Issue 24

Ig. S. Konovalenko et alii, Frattura ed Integrità Strutturale, 24 (2013) 75-80 ; DOI: 10.3221/IGF-ESIS.24.07 75 Special Issue: Russian Fracture Mechanics School 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 Institute of Strength Physics and Materials Science SB RAS, 2/4 Akademicheskii pr., Tomsk, 634021, Russia igkon@ispms.tsc.ru A. Yu. Smolin, S. G. Psakhie Institute of Strength Physics and Materials Science SB RAS, 2/4 Akademicheskii pr., Tomsk, 634021, Russia Tomsk State University, 36 Lenin pr., Tomsk, 634050, Russia A BSTRACT . 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. K EYWORDS . Deformation and fracture; Brittle materials; Porous ceramics; 2D modeling; Particle-based approach, Movable cellular automaton method. I NTRODUCTION t is well known that real porous materials are characterized by hierarchical pore structure and complex mechanical behavior, including fracture [1-3]. To study and describe these materials the information about the relationship of their structure and mechanical properties at various scales is needed. One of the ways of getting this information is numerical simulation. In the framework of one-scale approach direct taking into account all peculiarities of structure and mechanical behavior of a material at each scale seems to be impossible. Therefore the goal of this paper is development of the multiscale approach, represented in [4], and construction of the corresponding hierarchical model for describing deformation and fracture of nanostructured porous ceramics under compression and shear on the basis of movable cellular automaton method (MCA). Detailed description of the MCA method can be found in paper [5] published in this issue of the journal. Note, that this method have been chosen because it has successfully proved itself in studying I