Analyzing the Deformation of a Porous Medium with Account for the Collapse of Pores
V. M. Sadovskii, O. V. Sadovskaya
Institute of Computational Modelling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia
Keywords: пористая среда, схлопывание пор, упругий предвестник, пластическая ударная волна, метод сквозного счета, параллельный вычислительный алгоритм, porous medium, pore collapse, elastic precursor, plastic shock wave, shock-capturing method, parallel computational algorithm
Abstract
The generalized rheological method is used to construct a mathematical model of small deformations of a porous media with open pores. Changes in the resistance of the material to external mechanical impact at the moment of collapse of the pores is described using the Mises~--- Schleicher strength condition. The irreversible deformation is accounted for with the help of the classic versions of the von Mises - Tresca - Saint-Venant yield condition and the condition that simulates the plastic loss of stability of the porous skeleton. Within the framework of the constructed model, this paper describes the analysis of the propagation of plane longitudinal compression waves in a homogeneous medium accompanied with plastic strain of the skeleton and densification of the material. A parallel computational algorithm is developed for the study of the elastoplastic deformation of the porous medium under external dynamics loads. The algorithm and the program are tested by calculating the propagation of plane longitudinal shock waves of compression and cylindrical cavity of in an infinite porous medium. The calculation results are compared with exact solutions, and it is shown that they are in good agreement.
DOI: 10.1134/S0021894416050072
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