Matei, Andaluzia; Sofonea, Mircea Dual formulation of a viscoplastic contact problem with unilateral constraint. (English) Zbl 1448.74077 Discrete Contin. Dyn. Syst., Ser. S 6, No. 6, 1587-1598 (2013). 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)]. Cited in 2 Documents 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 Keywords:viscoplastic material; frictionless contact; unilateral constraint; dual formulation; quasivariational inequality Citations:Zbl 1226.49012 PDFBibTeX XMLCite \textit{A. Matei} and \textit{M. Sofonea}, Discrete Contin. Dyn. Syst., Ser. S 6, No. 6, 1587--1598 (2013; Zbl 1448.74077) Full Text: DOI