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Implementation of an elastoplastic solver based on the Moreau–Yosida Theorem

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  • Gruber, Peter
  • Valdman, Jan

Abstract

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 ɛ(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.

Suggested Citation

  • Gruber, Peter & Valdman, Jan, 2007. "Implementation of an elastoplastic solver based on the Moreau–Yosida Theorem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 73-81.
    • Handle: RePEc:eee:matcom:v:76:y:2007:i:1:p:73-81
    DOI: 10.1016/j.matcom.2007.01.036
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