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Title: Mathematical modeling of deformation of a porous medium, considering its strengthening due to pore collapse

Based on the generalized rheological method, the mathematical model describing small deformations of a single-phase porous medium without regard to the effects of a fluid or gas in pores is constructed. The change in resistance of a material to the external mechanical impacts at the moment of pore collapse is taken into account by means of the von Mises–Schleicher strength condition. In order to consider irreversible deformations, alongside with the classical yield conditions by von Mises and Tresca– Saint-Venant, the special condition modeling the plastic loss of stability of a porous skeleton is used. The random nature of the pore size distribution is taken into account. It is shown that the proposed mathematical model satisfies the principles of thermodynamics of irreversible processes. Phenomenological parameters of the model are determined on the basis of the approximate calculation of the problem on quasi-static loading of a cubic periodicity cell with spherical voids. In the framework of the obtained model, the process of propagation of plane longitudinal waves of the compression in a homogenous porous medium, accompanied by the plastic deformation of a skeleton and the collapse of pores, is analyzed.
Authors:
;  [1]
  1. Institute of Computational Modeling, SB RAS, Akademgorodok 50/44, 660036 Krasnoyarsk (Russian Federation)
Publication Date:
OSTI Identifier:
22492612
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1684; Journal Issue: 1; Conference: AMiTaNS'15: 7. international conference for promoting the application of mathematics in technical and natural sciences, Albena (Bulgaria), 28 Jun - 3 Jul 2015; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; APPROXIMATIONS; COMPRESSION; DEFORMATION; DISTRIBUTION; FLUIDS; IRREVERSIBLE PROCESSES; MATHEMATICAL MODELS; PERIODICITY; PLASTICITY; POROUS MATERIALS; RANDOMNESS; SIMULATION; SKELETON; SPHERICAL CONFIGURATION; STABILITY; STATIC LOADS; THERMODYNAMICS