Volume 10, Issue 4
Numerical Analysis and Simulation of a Frictional Contact Problem with Wear, Damage and Long Memory

Hailing Xuan & Xiaoliang Cheng

East Asian J. Appl. Math., 10 (2020), pp. 659-678.

Published online: 2020-08

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M15, 65N21, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-659, author = {Hailing Xuan , and Xiaoliang Cheng , }, title = {Numerical Analysis and Simulation of a Frictional Contact Problem with Wear, Damage and Long Memory}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130320.260520}, url = {http://global-sci.org/intro/article_detail/eajam/17945.html} }
TY - JOUR T1 - Numerical Analysis and Simulation of a Frictional Contact Problem with Wear, Damage and Long Memory AU - Hailing Xuan , AU - Xiaoliang Cheng , JO - East Asian Journal on Applied Mathematics VL - 4 SP - 659 EP - 678 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.130320.260520 UR - https://global-sci.org/intro/article_detail/eajam/17945.html KW - Variational inequality, damage, integral equation, numerical approximation, optimal order error estimate. AB -

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.

Hailing Xuan & Xiaoliang Cheng. (2020). Numerical Analysis and Simulation of a Frictional Contact Problem with Wear, Damage and Long Memory. East Asian Journal on Applied Mathematics. 10 (4). 659-678. doi:10.4208/eajam.130320.260520
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