Approaches to the Solution of the Lamé–Gadolin Problem for a Composite Hollow Ball Made of Nonlinear Elastic and Elasto-Plastic Materials Under Superimposed Finite Deformations

The formulation of the Lamé–Gadolin problem on the equilibrium of a hollow sphere consisting of two parts, one of which is preliminarily deformed, is given for finite deformations. An analytical solution of the problem for the elastic potential of a special form is obtained. A numerical solution of the problem for an elastoplastic material is obtained. When modeling plastic deformations, the Drucker–Prager plasticity condition is used, and the plastic flow is described using an unassociated law.