TY - JOUR T1 - A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2013 A1 - Elisa Davoli A1 - Maria Giovanna Mora KW - -convergence KW - Perfect plasticity KW - Prandtl–Reuss plasticity KW - Quasistatic evolution KW - Rate-independent processes KW - Thin plates AB -

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.

VL - 30 UR - http://www.sciencedirect.com/science/article/pii/S0294144912001035 ER -