Multi-Scale Mathematical Models of Geomedium
A. F. Revuzhenko
Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630091 Russia
Keywords: Geomechanics, mathematical models, role of internal structure, S-waves
Abstract
The author describes the specifics of the multi-scale mathematical modeling of geomedium as a case-study of a two-scale model. The first scale modeling assumes the linearly elastic medium, and the second scale model includes the plastic strains and internal friction. It is shown that in the first approximation, when the micro-level stress gradients are assumed to be constant, the model acquires elastoplasticity with regard to local bends of structural elements of the geomedium. The solution of the problem on plane S-waves reveals that the waves possess dispersion and their velocity decreases with increasing plastic strains.
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