On the existence of solutions to quasistatic frictional rationalcontact problems with limited interpenetration br

The existence of solutions to quasistatic frictional contact problems with limitedinterpenetration with an ahead prescribed bound is proved here. If the depth ofthe interpenetration tends to zero, then there are some sequence of solutions ofsuch problems and a solution of the corresponding Signorini contact problem suchthat it is the limit of the sequence.(c) 2021 Elsevier Ltd. All rights reserved.1. Introduction and formulation of the problem solvedThe model of the rational contact with limited interpenetration has been introduced in [1]. There andin [2] the solvability of its static version has been treated. In [3] the dynamic frictionless boundary contactfor a viscoelastic body has been studied while in [4] the dynamic frictionless domain contact for viscoelasticplates has been investigated.The aim of this paper is to enrich these results by some time-dependent frictional problems. Like in theSignorini case there is no method available to prove the existence of solutions for frictional dynamic contactproblems with unilateral contact condition formulated in displacements. Hence we concentrate here on theappropriate quasistatic problems where the body is assumed to be deformed very slowly and the inertialforces in the dynamic formulation are therefore neglected. For the Signorini contact this problem was solvedby L.E. Andersson [5]. With a somewhat modified proof this result was included into the monograph [6]. Heresome ideas of both texts are adapted for the purpose of the rational contact with limited interpenetration.We formulate and solve a series of approximate problems at first, then we prove the solvability of the originalproblem using certain regularity results and, finally, we prove a certain convergence of the solutions of theE-mail address:jarusek@math.cas.cz.https://doi.org/10.1016/j.nonrwa.2021.1034681468-1218/(c) 2021 Elsevier Ltd. All rights reserved.T

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This paper proves the existence of solutions to quasistatic frictional contact problems with limited interpenetration. If the depth of the interpenetration approaches zero, there are some sequence of solutions and a solution of the corresponding Signorini contact problem that serves as the limit of the sequence.