Abstract
Cellular automata (CA) are efficient and effective numerical tools for modeling various phenomena and processes, e.g., microstructure evolution in plastic working processes. In many cases, the analysis of phenomena can be carried out only in a limited space and on representative volume. This limitation determines the geometry of CA space hence boundary conditions are very important issues in modeling. The paper discusses different boundary conditions that can be applied to modeling. Taking into account the transformation of the modeling space, the model should allow the selection of boundary conditions. The modeling of certain phenomena and processes is directly related to changes in the geometry of a representative volume and therefore may require changes or reorganization of the modeled CA space. Four reorganization options are presented: halving, cutting and bonding, doubling, and straightening. A choice of boundary conditions may depend on particular space reorganization as used for the modeling of microstructure evolution. A set of decision rules for selecting space reorganization options taking into account the changes of CA shape and sizes is also presented. The modeling of flat and shape rolling processes utilizing some of the described techniques is shown.
Highlights
The paper presents two very important issues related to the modeling of plastic processes by cellular automata, i.e., the CA geometry and boundary conditions
There is a direct relationship between them because the boundary condition is a result of the selected geometry of the space
Simulations of the microstructure evolution in different processes are mainly realized with the use of the periodic conditions and many of them are discussed in the literature
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Boundary conditions are directly connected with the selection of the cellular automata space geometry. They should eliminate the edge impact because all the elements (cells) in the CA space should be in the same, equal conditions. The deformation has an impact on the level of anisotropy of the CA modeling space, i.e., the cell size ratio may be too large, calculations slower and the quality of the obtained structure unsatisfactory Taking these conditions into account, the structure of cellular automata should be reorganized. Such actions have a direct impact on boundary conditions, which may require changes Another important element related to space geometry is an appropriate choice of the cell grid. The application of the presented techniques for modeling of flat and shape rolling processes was shown
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