A Thermodynamic Contact Problem for Elastic-Viscoplastic Materials

Abstract

Mathematical modeling of stress generation and heat transfer in casting processes is a difficult and complex subject that is now receiving increased attention. In this paper, we study a dynamic problem which describes the frictional contact between an elastic-viscoplastic body (a deformable product of casting process: slab, bloom etc.) and a rigid obstacle (walls of the mold or cilindrical rolls system employed for support – traction – soft reduction) in complicated conditions concerning heat conduction on contact interface in the solidification process.
In the next sections we will briefly formulate the fundamentals of the kinematics for a large deformation approach and the basic equations governing our model. After this, we will explain, in more details, the classical problem statement and the foundation of the weak formulation of this problem, which consist of certain variational inequalities for the viscoelasticity and viscoplasticity parts, and, a variational parabolic equation for the heat conduction part.