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Dual formulation of a viscoplastic contact problem with unilateral constraint. (English) Zbl 1448.74077

Summary: We consider a mathematical model which describes the contact between a viscoplastic body and an obstacle, the so-called foundation. The process is quasistatic, the contact is frictionless and is modelled with unilateral constraint. We derive a variational formulation of the model which leads to a history-dependent quasivariational inequality for stress field, associated to a time-dependent convex. Then we prove the unique weak solvability of the model. The proof is based on an abstract existence and uniqueness result obtained in [the authors, Eur. J. Appl. Math. 22, No. 5, 471–491 (2011; Zbl 1226.49012)].

MSC:

74M15 Contact in solid mechanics
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
49J40 Variational inequalities

Citations:

Zbl 1226.49012
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