Numerical analysis of a dynamic bilateral thermoviscoelastic contact problem with nonmonotone friction law

Bartosz, Krzysztof; Danan, David; Szafraniec, Paweł

doi:10.1016/j.camwa.2016.12.026

Cited by 11 publications

(6 citation statements)

References 35 publications

(58 reference statements)

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“…In contrast to the model studied there, we deal with the non-clamped body, which introduces another difficulty to the problem. Moreover, our result is obtained without additional smallness assumptions on the data of the problem, which was the case in [12]. It was possible due to arguments contained in Corrolary 4.…”

Section: Introductionmentioning

confidence: 80%

“…The paper provides the generalization of the result obtained in [12]. In contrast to the model studied there, we deal with the non-clamped body, which introduces another difficulty to the problem.…”

Section: Introductionmentioning

confidence: 97%

“…Typically it includes approximate schemes based on temporal and spatial discretization, estimate of the error between the approximate and the exact solution and computer simulations. This kind of approach carried out for various contact problems of mechanics with or without thermal effect is presented in [6,7,8,9,10,11,12,14,15,20,22,24,25,26] for instance.…”

Section: Introductionmentioning

confidence: 99%

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Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

Bartosz¹,

Jureczka²,

Szafraniec³

2019

Preprint

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In this work we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity. This leads to a system of hyperbolic inclusion for displacement and parabolic equation for temperature. We provide a fully discrete approximation of studied problem and find optimal error estimates without any smallness assumption on the data. The theoretical result is illustrated numerically.

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Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

Bartosz¹,

Jureczka²,

Szafraniec³

2019

Preprint

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“…First, as mentioned before, the body under consideration is non-clamped, and second, an additional piezoelectric property of the body is considered. For other results concerning numerical analysis of a non-clamped body, we refer, for example, to [9]. The rest of the paper is structured as follows.…”

Section: Krzysztof Bartoszmentioning

confidence: 99%

Numerical analysis of a nonmonotone dynamic contact problem of a non-clamped piezoelectric viscoelastic body

Bartosz¹

2020

Evolution Equations &Amp; Control Theory

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We consider a contact process between a body and a foundation. The body is assumed to be viscoelastic and piezoelectric and the contact is dynamic. Unlike many related papers, the body is assumed to be non-clamped. The contact conditions has a form of inclusions involving the Clarke subdifferential of locally Lipschitz functionals and they have nonmonotone character. The problem in its weak formulation has a form of two coupled Clarke subdifferential inclusions, from which the first one is dynamic and the second one is stationary. The main goal of the paper is numerical analysis of the studied problem. The corresponding numerical scheme is based on the spatial and temporal discretization. Furthermore, the spatial discretization is based on the first order finite element method, while the temporal discretization is based on the backward Euler scheme. We show that under suitable regularity conditions the error between the exact solution and the approximate one is estimated in an optimal way, namely it depends linearly upon the parameters of discretization.

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“…In the study of a fully discrete scheme for the numerical solutions, a finite element approach is used to approximate the spatial variable and finite differences are used for the time derivatives, and as result, we obtain some error estimates on the approximate solutions. For further information on numerical aspects of elastic and electro-elastic contact problems, we refer [4,5,8,9,27].…”

Section: Introductionmentioning

confidence: 99%

Analysis and Approximation of Hemivariational Inequality for a Frictional Thermo-electro-visco-elastic Contact Problem with Damage

et al. 2023

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The aim of this paper is to investigate a contact problem involving thermoelectro-visco-elastic body with damage and a rigid foundation. The friction is modelled with a subgradient of a locally Lipschitz mapping, and the contact is described by the Signorini's unilateral contact condition. A parabolic differential inclusion for the damage function is used to include the damaging effect in the model. We establish the model's variational formulation using four systems of three hemivariational inequalities and a parabolic equation, we prove an existence and uniqueness result of this problem. The proof is based on a fixed point argument and a recent finding from hemivariational inequality theory. Finally, by employing the finite element approach, we investigate a fully discrete approximation of the model and we derive error estimates on the approximate solution.

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Numerical analysis of a dynamic bilateral thermoviscoelastic contact problem with nonmonotone friction law

Cited by 11 publications

References 35 publications

Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

Numerical analysis of a nonmonotone dynamic contact problem of a non-clamped piezoelectric viscoelastic body

Analysis and Approximation of Hemivariational Inequality for a Frictional Thermo-electro-visco-elastic Contact Problem with Damage

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