Convex analysis and computational plasticity

We consider the radial return algorithm which is commonly used in computational plasticity. We show that this method solves the primal and the dual problem in plasticity. Applying standard results in convex analysis, we show that criteria for the existence, the uniqueness, and for the convergence of discrete approximations can be easily derived.

This is applied to static and quasi-static plasticity. Using the transformation method of internal variables introduced by Alber, we show that the method can be analysed in the same way in case of nonlinear hardening.