Multiscale approach to description of deformation and fracture of brittle media with hierarchical porous structure on the basis of movable cellular automaton method

An approach to multiscale description of deformation and fracture of brittle porous materials on the basis of movable cellular automaton method was proposed. The material characterized by pore size distribution function having two maxima was considered. The core of the proposed approach consists in finding the automaton effective response function by means of direct numerical simulation of representative volume of the porous material. A hierarchical two-scale model of mechanical behavior of ceramics under compression and shear loading was developed. Zirconia based ceramics with pore size greater than the average grain size was considered. At the first scale of the model only small pores (corresponding to the first maximum of the pore size distribution function) were taking into account explicitly (by removing automata from the initial structure). The representative volume and effective elastic properties of the porous material at this scale were evaluated. At the second scale of the model, big pores were taking into account explicitly, the parameters of the matrix corresponded to the ones determined at the first scale. Simulation results showed that the proposed multiscale model allows qualitatively and quantitatively correct describing of deformation and fracture of brittle material with hierarchical porous structure.