Structural Model of the Earth and its Behavior under Dynamic Internal Influence

Within framework of complex continuous media, the structure is modeled and the stress-strain state of a spherical object approximated to the Earth model under dynamic internal and constant external influences is determined. The spherical body consists of four layers. The outer layer, modeling the mantle, is represented by a hardening elastic-viscoplastic dilating medium. The core has three layers, the outer one is represented by the model of an incompressible ideally plastic von Mises body, the second and third by the model of an incompressible elastic-viscoplastic body. The dynamic load is uniformly distributed along the inner surface of the third layer of the core, and the load of constant intensity is uniformly distributed along the outer surface of the spherical body. Within the framework of the axisymmetric stress-strain state, an analytical solution to the problem is obtained. Relationships for displacement and stress fields in plastic and elastic regions of layers are determined. A system of equations for determining the integration constants and radii of elastic-plastic boundaries is obtained. This system of equations requires a numerical solution. The paper also presents the conditions for exhaustion of the bearing capacity of a spherical object.