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Analysis of a contact problem with normal damped response and unilateral constraint
Author(s) -
Barboteu Mikaël,
Danan David,
Sofonea Mircea
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400304
Subject(s) - uniqueness , discretization , constraint (computer aided design) , convergence (economics) , unilateral contact , mathematics , weak solution , coulomb's law , variational inequality , obstacle , mathematical analysis , coulomb , finite element method , physics , geometry , quantum mechanics , economics , political science , law , thermodynamics , economic growth , electron
We consider a mathematical model which describes the equilibrium of a viscoelastic body in frictional contact with an obstacle. The contact is modeled with normal damped response and unilateral constraint for the velocity field, associated to a version of Coulomb's law of dry friction. We present a weak formulation of the problem, then we state and prove an existence and uniqueness result of the solution. The proof is based on arguments of history‐dependent quasivariational inequalities. We also study the dependence of the solution with respect to the data and prove a convergence result. Further, we introduce a fully discrete scheme to solve the problem numerically. Under certain solution regularity assumptions, we derive an optimal order error estimate of the discretization. Finally, we provide numerical simulations which illustrate the behavior of the solution with respect to the frictional contact conditions and validate the theoretical convergence results.