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 - <p style="text-align: justify;">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.<br/></p>