Stability of equilibrium of a compressible hyperelastic hollow sphere

An analytical algorithm for studying the stability of the equilibrium of compressible hyperelastic sphere with Lagrange variables is proposed. The problem is solved in a spherical coordinate system in a general three-dimensional formulation using linearized stability theory and the method of separation of variables with respect to the radial displacement, the displacement due to the rotation, and the resulting strain in the principal directions. Results of numerical and graphical analysis of the stress–strain state for a three-layer-sphere are used to analyze the gravity stress–strain state of the lithosphere of the Kuril island arc system.