Modeling of Microstructure Evolution during Deformation Processes by Cellular Automata—Boundary Conditions and Space Reorganization Aspects

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.

Review Study on Mechanical Properties of Cellular Materials

“…Microstructure Formation Method Reference architected cellular materials additive manufacturing [85] hard sphere packings with lognormal or gamma distributions investigating geometric characteristics [45] cellular ceramic composites 3d microarchitecture [3] cellular automata modeling for deformation processes [86] metals and alloys in laser additive manufacturing laser additive manufacturing [87] porous metals solid freeform fabrication techniques [88] neural cellular automata [89] hexagonal honeycomb cellular material polynomial interpolation method [35] metal foams 3D Voronoi structure [41] Poly-methacrylimide (PMI) foam in situ x-ray micro-computed tomography (CT) [39] The second and most popular approach uses computational techniques to virtually create cellular materials, such as topology optimization and finite element analysis. Using these techniques, materials' behavior under various conditions was simulated, and their microstructure was optimized to produce desirable characteristics like stiffness, strength, or thermal conductivity [46,[90][91][92].…”

New Platforms Based on Frontal Cellular Automata and Lattice Boltzmann Method for Modeling the Forming and Additive Manufacturing

“…Different space reorganization methods have been developed ( Figure 5 ). A detailed description of the solutions and algorithms developed in this area can be found elsewhere [ 26 ].…”

3D Model of Carbon Diffusion during Diffusional Phase Transformations

“…FCA has a very wide range of applications in the context of modeling various processes and phenomena occurring in materials. This method, among others, has been used successfully for the modeling of recrystallization [29], additive manufacturing [29,30], and rolling [31]. Recently, parallel computing modeling is also being realized on a larger scale; for example, Zhu et al [32] realized the three-dimensional multi-phase-field simulation of a eutectoid alloy based on an OpenCL parallel.…”