On thermoviscoelastic wheel-rail contact problems

This paper is concerned with the numerical solution of wheel - rail rolling contact problems. The unilateral dynamic contact problem between a viscoelastic body and a rigid foundation is considered. The contact with Coulomb friction law occurs at a portion of the boundary of the body. The contact condition is described in velocities. The friction coefficient is assumed to be bounded and suitable small. A frictional heat generation and heat transfer across the contact surface as well as Archard's law of wear in contact zone are assumed. The equlibrium state of this contact problem is described by the coupled hyperbolic variational inequality of the second order and a parabolic equation. To solve numerically this contact problem we will decouple it into mechanical and thermal parts. Finite difference and finite element methods are used to discretize the contact problem. The Augmented Lagrangian technique combined with the active set method are employed to solve the discretized contact problem. Numerical examples are provided.