Quasistatic evolution of perfectly plastic shallow shells: a rigorous variational derivation

In this paper, we rigorously deduce a quasistatic evolution model for shallow shells by means of (Formula presented.)-convergence. The starting point of the analysis is the three-dimensional model of Prandtl–Reuss elasto-plasticity. We study the asymptotic behaviour of the solutions, as the thickness of the shell tends to zero. As in the case of plates, the limiting model is genuinely three-dimensional, limiting displacements are of Kirchhoff–Love type, and the stretching and bending components of the stress are coupled in the flow rule and in the stress constraint. However, in contrast with the case of plates, the equilibrium equations are not decoupled, because of the presence of curvature terms. An equivalent formulation of the limiting problem in rate form is also discussed.