A mixed variational formulation of a contact problem with adhesion

Abstract

A mathematical model describing the contact between a viscoplastic body and a deformable foundation is analyzed under small deformation hypotheses. The process is quasistatic and in normal direction the contact is with adhesion, normal compliance, memory effects and unilateral constraint. We derive a mixed-variational formulation of the problem using Lagrange multipliers. Finally, we prove the unique weak solvability of the contact problem.

Keywords:

• Variational formulation
• frictional contact
• normal compliance
• unilateral constraint
• adhesion

AMS Subject Classifications:

• 74M10
• 74M15
• 74G25
• 74G30
• 49J40

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the author has been partially supported by projects LEA Math Mode 2014/2015 and POSDRU/159/1.5/S/132400: Young successful researchers-professional development in an international and interdisciplinary environment at Babeş-Bolyai University.