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Volume 10, Issue 1
Numerical Analysis of an Adhesive Contact Problem with Long Memory

Xiaoliang Cheng & Qichang Xiao

DOI: 10.4208/eajam.181018.020419

East Asian J. Appl. Math., 10 (2020), pp. 72-88.

Published online: 2020-01

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  • Abstract

Spatially semidiscrete and fully discrete schemes for a variational-hemivariational inequality, which describes adhesive contact between a deformable body of a viscoelastic material with long memory and a foundation are constructed. The variational formulation of the problem is represented by a system coupling a nonlinear integral equation with a history-dependent variational-hemivariational inequality. Assuming certain regularity of the solution and using piecewise linear finite element function for displacements and piecewise constant functions for bonding field, we obtain optimal order error estimates.

  • Keywords

Variational-hemivariational inequality, adhesion, memory term, numerical approximation, error estimate.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xiao_qc@126.com (Qichang Xiao)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-10-72, author = {Cheng , Xiaoliang and Xiao , Qichang}, title = {Numerical Analysis of an Adhesive Contact Problem with Long Memory}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {1}, pages = {72--88}, abstract = {

Spatially semidiscrete and fully discrete schemes for a variational-hemivariational inequality, which describes adhesive contact between a deformable body of a viscoelastic material with long memory and a foundation are constructed. The variational formulation of the problem is represented by a system coupling a nonlinear integral equation with a history-dependent variational-hemivariational inequality. Assuming certain regularity of the solution and using piecewise linear finite element function for displacements and piecewise constant functions for bonding field, we obtain optimal order error estimates.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.181018.020419}, url = {http://global-sci.org/intro/article_detail/eajam/13603.html} }
TY - JOUR T1 - Numerical Analysis of an Adhesive Contact Problem with Long Memory AU - Cheng , Xiaoliang AU - Xiao , Qichang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 72 EP - 88 PY - 2020 DA - 2020/01 SN - 10 DO - http://doi.org/10.4208/eajam.181018.020419 UR - https://global-sci.org/intro/article_detail/eajam/13603.html KW - Variational-hemivariational inequality, adhesion, memory term, numerical approximation, error estimate. AB -

Spatially semidiscrete and fully discrete schemes for a variational-hemivariational inequality, which describes adhesive contact between a deformable body of a viscoelastic material with long memory and a foundation are constructed. The variational formulation of the problem is represented by a system coupling a nonlinear integral equation with a history-dependent variational-hemivariational inequality. Assuming certain regularity of the solution and using piecewise linear finite element function for displacements and piecewise constant functions for bonding field, we obtain optimal order error estimates.

Cheng , Xiaoliang and Xiao , Qichang. (2020). Numerical Analysis of an Adhesive Contact Problem with Long Memory. East Asian Journal on Applied Mathematics. 10 (1). 72-88. doi:10.4208/eajam.181018.020419
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