WIAS Preprint No. 1585, (2010)

Quasistatic small-strain plasticity in the limit of vanishing hardening and its numerical approximation


  • Bartels, Sören
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Roubíček, Tomáš
    ORCID: 0000-0002-0651-5959

2010 Mathematics Subject Classification

  • 35K65 35K85 49S05 65M60 74C05


  • Rate-independent plasticity, hardening, Prandtl--Reuss elastic/perfectly plastic model, energetic solution, convergence, finite elements




The quasistatic rate-independent evolution of the Prager--Ziegler-type model of linearized plasticity with hardening is shown to converge to the rate-independent evolution of the Prandtl--Reuss elastic/perfectly plastic model. Based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coefficients converging to 0 by using the abstract method of Gamma-convergence for rate-independent systems. An unconditionally convergent numerical scheme is devised and 2D and 3D numerical experiments are presented. A two-sided energy inequality is a posteriori verified to document experimental convergence rates.

Appeared in

  • SIAM J. Numer. Anal., 50 (2012) pp. 951--976.

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