Calculus of Variations and Geometric Measure Theory

E. Davoli

Quasistatic evolution models for thin plates arising as low energy $\Gamma$-limits of finite plasticity

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


Inserted: 30 nov 2012
Last Updated: 9 jul 2014

Journal: M3AS
Volume: 24
Number: 10
Year: 2012


In this paper we deduce by $\Gamma$-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we study the case where the scaling factor of the elasto- plastic energy is of order $\epsilon^{2\alpha-2}$, with $\alpha\geq 3$. We show that solutions to the three- dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on $\alpha$.

Keywords: $\Gamma$-convergence, quasistatic evolution, rate-independent processes, thin plates, finite plasticity