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kulesh

HR: 1340h
AN: S23B-0151
TI: Modeling of the Propagation of Seismic Waves in Non-Classical Media: Reduced Cosserat Continuum
AU: Grekova, E
EM: elgreco@pdmi.ras.ru
AF: Institute for Problems in Mechanical Engineering RAS, Bolshoy pr, V.O., 61, St. Petersburg, 199176 Russian Federation
AU: * Kulesh, M
EM: mkulesh@math.uni-potsdam.de
AF: Institute for Mathematics, University of Potsdam, Am Neuen Palais 10, Potsdam, 14469 Germany
AU: Herman, G
EM: Gerard.Herman@Shell.com
AF: Shell International E&P, P.O. Box 60, Rijswijk, 2280 Netherlands
AU: Shardakov, I
EM: shardakov@icmm.ru
AF: Institute of Continua Media Mechanics, Ural Branch of RAS, street Academ. Koroleva, 1, Perm, 614013 Russian Federation
AB: In rock mechanics, elastic wave propagation is usually modeled in terms of classical elasticity. There are situations, however, when rock behaviour is still elastic but cannot be described by the classical model. In particular, current effective medium theories, based on classical elasticity, do not properly describe strong dispersive or attenuative behaviour of wave propagation observed sometimes. The approach we have taken to address this problem is to introduce supplementary and independent degrees of freedom of material particles, in our case rotational ones. Various models of this kind are widely used in continuum mechanics: Cosserat theory, micropolar model of Eringen, Cosserat pseudocontinuum, reduced Cosserat continuum etc. We have considered the reduced Cosserat medium where the couple stress is zero, while the rotation vector is independent of the translational displacement. In this model, the stress depends on the rotation of a particle relatively to the background continuum of mass centers, but it does not depend on the relative rotation of two neighboring particles. This model seems to be adequate for the description of granular media, consolidated soils, and rocks with inhomogeneous microstructure. A real inhomogeneous medium is considered as effective homogeneous enriched continuum, where proper rotational dynamics of inhomogeneities are taken into account by means of rotation of a particle of the enriched continuum. We have obtained and analyzed theoretical solutions for this model describing the propagation of body waves and surface waves. We have shown both the dispersive character of these waves in elastic space and half space, and the existence of forbidden frequency zones. These results can be used for the preparation, execution, and interpretation of seismic experiments, which would allow one to determine whether (and in which situations) polar theories are important in rock mechanics, and to help with the identification of material parameters of the reduced Cosserat continuum.
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 3909 Elasticity and anelasticity
DE: 7203 Body waves
DE: 7255 Surface waves and free oscillations
DE: 7260 Theory
SC: Seismology [S]
MN: 2006 Fall Meeting