Analysis of a unilateral contact problem taking into account adhesion and friction

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• 作者：Elena Bonetti^a ; ^{elena.bonetti@unipv.it} ; Giovanna Bonfanti^b ; ^{bonfanti@ing.unibs.it} ; Riccarda Rossi^b ; ^{riccarda.rossi@ing.unibs.it}
• 关键词：35K55 ; 74A15 ; 74M15
• 刊名：Journal of Differential Equations
• 出版年：2012
• 期刊代码：74_00220396
• 类别：mt
• 出版时间：15 July, 2012
• 卷：253
• 期：2
• 页码：438-462
• 文件大小：280 K

摘要

In this paper, we investigate a contact problem between a viscoelastic body and a rigid foundation, when both the effects of the (irreversible) adhesion and of the friction are taken into account. We describe the adhesion phenomenon in terms of a damage surface parameter according to Fr茅mond始s theory, and we model unilateral contact by Signorini conditions, and friction by a m>nonlocalm> Coulomb law. All the constraints on the internal variables as well as the contact and the friction conditions are rendered by means of subdifferential operators, whence the highly nonlinear character of the resulting PDE system. Our main result states the existence of a global-in-time solution (to a suitable variational formulation) of the related Cauchy problem. It is proved by an approximation procedure combined with time discretization.