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Auxetic materials are those which exhibit negative Poisson’s ratio, i.e. these solids expand transversely when stretched longitudinally. In recent years the concept of semi-auxetics has been examined for cellular solids based on combination of re-entrant and hexagonal microstructures. In this paper we identify a type of rotating unit that gives positive Poisson’s ratio so that a study can be made on rotating sub-structures that exhibit both positive and negative Poisson’s ratio characteristics. A second type of rotating geometry, whose Poisson’s ratio shifts from negative to positive as stretching increases, has also been identified. Based on kinematical studies we explore the relationship between the on-axis Poisson’s ratios in terms of novel lattice geometry and the magnitude of deformation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]