East Asian J. Appl. Math., 10 (2020), pp. 659-678.
Published online: 2020-08
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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} }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.