Analysis of a contact problem with wear and unilateral constraint

This paper represents a sequel to [13] where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. Some preliminary error analysis for a fully discrete approximation of the contact problem was provided in [13]. In this paper, we consider a more general fully discrete numerical scheme for the contact problem, derive optimal order error bounds and present computer simulation results showing that the numerical convergence orders match the theoretical predictions.Keywords. Quasistatic contact problem, variational inequality, numerical methods, optimal order error estimate.

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“…We recall the following existence and uniqueness result for Problem 2 from [24]. In addition, w(t) ≥ 0 for all t ∈ [0, T ], a.e.…”

Section: The Contact Problem and Its Variational Formulationmentioning

confidence: 99%

“…In this model, the friction between a deformable body and the foundation leads to wear of the contact surface of the body over time. Solution existence and uniqueness for the model are provided in [24]. Numerical approximation of the contact problem is the subject of [13] where some error bounds are derived for a fully discrete scheme.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of a contact problem with wear

Han

Jureczka

et al. 2020

Computers & Mathematics with Applications

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“…then equation (24) reduces the classical version of the Archard's law for wear function w. However, condition (25) represents the initial condition for the wear function. In fact, if we take w 0 = 0, then we can see that at the initial moment the material is new.…”

Section: (33)mentioning

confidence: 99%

“…(31) However, under the assumption that the velocity of the foundation v * is large in comparison with the tangential velocity of the elastic body, we have the equation (23), which stands for the sliding version of the classical Coulomb law of dry friction (see [24], for more details), where n * is the unitary vector given by…”

mentioning

confidence: 99%

History-dependent differential variational-hemivariational inequalities with applications to contact mechanics

Liu¹,

Nguyen²,

Yao³

et al. 2020

Evolution Equations &Amp; Control Theory

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The primary objective of this paper is to explore a complicated differential variational-hemivariational inequality involving a history-dependent operator in Banach spaces. A well-posedness result for the inequality, including the existence, uniqueness, and continuous dependence on the initial data of the solution is established by using a fixed point principle for history-dependent operators. Moreover, to illustrate the applicability of the theoretical results, an elastic contact problem with wear and long time dependent effort is explored.

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“…The related problems attracted the attention of many researchers and there have been a large number of articles in these fields. Such references include [6,14,21]. The friction process such as the flight of an aircraft or a sudden braking of a car is accompanied by the generation of heat.…”

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confidence: 99%

Numerical analysis of a thermal frictional contact problem with long memory

Xuan¹,

Cheng²

2021

CPAA

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The objective in this paper is to study a thermal frictional contact model. The deformable body consists of a viscoelastic material and the process is assumed to be dynamic. It is assumed that the material behaves in accordance with Kelvin-Voigt constitutive law and the thermal effect is added. The variational formulation of the model leads to a coupled system including a history-dependent hemivariational inequality for the displacement field and an evolution equation for the temperature field. In study of this system, we first consider a fully discrete scheme of it and then focus on deriving error estimates for numerical solutions. Under appropriate assumptions of solution regularity, an optimal order error estimate is obtained. At the end of this manuscript, we report some numerical simulation results for the contact problem so as to verify the theoretical results.

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Analysis of a contact problem with wear and unilateral constraint

Cited by 20 publications

References 22 publications

Numerical analysis of a contact problem with wear

Numerical analysis of a contact problem with wear

History-dependent differential variational-hemivariational inequalities with applications to contact mechanics

Numerical analysis of a thermal frictional contact problem with long memory

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