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 $\alpha$.

1 aDavoli, Elisa uhttps://doi.org/10.1142/S021820251450016X01461nas a2200217 4500008004100000022001400041245008900055210006900144300001400213490000700227520075100234653001700985653002301002653003101025653002601056653003101082653001601113100001801129700002501147856007101172 2013 eng d a0294-144900aA quasistatic evolution model for perfectly plastic plates derived by Γ-convergence0 aquasistatic evolution model for perfectly plastic plates derived a615 - 6600 v303 aThe 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.

10a-convergence10aPerfect plasticity10aPrandtl–Reuss plasticity10aQuasistatic evolution10aRate-independent processes10aThin plates1 aDavoli, Elisa1 aMora, Maria Giovanna uhttp://www.sciencedirect.com/science/article/pii/S0294144912001035