Geodesic
Movable cellular automaton method as a trend in discrete computational mechanics
Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 444-465

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The paper presents the basics of movable cellular automaton method aimed for simulating deformation and fracture of materials and media at different scales. Initially, the particle method has been employed in mechanics of materials only at microscale as molecular dynamics. Its further development has been led to a group of methods which are usually called as discrete element method and used for simulation of loose and granular materials at the macroscale. The presented method of movable cellular automata was developed for simulating deformation and fracture of materials at different scales: at mesoscale with an explicit account for material structure, and at macroscale within the framework of a media with effective properties. The main advantages and differences of the approach compared with the other methods of discrete computational mechanics are considered. These advantages, first of all, are determined by the fact that the considered approach is based on two basic methods of discrete simulation: particle method and cellular automaton method. Employing the formalism of cellular automata allows explicit description of both processes of damage generation and evolution as well as of crack healing and microwelding. More of that, it is possible to describe heat transfer, chemical reactions and phase transitions as well. The second important advantage of the movable cellular automaton method is the many-body type of interaction among its elements. The use of many-body interaction allows us to avoid artificial effect of the particle packing and locality of their interaction on the resulting behavior of the modeled material that is extremely important for modeling elastic-plastic matereials. As a further development of the considered approach, two techniques are discussed which enable to describe contact interaction of solid bodies surfaces at the micro- and mesoscopic scales within the framework of the particle method.
Keywords: computational mechanics, particle method, cellular automata, deformation and fracture. 
@article{CHEB_2017_18_3_a26,
     author = {S. G. Psakhie and A. Yu. Smolin and A. I. Dmitriev and E. V. Shilko and S. Yu. Korostelev},
     title = {Movable cellular automaton method as a trend in discrete computational mechanics},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {444--465},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a26/}
}
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S. G. Psakhie; A. Yu. Smolin; A. I. Dmitriev; E. V. Shilko; S. Yu. Korostelev. Movable cellular automaton method as a trend in discrete computational mechanics. Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 444-465. http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a26/