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Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity

TitleQuasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity
Publication TypeJournal Article
Year of Publication2014
AuthorsDavoli, E
JournalMathematical Models and Methods in Applied Sciences
Volume24
Pagination2085-2153
Abstract

In this paper we deduce by $\Gamma$-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we study the case where the scaling factor of the elasto-plastic energy is of order $\epsilon^{2 \alpha -2}$, with $\alpha\geq 3$. These scalings of the energy lead, in the absence of plastic dissipation, to the Von Kármán and linearized Von Kármán functionals for thin plates. We show that solutions to the three-dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on $\alpha$.

URLhttps://doi.org/10.1142/S021820251450016X
DOI10.1142/S021820251450016X

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