Effect of Cell Number and Arrangement on the Compressive Behavior of Cellular Structures

The mechanical response of cellular structures is governed not only by relative density and average cell geometry but also by the spatial arrangement of cells. However, the manner in which arrangement-dependent effects evolve with increasing cell number has not been systematically clarified. In this study, the compressive behavior of closed-cell structures with varying cell numbers was investigated using finite element analysis under dynamically equilibrated compression conditions while maintaining constant relative density and identical material parameters. Cellular models were generated using hierarchical Poisson disk sampling combined with Voronoi tessellation. The number of cells was increased through three distinct approaches: mirror replication of a reference structure, enlargement of the overall specimen size, and refinement of cell size under fixed external dimensions. To characterize arrangement-dependent effects, two distinct features of the compressive response were introduced: averaging, defined as a reduction in variability across responses from different initial cell arrangements, and smoothing, defined as the suppression of abrupt stress fluctuations within an individual response. Quantitative metrics were employed to evaluate both effects. Averaging was observed in plate-type models compressed in the z-direction and in fixed-size models, whereas mirror-connected models retained strong arrangement dependence despite large cell numbers. Smoothing occurred predominantly in plate-type models compressed in the z-direction and was strongly correlated with the number of cell layers aligned along the compression direction rather than with total cell number alone. The simulations were conducted in a dynamically equilibrated regime in which internal stress equilibrium was achieved during deformation. These results demonstrate that compressive behavior is governed not only by cell number but also by structural arrangement and directional cell-layer alignment, providing mechanistic insight into the transition from arrangement-dependent variability to stable macroscopic response under dynamic compression.