Browsing by Author "Davoli, Elisa"
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Item Linearized plastic plate models as gamma-limits of 3D finite elastoplasticity(SISSA, 2012-11) Davoli, Elisa; MathematicsItem A Quasistatic evolution model for perfectly plastic plates derived by Gamma-convergence(SISSA, 2012-04) Davoli, Elisa; Mora, Maria Giovanna; Mathematics; Functional Analysis and ApplicationsThe 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 Gamma-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.Item Quasistatic evolution models for thin plates arising as low energy gamma-limits of finite plasticity(SISSA, 2012-11) Davoli, Elisa; MathematicsItem Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity(SISSA, 2011-06-30) Davoli, Elisa; Mathematics; Functional Analysis and ApplicationsThe 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 {\delta}_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 {\epsilon}_h^2, with {\epsilon}_h/{\delta}_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of {\delta}_h with respect to h.