The behavior of most high temperature metals, polymers, concrete and wide range of composite materials are described as viscoplastic flows. The mathematical theory of plasticity adequately describes the time-independent aspect of the behavior of materials but is inadequate for analysis of time-dependent behavior. An approach to achieve a satisfactory formulation for time-dependent behavior has been generalized plasticity to cases within the strain-rate-sensitive range. One such generalization has been provided by the theory of viscoplasticity. On the other hand, when large, progressive deformation occurs under plastic or viscoplastic conditions, elastic deformations are negligible and the material flows in a viscous manner. In this study a novel Eulerian method based on solution algorithm for incompressible flows is developed for simulation of viscoplastic flows of materials. In order to develop a tool for modeling metal forming process we implemented in the flow formulation based on Eulerian finite difference method.In the extrusion and forming of solids the plastic (or viscoplastic) deformations are so large that the elastic strain is negligible. So in our work the viscoplastic materials are treated as incompressible non-Newtonian viscous fluids. By doing this we obtained a reliable and efficient Eulerian formulation for modeling steady and transient metal forming problems. Finally some cases were analyzed in order to test performance of the formulation. The governing equations consist of conservation of mass and momentum together with viscoplastic constitutive equation. Since both material and die are assumed to be at the same temperature, the energy equation and momentum equation become identical and it is not necessary to solve energy equation. An important advantage of the proposed method is its ability to simulate large deformations and longtime transient solutions. Despite of the justify; MARGIN: 12pt 0cm 0pt; unicode-bidi: Keywords: Viscoplastic forming, Perzyna, ghost fluid method, level-set, fifth order WENO, TVD Runge-Kutta, finite difference
