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

Peter Gruber and Jan Valdman

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 76, issue 1, 73-81

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.

Keywords: Elastoplasticity; Moreau–Yosida; Newton method; Finite element methods (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:76:y:2007:i:1:p:73-81

DOI: 10.1016/j.matcom.2007.01.036

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