This study formulates a universal velocity field that is kinematically admissible for application in the extrusion of non-axisymmetric rods. Then upper bound theorem dictates that a better upper bound solution heavily depends on the precise conformity of the velocity field postulated. However, a compromise must frequently be made, since the formulation is in general rather complicated. The kinematically admissible velocity field proposed herein has the following features: (a) it is three-dimensional, (b) it is non-uniformally distributed in the axial direction, and (c) the formulation is straight-forward once the boundary of the deformation zone is specified. In addition, the velocity field is applied to the extrusion of rectangular, hexagonal, and octagonal rods from round billets. Moreover, the extrusion loads are calculated against process variables such as the semi-die angle, the percentage reduction of area, and the friction factor. Furthermore, the velocity field is compared with results from the literature, indicating that the present results render a better upper bound solution for application in extrusion than do previous results.
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