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.

在这项工作中，讨论了热轧金属成形过程的纯粘塑性模型及其有限元离散化。给出了粘塑性流动规律和应力-应变率关系的推导。通过描述入口/出口边界约束的形式，以及引入接触条件和粘塑性摩擦定律，完成了变形问题的关联平衡系统。该系统使用连续有限元方法进行离散化，其中经典惩罚项已被构建并用于合并边界约束和接触条件。使用粘塑性摩擦定律需要估计摩擦参数，这是通过推导有限元方案的稳定性估计来实现的。