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MECHANICS
Modeling of inhomogeneous deformation of porous ceramics using Gaussian random fields
V. A. Zimina Institute of Strength Physics and Materials Science of the Siberian Branch of RAS,
Tomsk, Russian Federation
Abstract:
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.
Keywords:
inhomogeneous random structure, porous ceramics, diametral compression test, stochastic modeling, Gaussian random fields, strain inhomogeneity, numerical modeling.
Received: 07.10.2022 Accepted: October 10, 2023
Citation:
V. A. Zimina, “Modeling of inhomogeneous deformation of porous ceramics using Gaussian random fields”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2023, no. 85, 132–145
Linking options:
https://www.mathnet.ru/eng/vtgu1034 https://www.mathnet.ru/eng/vtgu/y2023/i85/p132
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