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The numerical solution of small-strain plasticity problems is widely considered to be a
solved problem. Somewhat surprisingly, we nevertheless demonstrate that
considerable speedup is still possible, by direct application of a nonsmooth multigrid
method of TNNMG type. The algorithm is globally convergent, and exhibits
convergence rates comparable to a multigrid solver for linear elasticity. It works both
for smooth and nonsmooth yield surfaces (multi-surface plasticity), and even for
certain gradient-plasticity models.