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Type: Report × Subject: Rate-independent systems ×

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Now showing 1 - 3 of 3
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    Averaging of time-periodic dissipation potentials in rate-independent processes : dedicated to Tomáš Roubícek on the occasion of his sixtieth birthday
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Heida, Martin; Mielke, Alexander
    We study the existence and well-posedness of rate-independent systems (or hysteresis operators) with a dissipation potential that oscillates in time with period. In particular, for the case of quadratic energies in a Hilbert space, we study the averaging limit → 0 and show that the effective dissipation potential is given by the minimum of all friction thresholds in one period, more precisely as the intersection of all the characteristic domains. We show that the rates of the process do not converge weakly, hence our analysis uses the notion of energetic solutions and relies on a detailed estimates to obtain a suitable qui-continuity of the solutions in the limit → 0.
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    From damage to delamination in nonlinearly elastic materials at small strains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Mielke, Alexander; Roubíček, Thomáš; Thomas, Marita
    Brittle 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
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    A rate-independent gradient system in damage coupled with plasticity via structured strains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Bonetti, Elena; Rocca, Elisabetta; Rossi, Riccarda; Thomas, Marita
    This contribution deals with a class of models combining isotropic damage with plasticity. It has been inspired by a work by Freddi and Royer-Carfagni [FRC10], including the case where the inelastic part of the strain only evolves in regions where the material is damaged. The evolution both of the damage and of the plastic variable is assumed to be rate-independent. Existence of solutions is established in the abstract energetic framework elaborated by Mielke and coworkers (cf., e.g., [Mie05, Mie11b]).