A mixed variational formulation for a class of contact problems in viscoelasticity

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.

Keywords:

• Unilateral contact
• viscoelasticity
• dual Lagrange multipliers
• primal-dual active set strategy
• 3D numerical examples

AMS Subject Classifications:

• 74D05
• 74M15
• 65N30
• 49J40

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was partly supported by DFG projects WO 671/11-1 and WO 671/15-1 within the Priority Program ‘Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis’ (SPP 1748). The work of Saskia Sitzmann was partly supported by the Federal Republic of Germany, Federal Ministry of Economics and Technology though the project ‘Lufo 4/4 R&E Turb’ [grant number: 20T1104A] in cooperation with MTU Aero Engines AG.