Quasi-Static Small-Strain Plasticity in the Limit of Vanishing Hardening and Its Numerical Approximation

The quasistatic rate-independent evolution of the Prager-Zieglertype 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 coe cients converging to 0 by using the abstract method of Γ-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 veri ed to document experimental convergence rates.