Calculus of Variations and Geometric Measure Theory

E. Davoli

Linearized plastic plate models as $\Gamma$-limits of 3D finite elastoplasticity

created by davoli on 30 Nov 2012
modified on 09 Jul 2014


Inserted: 30 nov 2012
Last Updated: 9 jul 2014

Journal: ESAIM:Control, Optimisation and calculus of variations
Volume: 20
Number: 3
Year: 2012


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 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 K ́arma ́n plate theory and the linearized plate theory.

Keywords: $\Gamma$-convergence, thin plates, finite plasticity