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, p. 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 : https://doi.org/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
@article{AIHPC_2013__30_4_615_0,
     author = {Davoli, Elisa and Mora, Maria Giovanna},
     title = {A quasistatic evolution model for perfectly plastic plates derived by $\Gamma$-convergence},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {30},
     number = {4},
     year = {2013},
     pages = {615-660},
     doi = {10.1016/j.anihpc.2012.11.001},
     zbl = {06295435},
     mrnumber = {3082478},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2013__30_4_615_0}
}
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/item/AIHPC_2013__30_4_615_0/

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