This paper is devoted to a study of time-dependent hemivariational inequality. We prove existence and uniqueness of its solution, provide fully discrete scheme and reformulate this scheme as a series of nonsmooth optimization problems. This theory is later applied to a sample quasistatic contact problem describing a viscoelastic body in frictional contact with a foundation. This contact is governed by a nonmonotone friction law with dependence on normal component of displacement and tangential component of velocity. Finally, computational simulations are performed to illustrate obtained results.
Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM
Technical University of Košice（科希策工业大学）；University of Seville（塞维利亚大学）；Charles University（查理大学）；Institute of Thermomechanics of the Czech Acad. Sci.（捷克科学院热力学研究所）
Quasistatic adhesive contact delaminating in mixed mode and its numerical treatment
Institute of Information Theory and Automation of the ASCR（ASC自动化与信息研究所）；Faculty of Civil Engineering, Czech Technical University（捷克理工大学土木工程学院）；University of Seville（塞维利亚大学）；Charles University（查理大学）；Institute of Thermomechanics of the ASCR（ASC热力学研究所）
Two adhesive-contact models for quasistatic mixed-mode delamination problems
Institute of Applied and Computational Mathematics, Foundation for Research and Technology - Hellas（应用与计算数学研究所，希腊研究与技术基金会）；Group of Elasticity and Strength of Materials, Dept. of Continuum Mechanics, School of Engineering, University of Seville（塞维利亚大学工程学院连续力学系弹性与材料强度研究组）；Mathematical Institute, Charles University（查理大学数学研究所）；Institute of Thermomechanics, Czech Academy of Sciences（捷克科学院热力学研究所）
