Hemivariational inequalities modeling dynamic viscoelastic contact problems with friction. (English) Zbl 1093.74047
Begehr, H. G. W. (ed.) et al., Advances in analysis. Proceedings of the 4th international ISAAC congress, Toronto, Canada, August 11–16, 2003. Hackensack, NJ: World Scientific (ISBN 981-256-398-9/hbk). 295-304 (2005).
Summary: We consider a mathematical model which describes the dynamic viscoelastic frictional contact between a deformable body and an obstacle. The contact process is modeled by a general normal damped response condition, and the dependence of normal stress on the normal velocity is assumed to have nonmonotone character of subdifferential form. The problem is formulated as a hyperbolic hemivariational inequality with nonmonotone multidimensional and multivalued boundary conditions. We establish the existence of solutions by using a surjectivity result for multivalued pseudomonotone operators. Under a stronger hypothesis, the uniqueness of solution is obtained.
For the entire collection see [Zbl 1076.35003].
For the entire collection see [Zbl 1076.35003].
MSC:
74M15 | Contact in solid mechanics |
74M10 | Friction in solid mechanics |
74D10 | Nonlinear constitutive equations for materials with memory |
74H20 | Existence of solutions of dynamical problems in solid mechanics |
74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
49J40 | Variational inequalities |