A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence

Davoli, Elisa; Mora, Maria Giovanna

Annales de l'I.H.P. Analyse non linéaire, Tome 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.

Classification : 74C05, 74G65, 74K20, 49J45
Mots clés : Quasistatic evolution, Rate-independent processes, Perfect plasticity, Thin plates, Prandtl–Reuss plasticity, Γ-convergence

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