Nonsmooth dynamic frictional contact of a thermoviscoelastic body

Abstract

This paper studies a system of two hemivariational inequalities modeling a dynamic thermoviscoelastic contact problem with general nonmonotone and multivalued subdifferential boundary conditions. Thermal effects are included in the Kelvin–Voigt thermoviscoelastic constitutive law and in the boundary conditions, and so in frictional heat generation, which takes place on the boundary and enters the condition for the temperature. The existence of a weak solution to the problem is established using a recent surjectivity result for differential inclusions associated with pseudomonotone operators.

Keywords:

• Hemivariational inequality
• Clarke subdifferential
• thermoviscoelastic material
• frictional heat generation
• evolutionary inclusion
• existence

AMS Subject Classifications:

• 47J20
• 74H20
• 47J22
• 49J40
• 74M15
• 74M10
• 35L85
• 35K85

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported in part by [grant Maestro number DEC-2012/06/A/ST1/00262] provided by the National Science Centre of Poland.