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

The quasi-static rate-independent evolution of the Prager-Ziegler-type model of 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 two- and three-dimensional numerical experiments are presented. A two-sided energy inequality is a posteriori verified to document experimental convergence rates.

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