Two-dimensional analysis of rolling process using a generalized upper bound approach based on a polynomial velocity field

In order to predict material flow and mechanical loads in a 2D plain strain rolling process, in this work, a mathematical rolling model based on the Upper Bound Method (UBM) was developed. In particular, a family of polynomial kinematically admissible velocity fields is proposed and used. Some of these velocity fields with a low number of parameters are used. Among the infinite values ​​that the velocity field coefficients can take on, the most plausible ones will be those that minimize the function that expresses the power necessary to carry out the rolling process. It is possible to observe that non linear fields of that family give a better approximation than the classic one. Predictions were compared with FEM analysis in terms of rolling loads, and results are in good agreement, especially using high degree polynomial fields.