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Numerical Analysis and Simulation of a Frictional Contact Problem with Wear, Damage and Long Memory

Numerical Analysis and Simulation of a Frictional Contact Problem with Wear, Damage and Long Memory
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Year:    2020

Author:    Hailing Xuan, Xiaoliang Cheng

East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 659–678

Abstract

A frictional contact model accounting the wear of the contact surface caused by the friction and the mechanical damage of the material is considered. The deformable body is comprised of a viscoelastic material with long memory and the process is assumed to be quasistatic. The mechanical damage caused by tension or compression is included in the constitutive law and the damage function is modelled by a nonlinear parabolic inclusion. The wear is contained in the contact boundary conditions and wear function is modelled by a differential equation. Variational formulation of the model is governed by a coupled system consisting of a history-dependent variational inequality, a nonlinear parabolic variational inequality and an integral equation. A fully discrete scheme of the problem is studied and optimal error estimates are derived for the linear finite element method. Numerical simulations illustrate the model behaviour.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.130320.260520

East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 659–678

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Variational inequality damage integral equation numerical approximation optimal order error estimate.

Author Details

Hailing Xuan

Xiaoliang Cheng

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