Solving Quasistatic Contact Problems Using Nonsmooth Optimization Approach

2020/03/27 by Jureczka, Michal, Ochal, Anna, Han, Weimin
#35Q74 #49J40 #65K10 #65M60 #74G15 #74M10 #74M15 #74S05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2003.12369

Abstract

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.

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