Reduced cosserat continuum as a possible model for granular medium

Vladimir Lalin, Elizaveta Zdanchuk

Abstract


We considered a nonlinear reduced Cosserat continuum: an elastic medium, whose translations and rotations are independent, the force stress tensor is asymmetric and the couple stress tensor is zero. We suggested the reduced Cosserat continuum as a possible model for granular medium. Granular materials are ubiquitous in our daily lives. They play an important role in many industries, such as mining, agriculture, and construction. We considered a nonlinear reduced Cosserat continuum for reference and current configurations and obtained the set of equations for each configuration.


Keywords:

reduced Cosserat continuum, current configuration, reference configuration, energy coupling tensors

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References


Badanin, A.; Bugrov, A.; Krotov, A., 2012. The determination of the first critical load on particulate medium of sandy loam foundation. Magazine of civil engineering, 9, pp. 29-34. (in Rus).

Grekova, E.F.; Herman, G.C., 2004. Wave propagation in rocks modelled as reduced Cosserat continuum. Proceedings of 66th EAGE conference, Paris.

Grekova, E.F., 2012a. Linear reduced cosserat medium with spherical tensor of inertia, where rotations are not observed in experiment. Mechanics of solids, 47(5), pp. 538-543. http://dx.doi.org/10.3103/S002565441205007X

Grekova, E.F., 2012b. Nonlinear isotropic elastic reduced Cosserat continuum as a possible model for geomedium and geomaterials. Spherical prestressed state in the semilinear material. Journal of seismology, 16(4), pp. 695-707. http://dx.doi.org/10.1007/s10950-012-9299-2

Harris, D., 2006. Douple-slip and Spin: Dilatant Shear in a Reduced Cosserat Model. Modern Trends in Geomechanics, Springer.

Harris, D., 2009. Double-slip and Spin: A generalisation of the plastic potential model in the mechanics of granular materials. International Journal of Engineering Science, 47, pp. 208-1215. http://dx.doi.org/10.1016/j.ijengsci.2008.12.005

Heinrich, M.; Jaeger&Sidney, R.; Nagel, 1996. Granular solids, liquids, and gases. Reviews of modern physics, 68(4), pp. 1259-1273. http://dx.doi.org/10.1103/RevModPhys.68.1259

Kulesh, M. A.; Grekova, E. F.; Shardakov, I. N., 2009. The problem of propagation of surface waves in the reduced Cosserat medium. Akusticheskiy zhurnal, 55(2), pp. 216-225. (in Rus).

Kurbatskiy, E.N.; Golosova, O.A., 2011. Features of the propagation of stress waves in natural and artificial granular media. Structural mechanics and calculation of structures, 2, pp. 45-50. (in Rus).

Lalin, V., 2007. Non-linear dynamics equations of the moment elastic medium. Scientific and technical Sheets SPbGPU. (in Rus).

Lalin, V.; Zdanchuk, E., 2011. On the Cauchy problem for nonlinear reduced Cosserat continuum. In Proc. of the XXXIX Summer school- conference “Advanced Problems in Mechanics”, St.Petersburg, Russia.

Lalin, V.; Zdanchuk, E., 2012. A model of continuous granular medium. Waves in the reduced Cosserat continuum. Magazine of civil engineering, 5(31), pp. 65-71. (in Rus.).

Lurie, A.I., 1990. Nonlinear theory of elasticity. Amsterdam.

Schwartz, L.M.; Johnson, D.L.; Feng, S., 1984. Vibrational modes in granular materials. Physical review letters, 52(10), pp. 831-834. http://dx.doi.org/10.1103/PhysRevLett.52.831

Zdanchuk, E.; Lalin, V., 2010. The Theory of Continuous Medium with Free Rotation without Coupled Stresses. In Proc. of the XXXVIII Summer school- conference “Advanced Problems in Mechanics”, St.Petersburg, Russia.

Zhilin, P.A., 1996. A new approach to the analysis of free rotations of rigid bodies. ZAMM-Z. angew. Math.Mech, 76(4), pp. 187-204. http://dx.doi.org/10.1002/zamm.19960760402




DOI: 10.7250/iscconstrs.2014.15

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