Sofonea, Mircea; Avramescu, Cezar; Matei, Andaluzia A fixed point result with applications in the study of viscoplastic frictionless contact problems. (English) Zbl 1171.47047 Commun. Pure Appl. Anal. 7, No. 3, 645-658 (2008). 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)]. Reviewer: Georgios E. Stavroulakis (Chania) Cited in 2 ReviewsCited in 32 Documents 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 Keywords:viscoplasticity; contact; fixed point theory Citations:Zbl 1013.74001 PDFBibTeX XMLCite \textit{M. Sofonea} et al., Commun. Pure Appl. Anal. 7, No. 3, 645--658 (2008; Zbl 1171.47047) Full Text: DOI