay criterion, a visco-elastic constitutive law with a small viscosity is used here. An existence and uniqueness result is obtained in three dimensions. The assumptions on the functions implied in the contact model are weak enough to include both the normal compliance and the Tresca model. The following conjecture, based on results of numerical simulations, is stated: in the elastic case, the solution chosen by the perfect delay convention is the one obtained from the solutions of the problem with viscosity, when the viscosity tends to zero.

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On the contact problem with slip displacement dependent friction in elastostatics

Cited by 58 publications

References 16 publications

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

A Dynamic Contact Problem with History-Dependent Operators

Viscosity solutions for dynamic problems with slip-rate dependent friction

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