Analyzing the deformation of a porous medium with account for the collapse of pores

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.