A mixed variational formulation for a class of contact problems in viscoelasticity. Issue 8 (11th June 2018)

• Record Type: Journal Article
• Authors: Matei, A.; Sitzmann, S.; Willner, K.; Wohlmuth, B. I.
• Is Part Of: Applicable analysis. Volume 97:Issue 8(2018)
• Page Start: 1340
• Page End: 1356
• Publication Date: 2018-06-11
• Subjects: Unilateral contact -- viscoelasticity -- dual Lagrange multipliers -- primal-dual active set strategy -- 3D numerical examples; 74D05 -- 74M15 -- 65N30 -- 49J40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1359569
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We consider a deformable body in frictionless unilateral contact with a moving rigid obstacle. The material is described by a viscoelastic law with short memory, and the contact is modeled by a Signorini condition with a time-dependent gap. The existence and uniqueness results for a weak formulation based on a Lagrange multipliers approach are provided. Furthermore, we discuss an efficient algorithm approximating the weak solution for the more general case of a two-body contact problem including friction. In order to illustrate the theory we present two numerical examples in 3D.