Efficient Elasto-Plastic Simulation

  • C. Wieners


In this paper we describe a method for the construction of radial return algorithms to the plasticity models discussed in Alber [1]. For the classical examples this shows that the algorithms in Simo-Hughes [5] can be derived by this method in a systematic way. We apply the method to viscoplasticity with nonlinear isotropic and kinematic hardening. The combination of parallel multigrid methods with the radial return algorithm results in a very efficient algorithm. The performance of the method is illustrated by a numerical example.


Kinematic Hardening Radial Return Implicit Euler Method Return Parameter Return Mapping Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H.-D. Alber, Materials with memory, vol. 1682 of Lecture Notes in Mathematics, Springer, 1998.MATHGoogle Scholar
  2. 2.
    P. Bastian, K. Birken, K. Johannsen, S. Lang, N. Neuss, H. Rentzreichert, and C. Wieners, Ug — a flexible software toolbox for solving partial differential equations, Computing and Visualization in Science, 1 (1997), pp. 27–40.MATHCrossRefGoogle Scholar
  3. 3.
    R. Blaheta, Convergence of Netwon-type methods in incremental return mapping analysis of elasto-plastic problems, Comput. Meth. Appl. Mech. Engrg., 147 (1997), pp. 167–185.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    J. Lemaitre and J. L. Chaboche, Mechanics of solid materials, Cambridge University press, 1994.Google Scholar
  5. 5.
    J. C. Simo and T. J. R. Hughes, Computational inelasticity, Springer, 1998.MATHGoogle Scholar
  6. 6.
    J. C. Simo and R. L. Taylor, Consistent tangent operators for rateindependent elastoplasticity, Comput. Meth. Appl. Mech. Engrg., 48 (1985), pp. 101–118.MATHCrossRefGoogle Scholar
  7. 7.
    C. Wieners, Orthogonal projections onto convex sets and the application to problems in plasticity, tech. rep., Universität Stuttgart, Sfb 404 Preprint 99/15, 1999.Google Scholar
  8. 8.
    C. Wieners, Theorie und Numerik der Prandtl-Reufβ Plastizität, Universität Heidelberg, 1999. Habilitationsschrift, submitted.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • C. Wieners
    • 1
  1. 1.ICAUniversity of StuttgartGermany

Personalised recommendations