A quasistatic contact problem with directional friction and damped response

Abstract

The quasistatic contact of a viscoelastic body with a rigid foundation is studied. The material behavior is modeled by a general nonlinear viscoelastic constitutive law. The contact is with directional friction and the foundation's resistance is proportional to the normal velocity. The existence of a unique weak solution to the problem is proved. The sliding frictional contact problem with wear is introduced, too, and the existence of its unique weak solution established. The proofs are based on fixed point theorems and elliptic variational inequalities, and the results hold when the friction and damping coefficients are small.

Keywords:

• Quasistatic contact
• directional friction
• damped normal response
• viscoelastic constitutive law
• existence and uniqueness
• weak solutions
• elliptic variational inequalities
• fixed points
• sliding contact
• wear

Additional information

Notes on contributors

M. Rochdi

†

M. Shillor

†

M. Sofonea

†