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 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.
A quasistatic evolution model for perfectly plastic plates derived by Gamma-convergence
Mora, M. G.
2013-01-01
Abstract
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
