Solving the Problem of Gravitational Compression of a Layered Sphere (by the Example of the Earth)

Abstract

The problem of spherically symmetric, gravitational compression of an isotropic hyperelastic layered sphere which modeling the region of the Earth below the Mohorovicic boundary is solved. The known mechanical characteristics of the Earth in the compressed state are used to find its characteristics in the unstrained state obtained by adiabatic or isothermal stress relief. The stress state differs significantly from the state of purely hydrostatic compression. The minimum bulk compression and maximum radial tension occur not on the boundary of the sphere but in depth at certain distances from the boundary.