The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of $\Gamma$-convergence, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order $\epsilon^{2 \alpha -2}$, with $\alpha \geq 3$. According to the value of $\alpha$, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.

1 aDavoli, Elisa uhttps://www.math.sissa.it/publication/linearized-plastic-plate-models-%CE%B3-limits-3d-finite-elastoplasticity01155nas a2200121 4500008004100000245010200041210006900143300001400212490000700226520073600233100001800969856004600987 2014 eng d00aQuasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity0 aQuasistatic evolution models for thin plates arising as low ener a2085-21530 v243 aIn 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/S029414491200103501043nas a2200097 4500008004100000245013400041210006900175520055400244100001800798856012900816 2011 eng d00aThin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity0 aThinwalled beams with a crosssection of arbitrary geometry deriv3 aThe subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

1 aDavoli, Elisa uhttps://www.math.sissa.it/publication/thin-walled-beams-cross-section-arbitrary-geometry-derivation-linear-theories-starting00908nas a2200109 4500008004300000245010700043210006900150520050000219100001800719700002500737856003600762 2010 en_Ud 00aConvergence of equilibria of thin elastic rods under physical growth conditions for the energy density0 aConvergence of equilibria of thin elastic rods under physical gr3 aThe subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory.1 aDavoli, Elisa1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/4086