A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 4, pp. 615-660.

The subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic–perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl–Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff–Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.

DOI: 10.1016/j.anihpc.2012.11.001
Classification: 74C05, 74G65, 74K20, 49J45
Keywords: Quasistatic evolution, Rate-independent processes, Perfect plasticity, Thin plates, Prandtl–Reuss plasticity, Γ-convergence
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     title = {A quasistatic evolution model for perfectly plastic plates derived by {\protect\emph{\ensuremath{\Gamma}}-convergence}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Davoli, Elisa; Mora, Maria Giovanna. A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence. Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 4, pp. 615-660. doi : 10.1016/j.anihpc.2012.11.001. http://www.numdam.org/articles/10.1016/j.anihpc.2012.11.001/

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