Accuracies of numerical solution methods for the pressure‐modified von Mises model

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Abstract
The accuracy of three numerical algorithms—the tangent‐stiffness radial‐return, secant‐stiffness radial‐return and simple radial‐return methods—is analysed against exact solutions for the pressure‐modified von Mises yield criterion with the associated flow rule. The governing equations of the exact solutions are derived using a simple and innovative geometrical approach, in terms of a pair of non‐linear, first order differential equations, in rate change of the deviatoric radius and in rate change of angular locations on the deviatoric plane. For both accuracy and efficiency, and for small and large time steps, the secant‐stiffness radial‐return method is the best of all.

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