Implementation of an elastoplastic solver based on the Moreau-Yosida theorem
We discuss a technique for solving elastoplastic problems with hardening. The one time-step elastoplastic problem can be formulated as a convex minimization problem with a continuous but non-smooth objective. We actually show that its objective structure satisfies conditions of the Moreau-Yosida Theorem known from convex analysis. Therefore, the substitution of the non-smooth plastic-strain p as a function of the total strain epsilon(u) yields an already smooth functional in the displacement u only. The second derivative of such functional exists in all continuum points apart from interfaces where elastic and plastic zones intersect. The numerical experiment states super-linear convergence of a Newton method or even quadratic convergence as long as the interface is detected sufficiently. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
elastoplasticity moreau-yosida newton method finite element methods