Finite deformation of a panel in the cases of ideal plasticity and superplasticity

Finite deformation of the panel under the influence of pressure is considered. The statement of the problem in displacements with equilibrium conditions represented via true stresses in Lagrangian coordinates is proposed. It is proven that the initial equations are satisfied when the panel is uniformly curved during deformation. The use of the previously proposed defining relation make it possible to determine a differential relationship between the laws of pressure and curvature with time at an arbitrary strain rate. Ideally plastic and superplastic deformations are considered. The dependences of pressure on the curvature and strain time are obtained at which superplasticity occurs. It is revealed that in this case that the range of stable changes in the curvature does not depend on the strain rate, and the threshold stress does not affect the time it takes to reach a given curvature of the panel.