Mathematics

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 $\alpha\geq 3$. These scalings of the energy lead, in the absence of plastic dissipation, to the Von Kármán and linearized Von Kármán functionals for thin plates. 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 $\alpha$.