Multilevel simulation of deformation and fracture of brittle porous materials in the method of movable cellular automata

In the framework of the method of movable cellular automata, an approach is proposed to multilevel description of deformation and fracture of brittle porous media with a single maximum in the pore size distribution histogram. In the approach, the effective response function of a cellular automaton is defined through direct simulation of the representative volume of a porous medium. A hierarchical model is developed for the mechanical behavior of ZrO2-based ceramics with the pore size comparable with the average grain size under shear and uniaxial compression. The developed approach is analyzed for feasibility of taking into account the spatial distribution nonuni-formity of strength properties of porous media by varying the automata interaction parameters in stochastically chosen directions. It is shown that this method of considering the nonuniformity holds much promise for multilevel description of porous media with a hierarchical pore space structure.