Volume 17, Issue 6
Numerical Analysis of a History-Dependent Variational-Hemivariational Inequality for a Viscoplastic Contact Problem

​Xiaoliang Cheng & ​Xilu Wang

DOI:

Int. J. Numer. Anal. Mod., 17 (2020), pp. 820-838.

Published online: 2020-10

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  • Abstract

In this paper, we consider a mathematical model which describes the quasistatic frictionless contact between a viscoplastic body and a foundation. The contact is modeled with normal compliance and unilateral constraint. We present the variational-hemivariational formulation of the model and prove its unique solvability. Then we introduce a fully discrete scheme to solve the problem and derive an error estimate. Under appropriate regularity assumptions of the exact solution, we obtain the optimal order error estimate. Finally, numerical results are reported to show the performance of the numerical method.

  • Keywords

Variational-hemivariational inequality, viscoplastic material, numerical approximation, optimal order error estimate.

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@Article{IJNAM-17-820, author = {​Xiaoliang Cheng , and ​Xilu Wang , }, title = {Numerical Analysis of a History-Dependent Variational-Hemivariational Inequality for a Viscoplastic Contact Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {6}, pages = {820--838}, abstract = {

In this paper, we consider a mathematical model which describes the quasistatic frictionless contact between a viscoplastic body and a foundation. The contact is modeled with normal compliance and unilateral constraint. We present the variational-hemivariational formulation of the model and prove its unique solvability. Then we introduce a fully discrete scheme to solve the problem and derive an error estimate. Under appropriate regularity assumptions of the exact solution, we obtain the optimal order error estimate. Finally, numerical results are reported to show the performance of the numerical method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18353.html} }
TY - JOUR T1 - Numerical Analysis of a History-Dependent Variational-Hemivariational Inequality for a Viscoplastic Contact Problem AU - ​Xiaoliang Cheng , AU - ​Xilu Wang , JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 820 EP - 838 PY - 2020 DA - 2020/10 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18353.html KW - Variational-hemivariational inequality, viscoplastic material, numerical approximation, optimal order error estimate. AB -

In this paper, we consider a mathematical model which describes the quasistatic frictionless contact between a viscoplastic body and a foundation. The contact is modeled with normal compliance and unilateral constraint. We present the variational-hemivariational formulation of the model and prove its unique solvability. Then we introduce a fully discrete scheme to solve the problem and derive an error estimate. Under appropriate regularity assumptions of the exact solution, we obtain the optimal order error estimate. Finally, numerical results are reported to show the performance of the numerical method.

​Xiaoliang Cheng & ​Xilu Wang. (2020). Numerical Analysis of a History-Dependent Variational-Hemivariational Inequality for a Viscoplastic Contact Problem. International Journal of Numerical Analysis and Modeling. 17 (6). 820-838. doi:
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