Approach to simulation of deformation and fracture of hierarchically organized heterogeneous media, including contrast media

The paper concerns the development of a formalism of the movable cellular automata method for simulation of consolidated heterogeneous elastoplastic media at different scale levels. Using the developed formalism as the basis, an approach was formulated for construction of structural models that describe mesoscopic response (including fracture) of heterogeneous media to loading with regard to hierarchical organization of their internal structure. In the approach, the effect of structural scale levels higher than the level under consideration is taken into account by a technique combining the particle method and conventional methods of continuum mechanics. The effect of lower structural scale levels is taken into account by determining integral response characteristics of lower-scale representative volumes and by specifying appropriate values of particle interaction parameters. The proposed formalism was advanced for description of contrast heterogeneous media whose components can assume different aggregate states. The potentialities of the particle method for description of hierarchically organized media are illustrated by studying the response and fracture mechanisms of materials, including contrast media, with a developed porous structure.