A model and numerical investigation for rolling metal process using continuous finite element discretizations

In this work, pure viscoplastic models and their finite element discretizations for hot rolling metal-forming processes are discussed. The derivation of the viscoplastic flow rule and the stress-strain rate relation are presented. The associated equilibrium system of the deformation problem is completed by describing the form of the inlet/outlet boundary constraints, as well as introducing the contact conditions and the viscoplastic friction law. The system is discretized using continuous finite element methods where classical penalty terms have been constructed and used for incorporating the boundary constraints and the contact conditions. The use of viscoplastic friction law requires an estimation of the friction parameter, which is achieved through the derivation of stability estimates for the finite element scheme. Numerical tests have been performed and compared for investigating the effect of the strain sensitivity parameter on the behaviour of the plate velocity and on the magnitude of the interfacial stresses.