Modeling of inhomogeneous deformation of porous ceramics using Gaussian random fields

In this paper, the inhomogeneous distribution of strain in porous ceramic specimens under diametral compression is numerically analyzed using a stochastic representation of the material structure. Models of the structure of porous ceramics are based on a probabilistic description of mechanical properties of ceramics using Gaussian random fields. Numerical simulation is performed for zirconium ceramics with porosities of 4 and 42 %. In the framework of the modeling method used, different porosities of ceramics are taken into account in terms of effective mechanical properties and parameters of the covariation matrix of a random Gaussian field. The simulation of the diametral compression of porous ceramic specimens is carried out in a two-dimensional formulation under plane-strain conditions. The loading is set in the upper and lower parts of the specimen near the central vertical axis through the velocities of the selected nodes. Distributions of the strain tensor components for the studied specimens are analyzed, and their evolution in the central part of the specimens is studied in detail. It is shown that the strain is localized in the form of bands of different sizes and intensities inclined at an angle of approximately 45° to the loading axis. The difference in the strain distributions for the specimens with various porosities in the performed calculations is a result of different models of the inhomogeneous structure. The specimen with a porosity of 4 % is characterized by a greater number of heterogeneous regions of smaller size compared with a specimen with a porosity of 42 %. The proposed method of describing the material structure allows one to obtain various types of inhomogeneous strain distributions under diametral compression, as well as to control the size of heterogeneous regions in the strain distributions.