Volume 18, Issue 3
Analysis of Rothe Method for a Variational-Hemivariational Inequality in Adhesive Contact Problem for Locking Materials

Xiaoliang Cheng, Hailing Xuan & Qichang Xiao

Int. J. Numer. Anal. Mod., 18 (2021), pp. 287-310.

Published online: 2021-03

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  • Abstract

We study a system of differential variational–hemivariational inequality arising in the modelling of adhesive viscoelastic contact problems for locking materials. The system consists of a variational-hemivariational inequality for the displacement field and an ordinary differential equation for the adhesion field. The contact is described by the unilateral constraint and normal compliance contact condition in which adhesion is taken into account and the friction is modelled by the nonmonotone multivalued subdifferential condition with adhesion. The problem is governed by a linear viscoelastic operator, a nonconvex locally Lipschitz friction potential and the subdifferential of the indicator function of a convex set which describes the locking constraints. The existence and uniqueness of solution to the coupled system are proved. The proof is based on a time-discretization method, known as the Rothe method.

  • Keywords

Variational-hemivariational inequality, Rothe method, adhesion, locking material, unilateral constraint, normal compliance, nonmonotone friction.

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@Article{IJNAM-18-287, author = {Cheng , Xiaoliang and Xuan , Hailing and Xiao , Qichang}, title = {Analysis of Rothe Method for a Variational-Hemivariational Inequality in Adhesive Contact Problem for Locking Materials}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {3}, pages = {287--310}, abstract = {

We study a system of differential variational–hemivariational inequality arising in the modelling of adhesive viscoelastic contact problems for locking materials. The system consists of a variational-hemivariational inequality for the displacement field and an ordinary differential equation for the adhesion field. The contact is described by the unilateral constraint and normal compliance contact condition in which adhesion is taken into account and the friction is modelled by the nonmonotone multivalued subdifferential condition with adhesion. The problem is governed by a linear viscoelastic operator, a nonconvex locally Lipschitz friction potential and the subdifferential of the indicator function of a convex set which describes the locking constraints. The existence and uniqueness of solution to the coupled system are proved. The proof is based on a time-discretization method, known as the Rothe method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18726.html} }
TY - JOUR T1 - Analysis of Rothe Method for a Variational-Hemivariational Inequality in Adhesive Contact Problem for Locking Materials AU - Cheng , Xiaoliang AU - Xuan , Hailing AU - Xiao , Qichang JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 287 EP - 310 PY - 2021 DA - 2021/03 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18726.html KW - Variational-hemivariational inequality, Rothe method, adhesion, locking material, unilateral constraint, normal compliance, nonmonotone friction. AB -

We study a system of differential variational–hemivariational inequality arising in the modelling of adhesive viscoelastic contact problems for locking materials. The system consists of a variational-hemivariational inequality for the displacement field and an ordinary differential equation for the adhesion field. The contact is described by the unilateral constraint and normal compliance contact condition in which adhesion is taken into account and the friction is modelled by the nonmonotone multivalued subdifferential condition with adhesion. The problem is governed by a linear viscoelastic operator, a nonconvex locally Lipschitz friction potential and the subdifferential of the indicator function of a convex set which describes the locking constraints. The existence and uniqueness of solution to the coupled system are proved. The proof is based on a time-discretization method, known as the Rothe method.

Xiaoliang Cheng, Hailing Xuan & Qichang Xiao. (2021). Analysis of Rothe Method for a Variational-Hemivariational Inequality in Adhesive Contact Problem for Locking Materials. International Journal of Numerical Analysis and Modeling. 18 (3). 287-310. doi:
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