In this paper, an analytical method for noncircular shape extrusion is presented. Using this method, non-linear deformation field can be described with Hermit cubic spline which is prescribed by the boundary conditions of the die at its entryand exit. The upper bound method has been used to obtain optimum coefficient of the tangential boundary conditions. The results show that the optimum tangential parameter and the extrusion force determined by this method have good agreement with those obtained from other established methods. Also physical modeling tests show that optimum non-linear die could reduce extrusion force and strain variation compared with those in a linear die.

Keywords: Extrusion, Upper bound method, Non-linear die, Physical modeling

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