Effects of Cell Size and Spatial Distribution on the Apparent Poisson's Ratio in Flexible Cellular Structures

This work investigates how the size and spatial distribution of cells influence the apparent Poisson's ratio of ordered and unordered (stochastic) flexible cellular structures at constant relative densities. A unifying semiempirical model that captures the structures' mechanical behavior is first developed. The model assumes that adding cells with various diameters alters the apparent Poisson's ratio in an exponentially decaying or growing fashion. The model is parameterized by combinations of cell volume fractions that capture cell morphology and response, an exponential constant, and the apparent Poisson's ratio of a structure with equal cell sizes for a structure class. To validate the model, flexible structures with ordered and unordered cell arrangements are designed, manufactured, and characterized using experimental full-field measurements and finite element simulations. Experimental results validate that the apparent Poisson's ratios and elastic moduli of the ordered structures decrease with an increase in the cell size distribution in the linear deformation regime. Unordered structures show smaller systematic changes in apparent mechanical parameters with a change in cell size distribution. Full-field deformation analyses are performed at various length scales to discuss the contributions of the model parameters and structural deformation mechanisms. Experimental and finite element data are used to fit models for known cell volume fraction functions. Numerical simulations are then performed using the model to study the influence of key model parameters on the apparent Poisson's ratio behaviors in broad classes of cellular solids.