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A fixed point result with applications in the study of viscoplastic frictionless contact problems. (English) Zbl 1171.47047

The paper studies a mathematical model which describes the frictionless contact between a viscoplastic body and a deformable foundation. The process is quasistatic and is studied on the general unbounded interval of time [0,1). First, the variational formulation of the problem is given. Then an abstract fixed point theorem is used in order to prove the existence of a unique weak solution to the model. The study contains in addition a regularity result. The techniques used in this paper are based on a recent monograph of the first author [W.Han and M.Sofonea, “Quasistatic contact problems in viscoelasticity and viscoplasticity” (AMS/IP Studies in Advanced Mathematics 30; Providence/RI:AMS International Press) (2002; Zbl 1013.74001)].

MSC:

47H10 Fixed-point theorems
74M15 Contact in solid mechanics
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
46T20 Continuous and differentiable maps in nonlinear functional analysis
47N99 Miscellaneous applications of operator theory

Citations:

Zbl 1013.74001
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