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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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1569-3953
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Volume 10, Issue 3 (Jan 2002)

Issues

Elastoviscoplastic Finite Element analysis in 100 lines of Matlab

C. Carstensen
  • *Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ R. Klose
  • Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2010-11-15 | DOI: https://doi.org/10.1515/JNMA.2002.157

Abstract

This paper provides a short Matlab implementation with documentation of the P 1 finite element method for the numerical solution of viscoplastic and elastoplastic evolution problems in 2D and 3D for von-Mises yield functions and Prandtl-Reuß flow rules. The material behaviour includes perfect plasticity as well as isotropic and kinematic hardening with or without a viscoplastic penalisation in a dual model, i.e. with displacements and the stresses as the main variables. The numerical realisation, however, eliminates the internal variables and becomes displacement-oriented in the end. Any adaption from the given three time-depending examples to more complex applications can easily be performed because of the shortness of the program and the given documentation. In the numerical 2D and 3D examples an efficient error estimator is realized to monitor the stress error.

Keywords:: finite element method; viscoplasticity; elastoplasticity; Matlab

About the article

Received: 2002-07-03

Published Online: 2010-11-15

Published in Print: 2002-09-01


Citation Information: Journal of Numerical Mathematics, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/JNMA.2002.157.

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