Abstract
An exact solution that describes the fields of displacements and stresses in an expanding spherical layer is constructed within the framework of the theory of small strains of a granular medium with rigid particles. For finite strains, the problem reduces to a nonlinear system of ordinary differential equations, which is solved by numerical methods. Similar solutions are found in the problem for a cylindrical layer. Based on these solutions, the effect of the dilatancy of the granular medium on the stress-strain state near expanding cavities is found.
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References
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O. V. Sadovskaya and V. M. Sadovskii, Mathematical Modeling in Problems of Mechanics of Granular Materials [in Russian], Fizmatlit, Moscow (2008).
O. V. Sadovskaya and V. M. Sadovskii, “On the theory of finite strains of a granular medium,” Prikl. Mat. Mekh., 71, No. 1, 102–121 (2007).
G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow (1989).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 190–196, May–June, 2009.
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Sadovskii, V.M. Radial expansion of a granular medium in spherical and cylindrical layers. J Appl Mech Tech Phy 50, 519–524 (2009). https://doi.org/10.1007/s10808-009-0069-z
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DOI: https://doi.org/10.1007/s10808-009-0069-z