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 von 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 compression shock waves and the extension of the cylindrical cavity in an infinite porous medium. The calculation results are compared with exact solutions, and it is shown that they are in good agreement.
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References
M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. 1. Low Frequency Range,” J. Acoust. Soc. Amer. 28 (2), 168–178 (1956).
V. N. Dorovskii, Yu. V. Perepechko, and E. I. Romenskii, “Wave Processes in Saturated Porous Elastically Deformed Media,” Fiz. Goreniya Vzryva 29 (1), 99–110 (1993) [Combust., Expl., Shock Waves 29 (1), 93–103 (1993)].
J. M. Carcione, “Viscoelastic Effective Rheologies for Modelling Wave Propagation in Porous Media,” Geophys. Prospect. 46 (3), 249–270 (1998).
V. V. Zubkov, V. F. Koshelev, and A. M. Lin’kov, “Numerical Modeling of Hydraulic Fracture Initiation and Development,” Fiz.-Tekh. Probl. Razrab. Polez. Iskopaemykh, No. 1, 45–63 (2007) [J. Min. Sci 43 (1), 40–56 (2007)].
A. A. Lukyanov, N. V. Chugunov, V. M. Sadovskii, and O. V. Sadovskaya, “Modelling of Irreversible Deformation near the Tip of a Crack in a Porous Domain Containing Oil and Gas,” in Proc. of the 14th Europ. Conf. on the Mathematics of Oil Recovery, Sicily (Italy), Sept. 8–11, 2014 (EAGE, Houten, 2014).
L. J. Gibson and M. F. Ashby, Cellular Solids: Structure and Properties (Cambridge Univ. Press, Cambridge, 1997).
J. Banhart and J. Baumeister, “Deformation Characteristics of Metal Foams,” J. Materials Sci. 33 (6), 1431–1440 (1998).
K. Stobener, D. Lehmhus, M. Avalle, et al., “Aluminum Foam-Polymer Hybrid Structures (APM Aluminum Foam) in Compression Testing,” Int. J. Solids Structures 45 (21), 5627–5641 (2008).
T. A. Schaedler, A. J. Jacobsen, A. Torrents, et al., “Ultralight Metallic Microlattices,” Science 334 (6058), 962–965 (2011).
X. Badiche, S. Forest, T. Guibert, et al., “Mechanical Properties and Non-Homogeneous Deformation of Open- Cell Nickel Foams: Application of the Mechanics of Cellular Solids and of Porous Materials,” Materials Sci. Eng. Ser. A. 289 (1/2), 276–288 (2000).
A. E. Simone and L. J. Gibson, “The Effects of Solid Distribution on the Rigidity of Metallic Foams,” Acta Materialia 46 (6), 2139–2150 (1998).
S. Forest, J.- S. Blazy, Y. Chastel, and F. Moussy, “Continuum Modeling of Strain Localization Phenomena in Metallic Foams,” J. Materials Sci. 40 (22), 5903–5910 (2005).
V. M. Sadovskii and O. V. Sadovskaya, “Phenomenological Modeling of Deformation of Porous and Cellular Materials Taking into Account the Increase in Stiffness Because of the Collapse of Pores,” in Proc. of the 4th Int. Conf. on Computational Methods in Structural Dynamics and Earthquake Engineering, Kos Island (Greece), June 12–14, 2013 (Nat. Tech. Univ. of Athens, Athens, 2013).
V. M. Sadovskii, O. V. Sadovskaya, and A. A. Luk’yanov, “Radial Expansion of a Cylindrical or Spherical Cavity in an Infinite Porous Medium,” Prikl. Mekh. Tekh. Fiz. 55 (4), 160–173 (2014) [J. Appl. Mech. Tech. Phys 55 (4), 689–700 (2014)].
O. V. Sadovskaya and V. M. Sadovskii, “Mathematical Modeling in Mechanics of Granular Materials,” Ser. Advanced Structured Materials 21 (Springer, Heidelberg–New York–Dordrecht–London, 2012).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 5, pp. 53–65, September–October, 2016.
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Sadovskii, V.M., Sadovskaya, O.V. Analyzing the deformation of a porous medium with account for the collapse of pores. J Appl Mech Tech Phy 57, 808–818 (2016). https://doi.org/10.1134/S0021894416050072
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DOI: https://doi.org/10.1134/S0021894416050072