Quasistatic evolution in the theory of perfect elasto-plastic plates. Part II: Regularity of bending moments

Abstract

We study differentiability of solutions of quasistatic problems for perfect elasto-plastic plates. We prove that in the isotropic case bending moments has locally square-integrable first derivatives: $M\in L^{\infty }([0,T];W_{\mathrm{loc}}^{1,2}(\Omega ;{\mathbb{M}}_{\mathrm{sym}}^{2\times 2}))$. The result is based on discretization of time and uniform estimates of solutions of the incremental problems, which generalize the estimates in the static case of perfect elasto-plastic plates.