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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Bonetti, Elena¹  Bonfanti, Giovanna²  Rossi, Riccarda² 

[1] Univ Pavia, Dipartimento Matemat F Casorati, I-27100 Pavia, Italy

[2] Univ Brescia, Dipartimento Matemat, I-25133 Brescia, Italy

关键词: Contact;    Adhesion;    Friction;    Irreversibility;    Existence;   

DOI  :  10.1016/j.jde.2012.03.017

来源: Elsevier

【 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 FREMOND'S theory, and we model unilateral contact by Signorini conditions, and friction by a nonlocal 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. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free