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- ItemFrom damage to delamination in nonlinearly elastic materials at small strains(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Mielke, Alexander; Roubíček, Thomáš; Thomas, MaritaBrittle Griffith-type delamination of compounds is deduced by means of Gamma-convergence from partial, isotropic damage of three-specimen-sandwich-structures by flattening the middle component to the thickness 0. The models used here allow for nonlinearly elastic materials at small strains and consider the processes to be unidirectional and rate-independent. The limit passage is performed via a double limit: first, we gain a delamination model involving the gradient of the delamination variable, which is essential to overcome the lack of a uniform coercivity arising from the passage from partial damage to delamination. Second, the delamination-gradient is supressed. Noninterpenetration- and transmission-conditions along the interface are obtained
- ItemQuasistatic small-strain plasticity in the limit of vanishing hardening and its numerical approximation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Bartels, Sören; Mielke, Alexander; Roubíček, ThomášThe 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.