Jarušek, Jiří; Sofonea, Mircea On the solvability of dynamic elastic-visco-plastic contact problems with adhesion. (English) Zbl 1378.74049 Ann. Acad. Rom. Sci., Math. Appl. 1, No. 2, 191-214 (2009). Summary: We consider a dynamic contact problem between an elastic-viscoplastic body and an obstacle, the so-called foundation. The contact is frictionless and is modeled with normal compliance of such a type that the penetration is restricted with unilateral constraint. The adhesion of contact surfaces is taken into account and the evolution of the bonding field is described by a first-order differential equation. We provide a weak formulation of the contact problem in the form of an integro-differential system in which the unknowns are the displacement, the stress and the bonding fields, then we present an existence result for the solution. We consider a sequence of penalized problems which have a unique solution, derive a priori estimates and use compactness properties to obtain a solution to the original model, by passing to the limit as the penalization parameter converges to zero. Cited in 6 Documents MSC: 74M15 Contact in solid mechanics 35Q74 PDEs in connection with mechanics of deformable solids 74H20 Existence of solutions of dynamical problems in solid mechanics Keywords:elastic-visco-plastic material; dynamic process; frictionless contact; normal compliance; Signorini condition; adhesion; variational formulation; weak solution; a priori estimates PDFBibTeX XMLCite \textit{J. Jarušek} and \textit{M. Sofonea}, Ann. Acad. Rom. Sci., Math. Appl. 1, No. 2, 191--214 (2009; Zbl 1378.74049)