1. Introduction

The rolling process is one of the most popular processes in manufacturing industries in that almost 80% of metallic equipment has been exposed to rolling, at least one time in their production period. Among all kinds of the rolling processes, the flat rolling is the most practical one. In industrial countries, about 40–60% of rolling products are produced with this type of rolling. Therefore, many scientists have tried to enhance the quality and quantity of products by optimizing this process and identifying parameters affecting it to satisfy their costumers.

Throughout this century the rolling process has been analyzed by various analytical and numerical methods such as the slab method, the slip-line field method, the upper bound method, the boundary element method and the finite element method. In comparison with other methods for analyzing the rolling process, the finite element method is the most practical and accurate one. Galantucci and Tricarico (1999) have proposed many models developed using the FEM, differing with respect to: (i) the type of analysis (transient, steadystate); (ii) the type of formulation (incremental, variational or flow); (iii) the solution technique (updated Lagrangian, Eule-rian); (iv) the constitutive law hypothesized for the material behavior (elasto-plastic, elasto-viscoplastic, rigid-plastic, viscoplastic, etc.); (v) the type of discretization (2D in the case of plane deformation, 3D in form rolling); and (vi) the type of analysis (mechanical, thermal, uncoupled or coupled thermomechanical)