Study of ECAP based on stream function

•Velocity field for ECAPs was extracted using stream function approach.•Upper bound theorem was used to determine velocity fields.•Lagrangian descriptions of motion and flow pattern of material was derived.•Calculated flow pattern was fairly well correlated to experiment.

In the present study, for the first time velocity fields in ECAP’s deformation zone was extracted using stream function approach which is a powerful method in fluid mechanic. The extracted velocity field is based on the geometry of die and shape of streamlines. Considering the exponent of stream function (n), countless kinematically admissible velocity fields were derived. Then, the real field that minimizes the kinematically computed power was determined by the upper bound theorem. Lagrangian descriptions of motion as well as flow pattern of evolving material for different values of (n) were obtained. The flow pattern that was on the basis of the calculated velocity field was fairly well correlated to experimental results.