Calculus of Variations and Geometric Measure Theory

E. Davoli - M. G. Mora

A quasistatic evolution model for perfectly plastic plates derived by Gamma-convergence

created by mora on 03 Apr 2012
modified on 05 Dec 2015


Inserted: 3 apr 2012
Last Updated: 5 dec 2015

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2013


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.

Keywords: Gamma-convergence, quasistatic evolution, rate-independent processes, Prandtl-Reuss plasticity, perfect plasticity, thin plates