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

Ig. S. Konovalenko, A. Yu. Smolin,, S. G. Psakhie


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

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