Year: 2020
Author: Weimin Han, Hailing Xuan, Qichang Xiao, Xiaoliang Cheng, Weimin Han, Qichang Xiao
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 3 : pp. 569–594
Abstract
In this paper, we study a dynamic contact model with long memory which allows both the convex potential and nonconvex superpotentials to depend on history-dependent operators. The deformable body consists of a viscoelastic material with long memory and the process is assumed to be dynamic. The contact involves a nonmonotone Clarke subdifferential boundary condition and the friction is modeled by a version of the Coulomb's law of dry friction with the friction bound depending on the total slip. We introduce and study a fully discrete scheme of the problem, and derive error estimates for numerical solutions. Under appropriate solution regularity assumptions, an optimal order error estimate is derived for the linear finite element method. This theoretical result is illustrated numerically.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0130
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 3 : pp. 569–594
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Variational-hemivariational inequality history-dependent operators finite element method numerical approximation optimal order error estimate.
Author Details
-
Analysis of a quasistatic thermo‐electro‐viscoelastic contact problem modeled by variational‐hemivariational and hemivariational inequalities
Alaoui, Mohammed | Bouallala, Mustapha | Hassan Essoufi, EL | Ouaanabi, AbdelhafidMathematical Methods in the Applied Sciences, Vol. (2024), Iss.
https://doi.org/10.1002/mma.10411 [Citations: 0] -
Virtual element method for solving a viscoelastic contact problem with long memory
Xiao, Wenqiang | Ling, MinMathematics and Mechanics of Solids, Vol. (2024), Iss.
https://doi.org/10.1177/10812865241263039 [Citations: 0] -
Numerical analysis and simulations of a frictional contact problem with damage and memory
Xuan, Hailing | Cheng, XiaoliangMathematical Control and Related Fields, Vol. 12 (2022), Iss. 3 P.621
https://doi.org/10.3934/mcrf.2021037 [Citations: 0] -
Numerical analysis and simulation of an adhesive contact problem with damage and long memory
Xuan, Hailing | Cheng, XiaoliangDiscrete & Continuous Dynamical Systems - B, Vol. 26 (2021), Iss. 5 P.2781
https://doi.org/10.3934/dcdsb.2020205 [Citations: 1] -
A Fully-Discrete Finite Element Scheme and Projection-Iteration Algorithm for a Dynamic Contact Problem with Multi-contact Zones and Unilateral Constraint
Cai, Dong-Ling | Hu, Jingyan | Xiao, Yi-Bin | Zeng, Ping | Zhou, GuanyuJournal of Scientific Computing, Vol. 96 (2023), Iss. 1
https://doi.org/10.1007/s10915-023-02228-z [Citations: 1] -
Dynamic contact problem with moderate displacement and time‐dependent normal
Wu, Shen R.
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 102 (2022), Iss. 12
https://doi.org/10.1002/zamm.202100451 [Citations: 0] -
Error estimates and numerical simulations of a thermoviscoelastic contact problem with damage and long memory
Sun, Xinyu | Cheng, Xiaoliang | Xuan, HailingCommunications in Nonlinear Science and Numerical Simulation, Vol. 137 (2024), Iss. P.108165
https://doi.org/10.1016/j.cnsns.2024.108165 [Citations: 0]