UDC 550.343.6
THE CONSTRUCTION OF GLOBAL MATHEMATICAL MODEL ASSESSING STRESS-STRAIN STATE OF THE EARTH'S LITHOSPHERE
A. O. Faddeev, Dr. Sc. (Tech.), associate Professor, Professor of the Chair of Mathematics and Information Technologies of Management of the Academy of law management of the Federal penal service of Russia, Ryazan, Russia; This email address is being protected from spambots. You need JavaScript enabled to view it..
S. A. Pavlova, Ph.D. (Tech.), Senior Lecturer, Chair of Mathematics and Information Technologies of Management of the Academy of law management of the Federal penal service of Russia, Ryazan, Russia; This email address is being protected from spambots. You need JavaScript enabled to view it..
T. M. Nevdakh, teacher, Chair of Mathematics and Information Technologies of Management of the Academy of law management of the Federal penal service of Russia, Ryazan, Russia; This email address is being protected from spambots. You need JavaScript enabled to view it..
The article discusses a mathematical model for assessing stress-strain state of the Earth's lithosphere. The aim of is to build a mathematical model for estimating stress-strain state of the Earth’s lithosphere, and to reconstruct geodynamic stress fields that cause modern movements and deformations in the lithosphere. When constructing a mathematical model, methods of continuum mechanics, methods of the theory of differential equations were applied. Control of the correctness of the calculation of stresses was carried out according to the data on movement speeds on the surface of the earth's crust, known from satellite measurements, which are used to navigate and accurately measure geodetic coordinates of various objects. The mathematical model presented allows using it to restore the fields of both elastic and elastic-viscous deformations, which is a fundamental point when performing numerical estimates of elastic-viscous shear stresses at any deep level of the Earth's lithosphere.
Key words: mathematical model, geodynamic stability, stress tensor, displacement vector, shear deformations, viscosity, lithosphere.