Numerical analysis and simulations of contact problem with wear

Jureczka, Michal; Ochał, Anna

doi:10.1016/j.camwa.2018.08.044

Cited by 17 publications

(10 citation statements)

References 10 publications

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“…Compared to the pangolin scale model [10], there exists a cohesion between the sand particles, but the model displays weaker contact restraints. The DEM calculation parameters of the pangolin scale model and the sand particles are shown in Tables 1 and 2 [11,12]. The abrasive wear simulation system is shown in Figure 3.…”

Section: The Establishment Of Modelsmentioning

confidence: 99%

Analysis of Wear-Resistant Surface with Pangolin Scale Morphology by DEM Simulation

Zhang

Pang

et al. 2020

Applied Sciences

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Based on the Discrete Element Method (DEM), an abrasive wear system composed of pangolin scale models and abrasive sand was established. The wear morphology of pangolin scale models under different velocities were simulated by PFC2D®. Their wear behaviors were discussed with regard to the contact bond fields, the contact force chains, the velocity fields and the displacement fields of the abrasive wear system. Moreover, the resistance of the pangolin scale models under different velocities were analyzed. In the DEM simulation, the fracture and debris locomotion on the scale model were observed at a meso-microscopic scale. The results show that the geometrical shape of the pangolin scale is helpful for decreasing the boundary stress, with the wear rate decreasing when the velocity is higher than 0.62 m·s−1. The wear rate is no more than 0.006 g/m under the abrasive sand, with a radius of 0.11–0.20 mm. The wear rates of the pangolin scale model agree with the experimental results, and the DEM provides a new way to study the abrasive wear behavior of this non-smooth biological surface.

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Section: The Establishment Of Modelsmentioning

confidence: 99%

Analysis of Wear-Resistant Surface with Pangolin Scale Morphology by DEM Simulation

Zhang

Pang

et al. 2020

Applied Sciences

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“…[10] proposed a mathematical model to describe quasistatic frictional contact with wear between a thermoviscoelastic body and a moving foundation. Very recently, Jureczka and Ochal [17] obtained the numerical analysis and simulations for the quasistatic elastic frictional contact problem with wear.…”

Section: Introductionmentioning

confidence: 99%

Variational and numerical analysis of a dynamic viscoelastic contact problem with friction and wear

2020

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In this paper, we consider a dynamic viscoelastic contact problem with friction and wear, and describe it as a system of nonlinear partial differential equations. We formulate the previous problem as a hyperbolic quasi-variational inequality by employing the variational method. We adopt the Rothe method to show the existence and uniqueness of weak solution for the hyperbolic quasi-variational inequality under mild conditions. We also give a fully discrete scheme for solving the hyperbolic quasi-variational inequality and obtain error estimates for the fully discrete scheme.As a generalization of the contact problem considered in [5], Chau et al. [4] introduced and studied a dynamic frictionless contact problem and gave a fully discrete scheme for solving such problem. Bartosz[3] considered a dynamical viscoelastic contact problem to modify the model treated by Ciulcu et al. [7].Recently, Cocou [8] extended the static contact problem considered by Rabier et al.[18] to a dynamic viscoelastic contact problem with friction and obtained an existence and uniqueness of the weak solution for such problem. However, to our best knowledge, there is no study for the dynamic viscoelastic contact problem with friction and wear in the existing literature. The motivation of this paper is to make a new attempt in this direction.It is well known that Duvaut and Lions [9] were the first to study quasi-static frictional contact viscoelastic problems within the framework of variational inequalities. From then on, various variational inequalities, hemivariational inequalities and other related problems have been derived from different physical phenomena in contact mechanics and abundant research results have been obtained for their studies ([15, 20, 21, 27, 28, 30, 31, 33, 36]). Recently, Migórski and Zeng [23] studied a class of hyperbolic variational inequalities and applied their results to study the existence of weak solutions for the dynamic frictional contact problem without wear.In this paper, we consider a mathematical model which describes a dynamic viscoelastic contact problem with friction and wear, in which the material behavior is followed by the Kelvin-Voigt viscoelastic constitutive law and the frictional contact is modelled with a wear governed by a simplified version of Archard's law [33,34] for the velocity field associated to a version of Coulombs law of dry friction.The rest of this paper is organized as follows. Section 2 presents some necessary preliminaries and the weak formulation of the dynamic viscoelastic contact problem with friction and wear. Inspired by Migórski and Zeng [23], we prove the existence and uniqueness of the solution for the hyperbolic quasi-variational inequality under mild conditions by applying the Rothe method [19] in Section 3. We obtain the existence and uniqueness of weak solution for the dynamic viscoelastic contact problem with friction and wear in Section 4. Finally, we present the fully discrete scheme for solving the hyperbolic quasi-variational inequality and derive the error ...

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“…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. In this paper, we take a further step by considering a more general fully discrete numerical scheme for the contact problem that allows an arbitrary partition of the time interval, providing optimal order error estimates of the fully discrete scheme to solve the contact problem.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

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confidence: 97%

Numerical analysis of a contact problem with wear

Han

Jureczka

et al. 2020

Computers & Mathematics with Applications

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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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Numerical analysis and simulations of contact problem with wear

Cited by 17 publications

References 10 publications

Analysis of Wear-Resistant Surface with Pangolin Scale Morphology by DEM Simulation

Analysis of Wear-Resistant Surface with Pangolin Scale Morphology by DEM Simulation

Variational and numerical analysis of a dynamic viscoelastic contact problem with friction and wear

Numerical analysis of a contact problem with wear

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