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Numerical analysis of history-dependent variational-hemivariational inequalities with applications to contact problems. (English) Zbl 1439.74230

Summary: A new class of history-dependent variational-hemivariational inequalities was recently studied in [S. Migórski et al., Nonlinear Anal., Real World Appl. 22, 604–618 (2015; Zbl 1326.74101)]. There, an existence and uniqueness result was proved and used in the study of a mathematical model which describes the contact between a viscoelastic body and an obstacle. The aim of this paper is to continue the analysis of the inequalities introduced in Migórski et al. [loc. cit.] and to provide their numerical analysis. We start with a continuous dependence result. Then we introduce numerical schemes to solve the inequalities and derive error estimates. We apply the results to a quasistatic frictional contact problem in which the material is modelled with a viscoelastic constitutive law, the contact is given in the form of normal compliance, and friction is described with a total slip-dependent version of Coulomb’s law.

MSC:

74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74D05 Linear constitutive equations for materials with memory
74S05 Finite element methods applied to problems in solid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
49J40 Variational inequalities

Citations:

Zbl 1326.74101
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Full Text: DOI

References:

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