Quasistatic small-strain plasticity in the limit of vanishing hardening and its numerical approximation
- Bartels, Sören
- Mielke, Alexander
- Roubíček, Tomáš
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.
- SIAM J. Numer. Anal., 50 (2012) pp. 951--976.