This work presents a novel mechanism that causes stiffness size effects in periodic cellular materials in bending, but is absent in other boundary conditions. The work begins by demonstrating that in certain circumstances, a single set of micropolar elastic material properties can predict size effects accurately for either bending or shear but not both. This suggests that, for periodic cellular materials, size effects in shear and bending arise from different mechanisms. This work then presents a novel mechanism causing size effects in bending, called a material distribution effect. A sample with only a few unit cells can have its material concentrated close to the neutral axis, or far away, depending on topology and choice of unit cell. A sample with many cells must have its material spread more evenly. This can cause either a stiffening or softening size effect. This work derives formulas to predict the magnitude and direction of these size effects and shows that these formulas are able to predict size effects for a variety of different periodic cellular materials in different types of bending boundary conditions.