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XFEM for Deformation Theory of Plasticity
Author(s) -
Omerović Samir,
Fries ThomasPeter
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510102
Subject(s) - extended finite element method , finite element method , convergence (economics) , plasticity , work (physics) , simple (philosophy) , deformation (meteorology) , displacement (psychology) , mathematics , displacement field , section (typography) , mathematical analysis , computer science , structural engineering , physics , engineering , mechanical engineering , psychology , philosophy , epistemology , meteorology , economics , psychotherapist , thermodynamics , economic growth , operating system
In this work, an approach is presented to improve global accuracy properties for physically non‐linear problems in the frame of elastoplasticity. The work is motivated by the fact that convergence characteristics of a finite element solution are dominated by the regularity of the exact solution. For a material undergoing inelastic deformations, however, very few analytical solutions for the field variables are known, especially for the displacement field. Considering a simple, one‐dimensional example, it is shown that the convergence rates are far from optimal. The reason is explained by establishing ties to a familiar, but more demonstrative problem. In the next section two remedies for the problem, based on the Extended Finite Element Method (XFEM) are presented and discussed, in the last section a 2D‐problem is considered. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)