A dynamic contact problem for elastic–viscoplastic materials with normal damped response and damage

Abstract

We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is assumed to be dynamic and the material behavior is described by a elastic–viscoplastic constitutive law with damage. The frictional contact is modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is a coupled system of a hemivariational inequality for the displacement and a parabolic variational inequality for the damage field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of hyperbolic hemivariational inequality, a classical existence, and uniqueness result on parabolic inequalities and a fixed point argument.

Keywords:

• Hemivariational inequality
• elastic–viscoplastic
• frictional contact
• damage
• weak solution

AMS Subject Classifications:

• 74M15
• 49J40
• 47J20
• 35Q74
• 35J85

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This research is supported by the Science and Technology Department of Hunan Province [grant number 2011FJ3255]; by the Education Department of Hunan Province [grant number 12B024]. The research is also partially supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the Seventh European Community Framework Program under Grant Agreement number [295118]; the National Science Center of Poland under the Maestro Advanced Project number [DEC-2012/06/A/ST1/00262].