Plane-strain extrusion of a nonworkhardening material through a die with arbitrarily defined profile is analyzed using extremum principles. General kinematically admissible flow models for the extrusion process are obtained using the flow function approach. A closed-form expression for the rate of energy dissipated is derived with a special class of the flow models. For given process conditions, an approximate solution of extrusion pressure and metal flow is obtained by minimizing the rate of energy dissipated. Results obtained with the wedge-shaped dies, cosine dies, elliptic dies, and hyperbolic dies are presented. Optimal shapes of the dies for different frictional conditions at the die-material interface are derived from the solution.

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